ECE 752 001 - 统计代写答疑辅导

标签： ECE 752 001

数学代写|信息论作业代写information theory代考|INFSCI2120

Posted on 2022年7月5日2022年7月5日 by statistics-lab

如果你也在怎样代写信息论information theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

信息理论是对数字信息的量化、存储和通信的科学研究。该领域从根本上是由哈里-奈奎斯特和拉尔夫-哈特利在20世纪20年代以及克劳德-香农在20世纪40年代的作品所确立的。该领域处于概率论、统计学、计算机科学、统计力学、信息工程和电气工程的交叉点。

statistics-lab™ 为您的留学生涯保驾护航在代写信息论information theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写信息论information theory代写方面经验极为丰富，各种代写信息论information theory相关的作业也就用不着说。

我们提供的信息论information theory及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|INFSCI2120

数学代写|信息论作业代写information theory代考|Work in London and Down

The Beagle was now on its way home, and Darwin impatiently counted the days and miles which separated him from his family and friends. To his sisters he wrote: “I feel inclined to write about nothing else but to tell you, over and over again, how I long to be quietly seated among you”; and in a letter to Henslow he exclaimed: “Oh the degree to which I long to be living quietly, without one single novel object near me! No one can imagine it until he has been whirled around the world, during five long years, in a Ten Gun Brig.”

Professor Sedgwick had told Darwin’s father that he believed that Charles would take his place among the leading scientific men of England. This encouraging news from home reached Darwin on Ascension Island. “After reading this letter”, Darwin wrote, “I clambered over the mountains with a bounding step and made the rocks resound under my geological hammer.”

On October 2, 1836, the Beagle docked at Falmouth, and Darwin, “giddy with joy and confusion”, took the first available coach to The Mount, his family’s home in Shrewsbury. After a joyful reunion with his family, he visited the Wedgwood estate at Maer, where his Uncle Jos and his pretty cousins were equally impatient to see him. To Henslow he wrote: “I am in the clouds, and neither know what to do or where to go… My chief puzzle is about the geological specimens – who will have the charity to help me in describing their mineralogical nature?”

Soon Darwin found a collaborator and close friend in none other than Sir Charles Lyell, the great geologist whose book had so inspired him. One of Lyell’s best characteristics was his warmth in encouraging promising young scientists. Darwin’s theory of the formation of coral barrier reefs and atolls had supplanted Lyell’s own theory, but far from being offended, Lyell welcomed Darwin’s ideas with enthusiasm. According to Lyell’s earlier theory, coral atolls are circular in shape because they are based on the circular rims of submerged volcanos. However, Darwin showed that any island gradually sinking beneath the surface of a tropical ocean can develop into an atoll. He showed that the reef-building organisms of the coral are poisoned by the stagnant water of the central lagoon, but they flourish on the perimeter, where new water is constantly brought in by the waves. Darwin was able to use the presence of coral atolls to map whole regions of the Pacific which are gradually sinking. He pointed out that in the subsiding regions there are no active volcanos, while in regions where the land is rising, there is much volcanic activity.

数学代写|信息论作业代写information theory代考|The Origin of Species

In 1837 Darwin had begun a notebook on Transmutation of Species. During the voyage of the Beagle he had been deeply impressed by the great fossil animals which he had discovered, so like existing South American species except for their gigantic size. Also, as the Beagle had sailed southward, he had noticed the way in which animals were replaced by closely allied species. On the Galapagos Islands, he had been struck by the South American character of the unique species found there, and by the way in which they differed slightly on each island.

It seemed to Darwin that these facts, as well as many other observations which he had made on the voyage, could only be explained by assuming that species gradually became modified. The subject haunted him, but he was unable to find the exact mechanism by which species changed. Therefore he resolved to follow the Baconian method, which his friend Sir Charles Lyell had used so successfully in geology. He hoped that by the wholesale collection of all facts related in any way to the variation of animals and plants under domestication and in nature, he might be able to throw some light on the subject. He soon saw that in agriculture, the key to success in breeding new varieties was selection; but how could selection be applied to organisms living in a state of nature?

信息论代写

数学代写|信息论作业代写information theory代考|Work in London and Down

小猎犬号现在正在回家的路上，达尔文不耐烦地计算着他与家人和朋友分开的日子和里程。他对姐妹们写道：“我倾向于不写别的，只是一遍又一遍地告诉你们，我多么渴望安静地坐在你们中间”；在给亨斯洛的一封信中，他感叹道：“哦，我多么渴望安静地生活，身边没有一件新奇的东西！直到他在长达五年的十炮双桅船中环游世界之前，没有人能想象到这一点。”

塞奇威克教授曾告诉达尔文的父亲，他相信查尔斯会在英国领先的科学家中占据一席之地。这个来自家乡的令人鼓舞的消息传到了阿森松岛的达尔文。“读完这封信后，”达尔文写道，“我大踏步翻越山峦，让岩石在我的地质锤下响起。”

1836 年 10 月 2 日，小猎犬号停靠在法尔茅斯，达尔文“喜出望外”，带着第一辆可用的教练前往他家在什鲁斯伯里的家——山。在与家人欢聚一堂后，他参观了位于 Maer 的 Wedgwood 庄园，他的乔斯叔叔和他漂亮的堂兄弟们同样迫不及待地想见他。他对亨斯洛写道：“我在云端，不知道该做什么，也不知道该去哪里……我的主要难题是关于地质标本——谁将有慈善事业帮助我描述它们的矿物学性质？”

很快，达尔文在查尔斯·莱尔爵士（Sir Charles Lyell）身上找到了一位合作者和密友，这位伟大的地质学家的书给了他很大启发。莱尔最大的特点之一是他热情地鼓励有前途的年轻科学家。达尔文关于珊瑚堡礁和环礁形成的理论已经取代了莱尔自己的理论，但莱尔并没有被冒犯，而是热情地欢迎达尔文的想法。根据莱尔早期的理论，珊瑚环礁是圆形的，因为它们是基于水下火山的圆形边缘。然而，达尔文表明，任何逐渐沉入热带海洋表面的岛屿都可以发展成环礁。他表明，珊瑚的造礁生物被中央泻湖的死水毒害，但它们在周边繁盛，海浪不断引入新水。达尔文能够利用珊瑚环礁的存在来绘制整个太平洋地区正在逐渐下沉的地图。他指出，在下沉的地区没有活火山，而在地势上升的地区，火山活动较多。

数学代写|信息论作业代写information theory代考|The Origin of Species

1837 年，达尔文开始写一本关于物种嬗变的笔记本。在小猎犬号的航行中，他发现的巨大化石动物给他留下了深刻的印象，除了体型巨大外，与现存的南美物种一样。此外，随着小猎犬向南航行，他注意到动物被密切相关的物种所取代的方式。在加拉帕戈斯群岛，他被那里发现的独特物种的南美特征以及每个岛上它们的细微差别所震惊。

在达尔文看来，这些事实，以及他在航行中所做的许多其他观察，只能通过假设物种逐渐被改变来解释。这个主题一直困扰着他，但他无法找到物种变化的确切机制。因此，他决定采用他的朋友查尔斯·莱尔爵士在地质学中如此成功地使用的培根方法。他希望通过大量收集与驯化和自然界中动植物变异有关的所有事实，或许能够对这个主题有所了解。他很快就发现，在农业中，培育新品种成功的关键是选择；但是选择如何应用于生活在自然状态中的生物呢？

数学代写|信息论作业代写information theory代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。

有限元方法代写

有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

随机分析代写

随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习和应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|信息论作业代写information theory代考|MTHE874

Posted on 2022年7月5日2022年7月5日 by statistics-lab

如果你也在怎样代写信息论information theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的信息论information theory及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|MTHE874

数学代写|信息论作业代写information theory代考|Family background and early life

It was Erasmus Darwin’s grandson Charles (1809-1882) who finally worked out a detailed and correct theory of evolution and supported it by a massive weight of evidence.

As a boy, Charles Darwin was passionately fond of hunting and collecting beetles, but he was a mediocre student. His father once said to him in exasperation: “You care for nothing but shooting, dogs and rat-catching; and you will be a disgrace to yourself, and to all your family!”

Darwin’s father, a wealthy physician, sent him to Edinburgh University to study medicine; but Charles did not enjoy his studies there. “Dr. Duncan’s lectures on Materia Medica at 8 o’clock on a winter’s morning are something fearful to remember”, he wrote later. “I also attended the operating theatre in the hospital at Edinburgh and saw two very bad operations, one on a child, but I rushed away before they were completed. Nor did I ever attend again, for hardly any inducement would have been strong enough to make me do so; this being long before the blessed days of chloroform. The two cases fairly haunted me for many a long year.”

The time at Edinburgh was not entirely wasted, however, because several of Darwin’s friends at the university were natural philosophers, ${ }^{1}$ and contact with them helped to develop his interest in natural history. One of the most important of these scientific friends was Dr. R.E. Grant, an expert on marine invertebrate zoology with whom Darwin often collected small sea slugs in the cold waters of the Firth near Edinburgh. On one of these expeditions, Grant suddenly began to praise the evolutionary views of Lamarck, while Darwin listened in silent astonishment. Charles Darwin had previously read his own grandfather’s book Zoonomia and had greatly admired it; but after a few years he had read it again in a more critical spirit; and after the second reading he had decided that Zoonomia was too speculative and contained too few facts. Grant’s praise of Lamarck may have helped Darwin to become, later in his life, an advocate of evolution in a different form.

数学代写|信息论作业代写information theory代考|Aboard the Beagle

Thus it happened that on December 27, 1831, Charles Darwin sailed from Devonport on H.M.S. Beagle, a small brig of the British navy. The Beagle’s commander, Captain FitzRoy, was twenty-seven years old (four years older than Darwin), but he was already an excellent and experienced sailor. He had orders to survey the South American coast and to carry a chain of chronological measurements around the world. It was to be five years before the Beagle returned to England.

As the brig plowed through rough winter seas, Darwin lay in his hammock, miserably seasick and homesick, trying bravely to read a new book which Henslow had given to him as a sending-off present: Sir Charles Lyell’s Principles of Geology. It was an exciting and revolutionary book – so revolutionary, in fact, that Henslow had found it necessary to warn Darwin not to believe Lyell’s theories, but only to trust his observations. According to Lyell, “No causes have ever acted (in geology) but those which now are acting, and they have never acted with different degrees of energy from that which they now exert.” 2

Lyell’s hypothesis was directly opposed to the Catastrophist school of geology, a school which included deeply religious men like Cuvier, Henslow and Sedgwick, as well as most other naturalists of the time. The Catastrophists admitted that geological evidence shows the earth to be much older than the six thousand years calculated on the basis of the Bible, but they explained this by saying that the Bible describes only the most recent era. Before this, according to the Catastrophists, life on earth had been created many times, and just as many times destroyed by cataclysms like Noah’s flood. ${ }^{3}$ In this way they explained the fossils embedded in ancient rocks: These they believed were the remains of antediluvian creatures destroyed by the wrath of God. The Swiss naturalist Charles Bonnet $(1720-1793)$ even predicted a future catastrophe after which apes would become men and men would become angels. The Catastrophists believed that periodic cataclysms had created the earth’s great mountain ranges, deserts and oceans.

信息论代写

数学代写|信息论作业代写information theory代考|Family background and early life

伊拉斯谟·达尔文的孙子查尔斯（1809-1882）最终制定了详细而正确的进化论，并得到大量证据的支持。

作为一个男孩，查尔斯达尔文热衷于狩猎和收集甲虫，但他是一个平庸的学生。他的父亲曾气愤地对他说：“你只管打猎、打狗、抓老鼠；你会是你自己的耻辱，也是你全家的耻辱！”

达尔文的父亲是一位富有的医生，将他送到爱丁堡大学学习医学；但查尔斯并不喜欢在那里学习。“博士。邓肯在一个冬天的早晨 8 点钟的本草讲座是一件令人恐惧的事情，”他后来写道。“我还参加了爱丁堡医院的手术室，看到了两次非常糟糕的手术，一次是在一个孩子身上，但我在手术完成之前就匆匆离开了。我也没有再去参加，因为几乎没有任何诱因足以让我参加。这比氯仿的幸福日子还早。这两起案件相当困扰我多年。”

然而，在爱丁堡的时间并没有完全浪费，因为达尔文在大学的几个朋友都是自然哲学家，1与他们的接触有助于培养他对自然历史的兴趣。这些科学朋友中最重要的一位是海洋无脊椎动物学专家 RE Grant 博士，达尔文经常与他一起在爱丁堡附近的弗斯寒冷水域收集小型海蛞蝓。在其中一次探险中，格兰特突然开始赞扬拉马克的进化论观点，而达尔文则默默地惊讶地听着。查尔斯·达尔文以前读过他祖父的书《人兽共患》，非常钦佩。但几年后，他以更批判的精神再次阅读了它。在二读之后，他认为 Zoonomia 过于投机，包含的事实太少。格兰特对拉马克的赞扬可能帮助达尔文在他晚年成为不同形式进化论的倡导者。

数学代写|信息论作业代写information theory代考|Aboard the Beagle

因此，恰巧在 1831 年 12 月 27 日，查尔斯·达尔文 (Charles Darwin) 乘坐英国海军的小型双桅船 HMS Beagle 从德文波特启航。小猎犬号的指挥官菲茨罗伊船长二十七岁（比达尔文大四岁），但他已经是一名优秀且经验丰富的水手。他奉命调查南美海岸，并在世界各地进行一系列按时间顺序排列的测量。比格犬回到英国已经五年了。

当双桅船在波涛汹涌的冬季大海中航行时，达尔文躺在吊床上，痛苦地晕船和想家，勇敢地阅读亨斯洛作为送别礼物送给他的一本新书：查尔斯·莱尔爵士的地质学原理。这是一本令人兴奋和革命性的书——事实上，如此革命性，亨斯洛发现有必要警告达尔文不要相信莱尔的理论，而只是相信他的观察。根据莱尔的说法，“除了那些现在正在起作用的原因之外，没有任何原因（在地质学中）起作用，并且它们从未以与现在施加的能量不同程度的能量起作用。” 2

莱尔的假设直接反对地质学的灾变学派，该学派包括像居维叶、亨斯洛和塞奇威克这样的虔诚宗教人士，以及当时大多数其他自然主义者。灾变论者承认，地质证据表明地球比根据圣经计算的六千年要古老得多，但他们解释说，圣经只描述了最近的时代。在此之前，根据灾变论者的说法，地球上的生命已经被创造了很多次，也被像诺亚洪水这样的灾难摧毁了很多次。3他们以这种方式解释了嵌在古代岩石中的化石：他们认为这些是被上帝的愤怒摧毁的上古生物的遗骸。瑞士博物学家查尔斯·邦内(1720−1793)甚至预言了未来的灾难，之后猿会变成人，人会变成天使。灾变论者认为周期性的灾变造就了地球上巨大的山脉、沙漠和海洋。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|信息论作业代写information theory代考|MTHE474

Posted on 2022年7月5日2022年7月5日 by statistics-lab

如果你也在怎样代写信息论information theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的信息论information theory及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|MTHE474

数学代写|信息论作业代写information theory代考|The mystery of fossils

During the lifetime of Leonardo da Vinci (1452-1519) the existence of fossil shells in the rocks of high mountain ranges was recognized and discussed. “…the shells in Lombardy are at four levels”, Leonardo wrote, “and thus it is everywhere, having been made at various times… The stratified stones of the mountains are all layers of clay, deposited one above the other by the various floods of the rivers.” Leonardo had no patience with the explanation given by some of his contemporaries, that the shells had been carried to mountain tops by the deluge described in the Bible. “If the shells had been carried by the muddy waters of the deluge”, he wrote, “they would have been mixed up, and separated from each other amidst the mud, and not in regular steps and layers.” Nor did Leonardo agree with the opinion that the shells somehow grew within the rocks: “Such an opinion cannot exist in a brain of much reason”, he wrote, “because here are the years of their growth, numbered on their shells, and there are large and small ones to be seen, which could not have grown without food, and could not have fed without motion…and here they could not move.”

Leonardo believed that the fossil shells were once part of living organisms, that they were buried in strata under water, and much later lifted to the tops of mountains by geological upheavals. However his acute observations had little influence on the opinions of his contemporaries because they appear among the 4,000 or so pages of notes which he wrote for himself but never published.

It was left to the Danish scientist Niels Stensen (1638-1686) (usually known by his Latinized name, Steno) to independently rediscover and popularize the correct interpretation of fossils and of rock strata. Steno, who had studied medicine at the University of Leiden, was working in Florence, where his anatomical studies attracted the attention of the Grand Duke of Tuscany, Ferdenand II. When an enormous shark was caught by local fishermen, the Duke ordered that its head be brought to Steno for dissection. The Danish anatomist was struck by shape of the shark’s teeth, which reminded him of certain curiously shaped stones called glossopetrae that were sometimes found embedded in larger rocks. Steno concluded that the similarity of form was not just a coincidence, and that the glossopetrae were in fact the teeth of once-living sharks which had become embedded in the muddy sediments at the bottom of the sea and gradually changed to stone. Steno used the corpuscular theory of matter, a forerunner of atomic theory, to explain how the composition of the fossils could have changed while their form remained constant. Steno also formulated a law of strata, which states that in the deposition of layers of sediment, later converted to rock, the oldest layers are at the bottom.

数学代写|信息论作业代写information theory代考|Linnaeus

Meanwhile, during the 17 th and 18 th centuries, naturalists had been gathering information on thousands of species of plants and animals. This huge, undigested heap of information was put into some order by the great Swedish naturalist, Carl von Linné $(1707-1778)$, who is usually called by his Latin name, Carolus Linnaeus.

Linnaeus was the son of a Swedish pastor. Even as a young boy, he was fond of botany, and after medical studies at Lund, he became a lecturer in hotany at the Iniversity of ITprala, near Stockholm. In 1732 , the 25year-old Linnaeus was asked by his university to visit Lapland to study the plants in that remote northern region of Sweden.

Linnaeus travelled four thousand six hundred miles in Lapland, and he discovered more than a hundred new plant species. In 1735 , he published his famous book, Systema Naturae, in which he introduced a method for the classification of all living things.

Linnaeus not only arranged closely related species into genera, but he also grouped related genera into classes, and related classes into orders. (Later the French naturalist Cuvier (1769-1832) extended this system by grouping related orders into phyla.) Linnaeus introduced the binomial nomenclature, still used today, in which each plant or animal is given a name whose second part denotes the species while the first part denotes the genus.

Although he started a line of study which led inevitably to the theory of evolution, Linnaeus himself believed that species are immutable. He adhered to the then-conventional view that each species had been independently and miraculously created six thousand years ago, as described in the Book of Genesis.

Linnaeus did not attempt to explain why the different species within a genus resemble each other, nor why certain genera are related and can be grouped into classes, etc. It was not until a century later that these resem= blances were understood as true family likenesses, so that the resemblance between a cat and a lion came to be understood in terms of their descent from a common ancestor. ${ }^{4}$

信息论代写

数学代写|信息论作业代写information theory代考|The mystery of fossils

在达芬奇 (Leonardo da Vinci) (1452-1519) 的一生中，人们认识到并讨论了高山岩石中存在的化石壳。“……伦巴第的贝壳有四个层次”，莱昂纳多写道，“因此它无处不在，是在不同时期制造的……山上的层状石头都是粘土层，由各种洪水沉积在一层之上的河流。” 列奥纳多对他同时代的一些人的解释没有耐心，即贝壳是被圣经中描述的洪水带到山顶的。“如果贝壳被洪水的浑水携带，”他写道，“它们就会混在一起，在泥浆中相互分离，而不是按步骤和层级排列。” 莱昂纳多也不同意贝壳以某种方式在岩石中生长的观点：

莱昂纳多认为，化石贝壳曾经是生物体的一部分，它们被埋在水下的地层中，后来被地质剧变抬升到山顶。然而，他敏锐的观察对同时代人的观点几乎没有影响，因为它们出现在他为自己写的 4,000 页左右的笔记中，但从未发表过。

丹麦科学家 Niels Stensen (1638-1686)（通常以其拉丁化名称 Steno 着称）独立地重新发现和普及对化石和岩层的正确解释。Steno曾在莱顿大学学习医学，当时在佛罗伦萨工作，他的解剖学研究引起了托斯卡纳大公费德南德二世的注意。当当地渔民捕捉到一条巨大的鲨鱼时，公爵下令将其头部带到 Steno 进行解剖。丹麦解剖学家对鲨鱼牙齿的形状印象深刻，这让他想起了某些形状奇特的石头，称为舌骨，有时会发现嵌入较大的岩石中。Steno得出结论，形式的相似性不仅仅是巧合，而舌齿实际上是曾经活过的鲨鱼的牙齿，它们已经嵌入海底泥泞的沉积物中，逐渐变成石头。Steno 使用粒子理论（原子理论的先驱）来解释化石的成分如何在其形状保持不变的情况下发生变化。Steno还制定了地层定律，该定律指出，在沉积层的沉积中，后来转化为岩石，最古老的层位于底部。

数学代写|信息论作业代写information theory代考|Linnaeus

与此同时，在 17 世纪和 18 世纪，博物学家一直在收集关于数千种植物和动物的信息。伟大的瑞典博物学家卡尔·冯·林内（Carl von Linné）整理了这些巨大的、未消化的信息堆(1707−1778)，他通常被称为他的拉丁名字，Carolus Linnaeus。

林奈是一位瑞典牧师的儿子。小时候，他就喜欢植物学，在隆德完成医学学习后，他成为了斯德哥尔摩附近 ITprala 大学的热学讲师。1732 年，25 岁的林奈被他的大学邀请到拉普兰去研究瑞典北部偏远地区的植物。

林奈在拉普兰旅行了四千六百英里，他发现了一百多种新植物。1735年，他出版了他的名著《自然系统》，其中介绍了一种对所有生物进行分类的方法。

林奈不仅将密切相关的物种归类为属，而且他还将相关的属归类为类，相关的类归类为目。（后来法国博物学家居维叶（1769-1832）通过将相关的目归类为门扩展了这一系统。）林奈引入了今天仍在使用的二项式命名法，其中每一种植物或动物都有一个名称，其第二部分表示物种，而第二部分表示物种。第一部分表示属。

虽然他开始的研究路线不可避免地导致了进化论，但林奈本人认为物种是不可变的。他坚持当时的传统观点，即每个物种都是在六千年前独立奇迹般地创造出来的，正如《创世纪》中所描述的。

林奈没有试图解释为什么一个属内的不同物种彼此相似，也没有解释为什么某些属是相关的并且可以归类等等。直到一个世纪后，这些相似性才被理解为真正的家庭相似性，因此猫和狮子之间的相似之处可以从共同祖先的血统来理解。4

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|信息论作业代写information theory代考|Channel Capacity and Coding

Posted on 2022年5月28日2022年5月28日 by statistics-lab

如果你也在怎样代写信息论information theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的信息论information theory及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|Channel Capacity

Consider a DMC having an input alphabet $X=\left{x_{0}, x_{1}, \ldots, x_{q-1}\right}$ and an output alphabet $Y=\left{y_{0}, y_{1}, \ldots, y_{r-1}\right}$. Let us denote the set of channel transition probabilities by $P\left(y_{i} \mid x_{j}\right)$. The average mutual information provided by the output $Y$ about the input $X$ is given by (see Chapter 1, Section 1.3)
$$
I(X ; Y)=\sum_{j=0}^{q-1} \sum_{j=0}^{r-1} P\left(x_{j}\right) P\left(y_{i} \mid x_{j}\right) \log \frac{P\left(y_{i} \mid x_{j}\right)}{P\left(y_{i}\right)}
$$
The channel transition probabilities $P\left(y_{i} \mid x_{j}\right)$ are determined by the channel characteristics (primarily the noise in the channel). However, the input symbol probabilities $P\left(x_{j}\right)$ are within the control of the discrete channel encoder. The value of the average mutual information, $I(X ; Y)$, maximized over the set of input symbol probabilities $P\left(x_{j}\right)$ is a quantity that depends only on the channel transition probabilities $P\left(y_{i} \mid x_{j}\right)$ (hence only on the characteristics of the channel). This quantity is called the Capacity of the Channel.

数学代写|信息论作业代写information theory代考|Channel Coding

reliability (which is a component of the quality of service). Table $2.1$ lists the typical acceptable bit error rates for various applications.

In order to achieve such high levels of reliability we have to resort to the use of Channel Coding. The basic objective of channel coding is to increase the resistance of the digital communication system to channel noise. This is done by adding redundancies in the transmitted data stream in a controlled manner.

In channel coding, we map the incoming data sequence to a channel input sequence. This encoding procedure is done by the Channel Encoder. The encoded sequence is then transmitted over the noisy channel. The channel output sequence at the receiver is inverse mapped to an output data sequence. This is called the decoding procedure, and is carried out by the Channel Decoder. Both the encoder and the decoder are under the designer’s control.

As already mentioned, the encoder introduces redundancy in a prescribed manner. The decoder exploits this redundancy so as to reconstruct the original source sequence as accurately as possible. Thus, channel coding makes it possible to carry out reliable communication over unreliable (noisy) channels. Channel coding is also referred to as Error Control Coding. It is interesting to note here that the source coder reduces redundancy to improve efficiency, whereas, the channel coder adds redundancy in a controlled manner to improve reliability.

Definition 2.6 An Error Control Code for a channel, represented by the channel transition probability matrix $p(y \mid x)$, consists of:
(i) A message set ${1,2, \ldots, M}$.
(ii) An encoding function, $X^{n}$, which maps each message to a unique codeword, i.e., $1 \rightarrow X^{n}(1)$, $2 \rightarrow X^{n}(2), \ldots, M \rightarrow X^{n}(M)$. The set of codewords is called a codebook.
(iii) A decoding function, $D \rightarrow{1,2, \ldots, M}$, which makes a guess based on a decoding strategy in order to map back the received vector to one of the possible messages.

We first look at a class of channel codes called block codes. In this class of codes, the incoming message sequence is first sub-divided into sequential blocks, each of length $k$ bits. Thus the cardinality of the message set $M=2^{k}$. Each $k$-bit long information block is mapped into an $n$-bit block by the channel coder, where $n>k$. This means that for every $k$ bits of information, $(n-k)$ redundant bits are added. The ratio
$$
r=\frac{k}{n}=\frac{\log M}{n}
$$
is called the Code Rate. It represents the information bits per transmission. Code rate of any coding scheme is, naturally, less than unity. A small code rate implies that more and more bits per block are the redundant bits corresponding to a higher coding overhead. This may reduce the effect of noise, but will also reduce the communication rate as we will end up transmitting more of the redundant bits and fewer information bits. The question before us is whether there exists a coding scheme such that the probability that the message bit will be in error is arbitrarily small and yet the coding rate is not too small? The answer is yes, and was first provided by Shannon in his second theorem regarding the channel capacity. We will study this shortly.

数学代写|信息论作业代写information theory代考|Information Capacity Theorem

So far we have studied limits on the maximum rate at which information can be sent over a channel reliably in terms of the channel capacity. In this section we will formulate the information capacity theorem for band-limited, power-limited Gaussian channels. An important and useful channel is the Gaussian channel defined below.

Consider a zero mean, stationary random process $X(t)$ that is band limited to $W$ hertz. Let $X_{k}, k=1,2, \ldots, K$, denote the continuous random variables obtained by uniform sampling of the process $X(t)$ at the Nyquist rate of $2 W$ samples per second. These symbols are transmitted over a noisy channel which is also band-limited to $W$ Hertz. The channel output is corrupted by AWGN of zero mean and power spectral density (psd) $N_{0} / 2$. Because of the channel, the noise is band limited to $W$ Hertz. Let $Y_{k}, k=1,2, \ldots, K$, denote the samples of the received signal. Therefore,
$$
Y_{k}=X_{k}+N_{k}, k=1,2, \ldots, K
$$
where $N_{k}$ is the noise sample with zero mean and variance $\sigma^{2}=N_{0}$ W. It is assumed that $Y_{k}, k=1,2, \ldots, K$, are statistically independent. Since the transmitter is usually power-limited, let us put a constraint on the $a v e r a g e$ power in $X_{k}$ :
$$
E\left[X_{k}^{2}\right]=P, k=1,2, \ldots, K
$$
The information capacity of this band-limited, power-limited channel is the maximum of the mutual information between the channel input $X_{k}$ and the channel output $Y_{k}$. The maximization has to be done over all distributions on the input $X_{k}$ that satisfy the power constraint of equation (2.19). Thus, the information capacity of the channel (same as the channel capacity) is given by
$$
C=\max {f{X_{k}}(x)}\left{I(X ; Y) \mid E\left[X_{k}^{2}\right]=P\right}
$$
where $f_{x_{k}}(x)$ is the probability density function of $X_{k}$.
Now, from Chapter 1, equation (1.32), we have,
$$
I\left(X_{k} ; Y_{k}\right)=h\left(Y_{k}\right)-h\left(Y_{k} \mid X_{k}\right)
$$
Note that $X_{k}$ and $N_{k}$ are independent random variables. Therefore, the conditional differential entropy of $Y_{k}$. given $X_{k}$ is equal to the differential entropy of $N_{k^{*}}$. Intuitively, this is because given $X_{k}$ the uncertainty arising in $Y_{k}$ is purely due to $N_{k}$. That is,
$$
h\left(Y_{k} \mid X_{k}\right)=h\left(N_{k}\right)
$$

信息论代写

数学代写|信息论作业代写information theory代考|Channel Capacity

考虑一个具有输入字母表的 DMCX=\left{x_{0}, x_{1}, \ldots, x_{q-1}\right}X=\left{x_{0}, x_{1}, \ldots, x_{q-1}\right}和一个输出字母Y=\left{y_{0}, y_{1}, \ldots, y_{r-1}\right}Y=\left{y_{0}, y_{1}, \ldots, y_{r-1}\right}. 让我们将通道转换概率集表示为磷(是一世∣Xj). 输出提供的平均互信息是关于输入X由下式给出（参见第 1 章，第 1.3 节）

一世(X;是)=∑j=0q−1∑j=0r−1磷(Xj)磷(是一世∣Xj)日志⁡磷(是一世∣Xj)磷(是一世)
通道转换概率磷(是一世∣Xj)由通道特性（主要是通道中的噪声）决定。然而，输入符号概率磷(Xj)在离散通道编码器的控制范围内。平均互信息的值，一世(X;是), 在输入符号概率集上最大化磷(Xj)是一个仅取决于通道转换概率的量磷(是一世∣Xj)（因此仅针对通道的特性）。这个量称为通道容量。

数学代写|信息论作业代写information theory代考|Channel Coding

可靠性（这是服务质量的一个组成部分）。桌子2.1列出了各种应用的典型可接受误码率。

为了达到如此高水平的可靠性，我们不得不求助于信道编码。信道编码的基本目标是增加数字通信系统对信道噪声的抵抗力。这是通过以受控方式在传输的数据流中添加冗余来完成的。

在通道编码中，我们将输入数据序列映射到通道输入序列。此编码过程由通道编码器完成。然后在噪声信道上传输编码序列。接收器的通道输出序列被逆映射到输出数据序列。这称为解码过程，由通道解码器执行。编码器和解码器都在设计者的控制之下。

如前所述，编码器以规定的方式引入冗余。解码器利用这种冗余来尽可能准确地重建原始源序列。因此，信道编码可以在不可靠（嘈杂）的信道上进行可靠的通信。信道编码也称为差错控制编码。值得注意的是，源编码器减少冗余以提高效率，而信道编码器以受控方式增加冗余以提高可靠性。

定义 2.6 通道的错误控制码，由通道转移概率矩阵表示p(是∣X), 包括：
(i) 一个消息集1,2,…,米.
(ii) 编码功能，Xn，它将每条消息映射到一个唯一的代码字，即1→Xn(1), 2→Xn(2),…,米→Xn(米). 该组码字称为码本。
(iii) 解码功能，D→1,2,…,米，它根据解码策略进行猜测，以便将接收到的向量映射回可能的消息之一。

我们首先来看一类称为块码的信道码。在这类代码中，传入的消息序列首先被细分为连续的块，每个块的长度为ķ位。因此消息集的基数米=2ķ. 每个ķ-位长的信息块被映射到一个n- 通道编码器的位块，其中n>ķ. 这意味着对于每个ķ点点滴滴的信息，(n−ķ)添加了冗余位。比例

r=ķn=日志⁡米n
称为码率。它表示每次传输的信息比特。任何编码方案的编码率自然小于统一。较小的码率意味着每块越来越多的比特是对应于较高编码开销的冗余比特。这可能会降低噪声的影响，但也会降低通信速率，因为我们最终将传输更多的冗余位和更少的信息位。摆在我们面前的问题是，是否存在一种编码方案，使得消息比特出错的概率任意小，而编码率又不会太小？答案是肯定的，并且首先由香农在他关于信道容量的第二个定理中提供。我们将很快研究这个。

数学代写|信息论作业代写information theory代考|Information Capacity Theorem

到目前为止，我们已经研究了在信道容量方面可以通过信道可靠地发送信息的最大速率的限制。在本节中，我们将制定带宽受限、功率受限的高斯信道的信息容量定理。一个重要且有用的通道是下面定义的高斯通道。

考虑一个零均值的平稳随机过程X(吨)那是频段限制在在赫兹。让Xķ,ķ=1,2,…,ķ, 表示过程均匀抽样得到的连续随机变量X(吨)在奈奎斯特率2在每秒采样数。这些符号是通过一个有噪声的信道传输的，该信道也有频带限制在赫兹。通道输出被零均值和功率谱密度 (psd) 的 AWGN 破坏ñ0/2. 由于通道的原因，噪声被限制在在赫兹。让是ķ,ķ=1,2,…,ķ, 表示接收信号的样本。所以，

是ķ=Xķ+ñķ,ķ=1,2,…,ķ
在哪里ñķ是均值和方差为零的噪声样本σ2=ñ0W. 假设是ķ,ķ=1,2,…,ķ, 在统计上是独立的。由于发射机通常是功率受限的，让我们对一个在和r一个G和电源输入Xķ :

和[Xķ2]=磷,ķ=1,2,…,ķ
这个带宽受限、功率受限的信道的信息容量是信道输入之间互信息的最大值Xķ和通道输出是ķ. 必须对输入上的所有分布进行最大化Xķ满足方程（2.19）的功率约束。因此，通道的信息容量（与通道容量相同）由
$$
C=\max {f {X_{k}}(x)}\left{I(X ; Y) \mid E\left 给出[X_{k}^{2}\right]=P\right}

在H和r和$FXķ(X)$一世s吨H和pr○b一个b一世l一世吨是d和ns一世吨是F在nC吨一世○n○F$Xķ$.ñ○在,Fr○米CH一个p吨和r1,和q在一个吨一世○n(1.32),在和H一个在和,
I\left(X_{k} ; Y_{k}\right)=h\left(Y_{k}\right)-h\left(Y_{k} \mid X_{k}\right)

ñ○吨和吨H一个吨$Xķ$一个nd$ñķ$一个r和一世nd和p和nd和n吨r一个nd○米在一个r一世一个bl和s.吨H和r和F○r和,吨H和C○nd一世吨一世○n一个ld一世FF和r和n吨一世一个l和n吨r○p是○F$是ķ$.G一世在和n$Xķ$一世s和q在一个l吨○吨H和d一世FF和r和n吨一世一个l和n吨r○p是○F$ñķ∗$.一世n吨在一世吨一世在和l是,吨H一世s一世sb和C一个在s和G一世在和n$Xķ$吨H和在nC和r吨一个一世n吨是一个r一世s一世nG一世n$是ķ$一世sp在r和l是d在和吨○$ñķ$.吨H一个吨一世s,
h\left(Y_{k}\mid X_{k}\right)=h\left(N_{k}\right)
$$

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|信息论作业代写information theory代考|Introduction to Image Compression

Posted on 2022年5月28日2022年5月28日 by statistics-lab

如果你也在怎样代写信息论information theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的信息论information theory及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|Introduction to Image Compression

Earlier in this chapter we discussed the coding of data sets for compression. By applying these techniques we can store or transmit all of the information content of a string of data with fewer bits than are in the source data. The data stream can represent the original data to an extent that is satisfactory to the most discerning eye. Since we can represent a picture by something between a thousand and a million bytes of data, we should be able to apply the techniques studied earlier directly to the task of compressing that data for storage and transmission. First, we consider the following points:
$\begin{array}{ll}\text { DID YOU } & \text { 1. High quality images are represented by very large data sets. A photographic quality image } \ \text { KNOW } & \text { may require } 40 \text { to } 100 \text { million bits for representation. These large file sizes drive the need } \ \text { for extremely high compression ratios to make storage and transmission (particularly of }\end{array}$ movies) practical.

Applications that involve imagery seem to be inherently linked to immediate human consumption, and so need to be fast in execution on computers and in transmission. Television, movies, computer graphical user interfaces, and the World Wide Web are examples of applications in which imagery must be moved from storage or across some kind of distribution network very quickly for immediate human intake.
Imagery has the quality of higher redundancy than we can generally expect in arbitrary data. For example, a pair of adjacent horizontal lines in an image are nearly identical (typically), while, two adjacent lines in a book have essentially no commonality.
The first two points indicate that we will almost always want to apply the highest level of compression technology available for the movement and storage of image data. The third factor indicates that compression ratios will usually be quite high. The third factor also says that some special compression techniques may be possible that will take advantage of the structure and properties of image data. The close relationship between neighboring pixels in an image can be exploited to improve the compression ratios. This is very important for the task of coding and decoding image data for real-time applications.

Another interesting point to note is that the human eye is very tolerant to approximation error in an image. Thus, it may be possible to compress the image data in a manner in which the less important information (to the human eye) can be dropped. That is, by trading off some of the quality of the image we might obtain a significantly reduced data size. This technique is called lossy compression, as opposed to the lossless compression techniques discussed earlier. This sentiment, however, can never be expressed with regards to, say, financial data or even textual data! Lossy compression can only be applied to data such as images and audio for which human beings will tolerate some loss of fidelity.

数学代写|信息论作业代写information theory代考|The JPEG Standard for Lossless Compression

The two lossless JPEG compression options differ only in the form of the entropy code that is applied to the innovations data. The user can choose to use either a Huffman code or an Arithmetic code.

DID YOU We have seen earlier that Arithmetic code, like Huffman code, achieves compression by using KNOW = the probabilistic nature of the data to render the information with fewer bits than used in the original data stream. Its primary advantage over the Huffman code is that it can come closer to the Shannon entropy limit of compression for data streams that involve a relatively small alphabet. The reason is that Huffman codes work best (highest compression ratios) when the probabilities of the symbols can be expressed as fractions of powers of two. The Arithmetic code construction is not closely tied to these particular values, as is the Huffman code. The computation of coding and decoding Arithmetic codes is more costly than that of Huffiman codes. Typically a 5 to $10 \%$ reduction in file size is seen with the application of Arithmetic codes over that obtained with Huffman coding.

Some compression can be achieved if we can predict the next pixel using the previous pixels. In this way we just have to transmit the prediction coefficients (or difference in the values) instead of the entire pixel. The predictive process that is used in the lossless JPEG coding schemes to form the innovations data is also variable. However, in this case, the variation is not based upon the user’s choice, but rather, for any image on a line-by-line basis. The choice is made according to that prediction method that yields the best prediction overall for the entire line.

There are eight prediction methods available in the JPEG coding standards. One of the eight (which is the no prediction option) is not used for the lossless coding option that we are examining here. The other seven may be divided into the following categories:

Predict the next pixel on the line as having the same value as the last one.
Predict the next pixel on the line as having the same value as the pixel in this position on the previous line (that is, above it).
Predict the next pixel on the line as having a value related to a combination of the previous, above and previous to the above pixel values. One such combination is simply the average of the other three.

数学代写|信息论作业代写information theory代考|The JPEG Standard for Lossy Compression

The JPEG standard includes a set of sophisticated lossy compression options which resulted from much experimentation by the creators of JPEG with regard to human acceptance of types of image distortion. The JPEG standard was the result of years of effort by the JPEG which was formed as a joint effort by two large, standing, standards organizations, the CCITT (The European telecommunications standards organization) and the ISO (International Standards Organization).

The JPEG lossy compression algorithm consists of an image simplification stage, which removes the image complexity at some loss of fidelity, followed by a lossless compression step based on predictive filtering and Huffman or Arithmetic coding.

The lossy image simplification step, which we will call the image reduction, is based on the exploitation of an operation known as the Discrete Cosine Transform (DCT), defined as follows.
$$
Y(k, l)=\sum_{i=0}^{N-1} \sum_{j=0}^{M-1} 4 y(i, j) \cos \left(\frac{\pi k}{2 N}(2 i+1)\right) \cos \left(\frac{\pi l}{2 M}(2 j+1)\right)
$$
DID YOU where the input image is $N$ pixels by $M$ pixels, $y(i, j)$ is the intensity of the pixel in row $i$ and KNOW $=$ column $j, Y(k, l)$ is the DCT coefficient in row $k$ and column $l$ of the DCT matrix. All DCT multiplications are real. This lowers the number of required multiplications, as compared to the discrete Fourier transform. For most images, much of the signal energy lies at low frequencies, which appear in the upper left corner of the DCT. The lower right values represent higher frequencies, and are often small (usually small enough to be neglected with little visible distortion). The DCT is, unfortunately, computationally very expensive and its complexity increases as $O\left(N^{2}\right)$. Therefore, images compressed using DCT are first divided into blocks.

In the JPEG image reduction process, the DCT is applied to 8 by 8 pixel blocks of the image. Hence, if the image is 256 by 256 pixels in size, we break it into 32 by 32 square blocks of 8 by 8 pixels and treat each one independently. The 64 pixel values in each block are transformed by the DCT into a new set of 64 values. These new 64 values, known also as the DCT coefficients, form a whole new way of representing an image. The DCT coefficients represent the spatial frequency of the image sub-block. The upper left corner of the DCT matrix has low frequency components and the lower right-corner the high frequency components (see Fig. 1.19). The top left coefficient is called the DC coefficient. Its value is proportional to the average value of the 8 by 8 block of pixels. The rest are called the $\mathbf{A C}$ coefficients.

So far we have not obtained any reduction simply by taking the DCT. However, due to the nature of most natural images, maximum energy (information) lies in low frequency as opposed to high frequency. We can represent the high frequency components coarsely, or drop them altogether, without strongly affecting the quality of the resulting image reconstruction. This leads to a lot of compression (lossy). The JPEG lossy compression algorithm does the following operations:

First the lowest weights are trimmed by setting them to zero.
The remaining weights are quantized (that is, rounded off to the nearest of some number of discrete code represented values), some more coarsely than others according to observed levels of sensitivity of viewers to these degradations.

信息论代写

数学代写|信息论作业代写information theory代考|Introduction to Image Compression

本章前面我们讨论了压缩数据集的编码。通过应用这些技术，我们可以使用比源数据中更少的位来存储或传输数据串的所有信息内容。数据流可以将原始数据表示到最敏锐的眼睛满意的程度。由于我们可以用一千到一百万字节的数据来表示一张图片，我们应该能够将前面研究的技术直接应用于压缩该数据以进行存储和传输的任务。首先，我们考虑以下几点：
你是否 1. 高质量的图像由非常大的数据集表示。照片质量的图像知道可能需要 40 至 100 百万位用于表示。这些大文件大小推动了需求以极高的压缩比进行存储和传输（尤其是电影）实用。

涉及图像的应用程序似乎与直接的人类消费有着内在的联系，因此需要在计算机上快速执行和传输。电视、电影、计算机图形用户界面和万维网都是应用程序的示例，在这些应用程序中，图像必须非常快速地从存储设备或某种分发网络中移动，以便立即供人使用。
图像具有比我们通常在任意数据中预期的更高冗余的质量。例如，图像中的一对相邻水平线（通常）几乎相同，而一本书中的两条相邻线基本上没有共性。
前两点表明我们几乎总是希望应用最高级别的压缩技术来移动和存储图像数据。第三个因素表明压缩比通常会很高。第三个因素还表明，一些特殊的压缩技术可能会利用图像数据的结构和属性。可以利用图像中相邻像素之间的密切关系来提高压缩比。这对于实时应用的图像数据编码和解码任务非常重要。

另一个值得注意的有趣点是，人眼对图像中的近似误差非常宽容。因此，可以以可以丢弃不太重要的信息（对于人眼）的方式来压缩图像数据。也就是说，通过权衡图像的一些质量，我们可能会获得显着减小的数据大小。这种技术称为有损压缩，与前面讨论的无损压缩技术相反。然而，这种情绪永远不能用财务数据甚至文本数据来表达！有损压缩只能应用于图像和音频等人类可以容忍某些保真度损失的数据。

数学代写|信息论作业代写information theory代考|The JPEG Standard for Lossless Compression

两种无损 JPEG 压缩选项的不同之处仅在于应用于创新数据的熵代码的形式。用户可以选择使用霍夫曼代码或算术代码。

你是不是我们之前已经看到，算术代码和霍夫曼代码一样，通过使用 KNOW = 数据的概率特性来实现压缩，从而使用比原始数据流中使用的更少的位来呈现信息。与霍夫曼编码相比，它的主要优势在于它可以更接近香农熵压缩限制，用于涉及相对较小字母的数据流。原因是当符号的概率可以表示为 2 的幂的分数时，霍夫曼码工作得最好（最高压缩比）。算术代码构造与这些特定值没有紧密联系，霍夫曼代码也是如此。编解码算术码的计算成本比霍夫曼码高。通常为 5 到10%使用算术代码比使用霍夫曼编码获得的文件大小更小。

如果我们可以使用先前的像素预测下一个像素，则可以实现一些压缩。通过这种方式，我们只需要传输预测系数（或值的差异）而不是整个像素。在无损 JPEG 编码方案中用于形成创新数据的预测过程也是可变的。然而，在这种情况下，变化不是基于用户的选择，而是基于逐行的任何图像。根据对整条生产线产生总体最佳预测的预测方法进行选择。

JPEG 编码标准中有八种预测方法可用。八种之一（即无预测选项）不用于我们在此处检查的无损编码选项。其他七种可分为以下几类：

预测线上的下一个像素与最后一个像素具有相同的值。
预测该行上的下一个像素与上一行（即在其上方）该位置的像素具有相同的值。
将线上的下一个像素预测为具有与上述像素值的先前、上方和先前的组合相关的值。一种这样的组合只是其他三种组合的平均值。

数学代写|信息论作业代写information theory代考|The JPEG Standard for Lossy Compression

JPEG 标准包括一组复杂的有损压缩选项，这些选项源于 JPEG 的创建者在人类接受图像失真类型方面的大量实验。JPEG 标准是 JPEG 多年努力的结果，它是由两个大型的常设标准组织 CCITT（欧洲电信标准组织）和 ISO（国际标准组织）共同努力形成的。

JPEG 有损压缩算法由图像简化阶段组成，该阶段在保真度损失的情况下消除图像复杂性，然后是基于预测滤波和霍夫曼或算术编码的无损压缩步骤。

有损图像简化步骤（我们将其称为图像缩减）基于对离散余弦变换 (DCT) 操作的利用，其定义如下。

是(ķ,l)=∑一世=0ñ−1∑j=0米−14是(一世,j)因⁡(圆周率ķ2ñ(2一世+1))因⁡(圆周率l2米(2j+1))
你知道输入图像在哪里吗ñ像素米像素，是(一世,j)是行中像素的强度一世并且知道=柱子j,是(ķ,l)是行中的 DCT 系数ķ和列lDCT 矩阵。所有 DCT 乘法都是实数。与离散傅里叶变换相比，这降低了所需的乘法次数。对于大多数图像，大部分信号能量位于低频，出现在 DCT 的左上角。右下方的值代表更高的频率，并且通常很小（通常小到可以忽略几乎没有可见的失真）。不幸的是，DCT 在计算上非常昂贵，并且它的复杂性随着这(ñ2). 因此，使用 DCT 压缩的图像首先被分成块。

在 JPEG 图像缩小过程中，DCT 应用于图像的 8 x 8 像素块。因此，如果图像大小为 256 x 256 像素，我们将其分成 8 x 8 像素的 32 x 32 正方形块，并独立处理每个块。每个块中的 64 个像素值由 DCT 转换为一组新的 64 个值。这些新的 64 个值，也称为 DCT 系数，形成了一种全新的图像表示方式。DCT 系数代表图像子块的空间频率。DCT 矩阵的左上角有低频分量，右下角有高频分量（见图 1.19）。左上角的系数称为 DC 系数。它的值与 8 x 8 像素块的平均值成正比。其余的称为一种C系数。

到目前为止，我们还没有仅仅通过 DCT 获得任何减少。然而，由于大多数自然图像的性质，最大能量（信息）位于低频而不是高频。我们可以粗略地表示高频分量，或者完全放弃它们，而不会强烈影响所得到的图像重建的质量。这会导致大量压缩（有损）。JPEG 有损压缩算法执行以下操作：

首先，通过将最低权重设置为零来修剪它们。
剩余的权重被量化（即，四舍五入到最接近的一些离散代码表示值），根据观察到的观众对这些退化的敏感度，一些权重比其他权重更粗略。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|信息论作业代写information theory代考|Run Length Encoding

Posted on 2022年5月28日2022年5月28日 by statistics-lab

如果你也在怎样代写信息论information theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的信息论information theory及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|Run Length Encoding

Run-length Encoding, or RLE is a technique used to reduce the size of a repeating string of characters. This repeating string is called a run. Typically RLE encodes a run of symbols into two bytes, a count and a symbol. RLE can compress any type of data regardless of its information content, but the content of data to be compressed affects the compression ratio. RLE cannot achieve high compression ratios compared to other compression methods, but it is easy to implement and is quick to execute. Run-length encoding is supported by most bitmap file formats such as TIFF, JPG, BMP, PCX and fax machines.

We will restrict ourselves to that portion of the PCX data stream that actually contains the coded image, and not those parts that store the color palette and image information such as number of lines, pixels per line, file and the coding method.

The basic scheme is as follows. If a string of pixels are identical in color value, encode them as a special flag byte which contains the count followed by a byte with the value of the repeated pixel. If the pixel is not repeated, simply encode it as the byte itself. Such simple schemes can often become more complicated in practice. Consider that in the above scheme, if all 256 colors in a palette are used in an image, then, we need all 256 values of a byte to represent those colors. Hence if we are going to use just bytes as our basic code unit, we don’t have any possible unused byte values that can be used as a flag/count byte. On the other hand, if we use two bytes for every coded pixel to leave room for the flag/count combinations, we might double the size of pathological images instead of compressing them.
DID YOU The compromise in the PCX format is based on the belief of its designers than many user-created KNOW $=$ drawings (which was the primary intended output of their software) would not use all 256 colors. So, they optimized their compression scheme for the case of up to 192 colors only. Images with more colors will also probably get good compression, just not quite as good, with this scheme.

数学代写|信息论作业代写information theory代考|Rate Distortion Function

Although we live in an analog world, most of the communication takes place in the digital form. Since most natural sources (e.g. speech, video etc.) are analog, they are first sampled, quantized and then processed. However, the representation of an arbitrary real number requires an infinite number of bits. Thus, a finite representation of a continuous random variable can never be perfect. Consider an analog message waveform $x(t)$ which is a sample waveform of a stochastic process $X(t)$. Assuming $X(t)$ is a bandlimited, stationary process, it can be represented by a sequence of uniform samples taken at the Nyquist rate. These samples are quantized in amplitude and encoded as a sequence of binary digits. A simple encoding strategy can be to define $L$ levels and encode every sample using
$$
\begin{aligned}
&R=\log {2} L \text { bits if } L \text { is a power of } 2 \text {, or } \ &R=\left\lfloor\log {2} L\right\rfloor+1 \text { bits if } L \text { is not a power of } 2
\end{aligned}
$$
If all levels are not equally probable we may use entropy coding for a more efficient representation. In order to represent the analog waveform more accurately, we need more number of levels, which would imply more number of bits per sample. Theoretically we need infinite bits per sample to perfectly represent an analog source. Quantization of amplitude results in data compression at the cost of signal distortion. It’s a form of lossy data compression. Distortion implies some measure of difference between the actual source samples $\left{x_{k}\right}$ and the corresponding quantized value $\left{\tilde{x}_{k}\right}$.

数学代写|信息论作业代写information theory代考|Optimum Quantizer Design

In this section, we look at optimum quantizers design. Consider a continuous amplitude signal whose amplitude is not uniformly distributed, but varies according to a certain probability density function, $p(x)$. We wish to design the optimum scalar quantizer that minimizes some function of the quantization error $q=\tilde{x}-x$, where $\tilde{x}$ is the quantized value of $x$. The distortion resulting due to the quantization can be expressed as
$$
D=\int_{-\infty}^{\infty} f(\tilde{x}-x) p(x) d x
$$
where $f(\tilde{x}-x)$ is the desired function of the error. An optimum quantizer is one that minimizes DID YOU $D$ by optimally selecting the output levels and the corresponding input range of each output
KNOW level. The resulting optimum quantizer is called the Lloyd-Max quantizer. For an L-level quantizer the distortion is given by
$$
D=\sum_{k=1}^{L} \int_{x_{k-1}}^{x_{k}} f\left(\tilde{x}_{k}-x\right) p(x) d x
$$

The necessary conditions for minimum distortion are obtained by differentiating $D$ with respect to $\left{x_{k}\right}$ and $\left{\tilde{x}{k}\right}$. As a result of the differentiation process we end up with the following system of equations $$ \begin{array}{ll} f\left(\tilde{x}{k}-x_{k}\right)=f\left(\tilde{x}{k+1}-x{k}\right), & k=1,2, \ldots, L-1 \
\int_{x_{k-1}}^{x_{k}} f^{\prime}\left(\tilde{x}{k+1}-x\right) p(x) d x, & k=1,2, \ldots, L \end{array} $$ For $f(x)=x^{2}$, i.e., the mean square value of the distortion, the above equations simplify to $$ \begin{array}{ll} x{k}=\frac{1}{2}\left(\tilde{x}{k}+\tilde{x}{k+1}\right), & k=1,2, \ldots, L-1 \
\int_{x_{k-1}}^{x_{k}}\left(\tilde{x}{k}-x\right) p(x) d x=0, & k=1,2, \ldots, L \end{array} $$ The non uniform quantizers are optimized with respect to the distortion. However, each quantized sample is represented by equal number of bits (say, $R$ bits/sample). It is possible to have a more efficient variable length coding. The discrete source outputs that result from quantization can be characterized by a set of probabilities $p{k^{*}}$. These probabilities can then be used to design efficient variable length codes (source coding). In order to compare the performance of different nonuniform quantizers, we first fix the distortion, $D$, and then compare the average number of bits required per sample.

信息论代写

数学代写|信息论作业代写information theory代考|Run Length Encoding

运行长度编码或 RLE 是一种用于减小重复字符串大小的技术。这个重复的字符串称为运行。通常，RLE 将一系列符号编码为两个字节，一个计数和一个符号。RLE 可以压缩任何类型的数据，无论其信息内容如何，但要压缩的数据内容会影响压缩率。与其他压缩方法相比，RLE 无法实现高压缩比，但它易于实现且执行速度快。大多数位图文件格式都支持游程编码，例如 TIFF、JPG、BMP、PCX 和传真机。

我们将把自己限制在 PCX 数据流中实际包含编码图像的那部分，而不是那些存储调色板和图像信息（例如行数、每行像素、文件和编码方法）的部分。

基本方案如下。如果一串像素的颜色值相同，则将它们编码为一个特殊的标志字节，其中包含计数，后跟一个带有重复像素值的字节。如果像素不重复，只需将其编码为字节本身。这种简单的方案在实践中往往会变得更加复杂。考虑在上述方案中，如果调色板中的所有 256 种颜色都用于图像中，那么，我们需要一个字节的所有 256 个值来表示这些颜色。因此，如果我们只使用字节作为我们的基本代码单元，我们没有任何可能的未使用字节值可以用作标志/计数字节。另一方面，如果我们为每个编码像素使用两个字节来为标志/计数组合留出空间，我们可能会将病理图像的大小加倍而不是压缩它们。
你是不是 PCX 格式的妥协是基于其设计师的信念而不是许多用户创建的 KNOW=图纸（这是他们软件的主要预期输出）不会使用所有 256 种颜色。因此，他们仅针对多达 192 种颜色的情况优化了压缩方案。使用此方案，具有更多颜色的图像也可能会得到很好的压缩，只是不太好。

数学代写|信息论作业代写information theory代考|Rate Distortion Function

尽管我们生活在一个模拟世界中，但大多数交流都是以数字形式进行的。由于大多数自然源（例如语音、视频等）都是模拟的，它们首先被采样、量化然后处理。但是，任意实数的表示需要无限多的位。因此，连续随机变量的有限表示永远不会是完美的。考虑一个模拟消息波形X(吨)这是一个随机过程的样本波形X(吨). 假设X(吨)是一个带限的平稳过程，它可以表示为以奈奎斯特速率采集的一系列均匀样本。这些样本在幅度上被量化并被编码为二进制数字序列。一个简单的编码策略可以是定义大号水平并使用编码每个样本

R=日志⁡2大号位如果大号是一种力量 2，或者 R=⌊日志⁡2大号⌋+1 位如果大号不是一种力量 2
如果所有级别的概率不均等，我们可以使用熵编码来获得更有效的表示。为了更准确地表示模拟波形，我们需要更多的电平，这意味着每个样本的位数更多。从理论上讲，我们需要每个样本无限位来完美地表示模拟源。幅度的量化以信号失真为代价导致数据压缩。这是有损数据压缩的一种形式。失真意味着实际源样本之间的某种差异度量\left{x_{k}\right}\left{x_{k}\right}和对应的量化值\left{\波浪号{x}_{k}\right}\left{\波浪号{x}_{k}\right}.

数学代写|信息论作业代写information theory代考|Optimum Quantizer Design

在本节中，我们着眼于最佳量化器设计。考虑一个连续幅度信号，其幅度不是均匀分布的，而是按照一定的概率密度函数变化的，p(X). 我们希望设计最优的标量量化器，使量化误差的某些函数最小化q=X~−X，在哪里X~是量化值X. 量化导致的失真可以表示为

D=∫−∞∞F(X~−X)p(X)dX
在哪里F(X~−X)是误差的期望函数。最佳量化器是最小化 DID YOUD
通过优化选择输出电平和每个输出KNOW 电平的相应输入范围。得到的最佳量化器称为 Lloyd-Max 量化器。对于 L 级量化器，失真由下式给出

D=∑ķ=1大号∫Xķ−1XķF(X~ķ−X)p(X)dX

通过微分获得最小失真的必要条件D关于\left{x_{k}\right}\left{x_{k}\right}和\left{\波浪号{x}{k}\right}\left{\波浪号{x}{k}\right}. 作为微分过程的结果，我们最终得到以下方程组

F(X~ķ−Xķ)=F(X~ķ+1−Xķ),ķ=1,2,…,大号−1 ∫Xķ−1XķF′(X~ķ+1−X)p(X)dX,ķ=1,2,…,大号为了F(X)=X2，即失真的均方值，上述方程简化为

Xķ=12(X~ķ+X~ķ+1),ķ=1,2,…,大号−1 ∫Xķ−1Xķ(X~ķ−X)p(X)dX=0,ķ=1,2,…,大号非均匀量化器针对失真进行了优化。但是，每个量化样本都由相同数量的比特表示（例如，R位/样本）。可以有更有效的可变长度编码。量化产生的离散源输出可以用一组概率来表征pķ∗. 然后可以使用这些概率来设计有效的可变长度代码（源编码）。为了比较不同非均匀量化器的性能，我们首先修复失真，D，然后比较每个样本所需的平均位数。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|信息论作业代写information theory代考|Shannon-Fano-Elias Coding

Posted on 2022年5月28日2022年5月28日 by statistics-lab

如果你也在怎样代写信息论information theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的信息论information theory及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|Shannon-Fano-Elias Coding

Codes that use the codeword lengths of $l(x)=\left[\log \frac{1}{P(x)}\right\rceil$ are called Shannon Codes. Shannon codeword lengths satisfy the Kraft inequality and can therefore be used to construct a uniquely decodable code. In this section we will study another simple method for constructing uniquely decodable codes based on ShannonFano-Elias encoding technique. It uses the Cumulative Distribution Function to allocate the codewords. The cumulative distribution function is defined as
$$
F(x)=\sum_{z \leq x} P(z)
$$
where $P(z)$ are the probability of occurrence of the $z$. The cumulative distribution function consists of steps of size $P(x)$, as shown in Fig. $1.15$. Let us define a modified cumulative distribution function as $$ \bar{F}(x)=\sum_{z<x} P(z)+\frac{1}{2} P(x) $$ symbols less than $x$ plus half the probability of the symbols $x$. The value of the function $\bar{F}(x)$ is the midpoint of the step corresponding to $x$ of the cumulative distribution function.
Fig. 1.15 The cumulative distribution Since probabilities are positive, $F(x) \neq F(y)$ if $x \neq y$. Thus it is function. possible to determine $x$ given $\bar{F}(x)$ merely by looking at the graph of the cumulative distribution function. Therefore, the value of $\bar{F}(x)$ can be used to code $x$.

In general, $\bar{F}(x)$ is a real number. This means we require an infinite number of bits to represent $\bar{F}(x)$, which would lead to an inefficient code. Suppose we round off $\bar{F}(x)$ and use only the first $l(x)$ bits, denoted by $\lfloor\bar{F}(x)\rfloor_{l(x)}$. By the definition of rounding off we have
$$
\bar{F}(x)-\lfloor\bar{F}(x)\rfloor_{l(x)} \leq \frac{1}{2^{l(x)}}
$$
If $l(x)=\left[\log \frac{1}{P(x)}\right]+1$, then,
$$
\frac{1}{2^{l(x)}}<\frac{P(x)}{2}=\bar{F}(x)-F(x-1)
$$
This implies that $\lfloor\bar{F}(x)\rfloor_{l(x)}$ lies within the step corresponding to $x$, and $l(x)$ bits are sufficient to describe $x$. The interval corresponding to any codeword is of length $2^{-l(x)}$. From (1.55) we see that this interval is less than half the height of the step corresponding to $x$. Since we use $l(x)=\left[\log \frac{1}{P(x)}\right]+1$ bits to represent $x$, the expected length of this code is
$$
\bar{R}=\sum_{x} P(x) l(x)=\sum_{x} P(x)\left(\left[\log \frac{1}{P(x)}\right]+1\right)<H(X)+2
$$
Thus the Shannon-Fano-Elias coding scheme achieves codeword length within two bits of the entropy.

数学代写|信息论作业代写information theory代考|Arithmetic Coding

As we have seen from Example 1.14, Huffiman codes are only optimal if the probabilities of the symbols are negative powers of two. This is because all prefix codes work at the bit level. There are two ways to look at it.
(a) Prefix codes try to match the self information of the symbols using codewords whose lengths are integers. The length matching may ascribe a codeword either longer than the self information or shorter. The exact match is possible if and only if the self information is in integral number of bits.
(b) If we consider the prefix codes being generated using a binary tree, the decisions between tree branches always take one bit. This is regardless of the fact whether the probabilities for the branches are $0.5 / 0.5$ or $0.9 / 0.1$. In the latter case it would theoretically take only $0.15$ bits

$\left(-\log {2}(0.9)\right)$ to select the first branch and $3.32$ bits $\left(-\log {2}(0.1)\right)$ to select the second branch, making the average code length $0.467$ bits $(0.9 \times 0.15+0.1 \times 3.32)$. The Huffiman code still needs one bit for each decision.

Arithmetic coding does not have this restriction. It works by representing the file to be encoded by an interval of real numbers between 0 and 1. Successive symbols in the message reduce this interval in accordance with the probability of that symbol. The more likely symbols reduce the range by less, and thus add fewer bits to the message.

数学代写|信息论作业代写information theory代考|The Lempel-Ziv Algorithm

Huffman coding requires symbol probabilities. But most real life scenarios do not provide the symbol probabilities in advance (i.e., the statistics of the source is unknown). In principle, it is possible to observe the output of the source for a long enough time period and estimate the symbol probabilities. However, this is impractical for real-time application. Also, Huffman coding is optimal for a DMS source where the occurrence of one symbol does not alter the probabilities of the subsequent symbols. Huffman coding is not the best choice for a source with memory. For example, consider the problem of compression of written text. We know that many letters occur in pairs or groups, like ‘ $q$ – $u$ ‘, ‘ $t-h$ ‘, ‘ $i=n-g$ ‘ etc. It might be more efficient to use the statistical inter-dependence of the letters in the alphabet along with their individual probabilities of occurrence. Such a scheme was proposed by Lempel and Ziv in 1977. Their source coding algorithm does not need the source statistics. It is a variable-to-fixed length source coding algorithm and belongs to the class of universal source coding algorithms.

The logic behind Lempel-Ziv universal coding is as follows. The compression of an arbitrary sequence of bits is possible by coding a series of 0 ‘s and l’s as some previous such string (the prefix string) plus one new bit. Then, the new string formed by adding the new bit to the previously used prefix string becomes a potential prefix string for future strings. These variable length blocks are called phrases. The phrases are listed in a dictionary which stores the existing phrases and their locations. In encoding a new phrase, we specify the location of the existing phrase in the dictionary and append the new letter. We can derive a better understanding of how the Lempel-Ziv algorithm works by the following example.

信息论代写

数学代写|信息论作业代写information theory代考|Shannon-Fano-Elias Coding

使用以下码字长度的代码l(X)=[日志⁡1磷(X)⌉称为香农码。香农码字长度满足卡夫不等式，因此可用于构造唯一可解码的码。在本节中，我们将研究另一种基于 ShannonFano-Elias 编码技术构建唯一可解码码的简单方法。它使用累积分布函数来分配码字。累积分布函数定义为

F(X)=∑和≤X磷(和)
在哪里磷(和)是发生的概率和. 累积分布函数由大小步长组成磷(X)，如图所示。1.15. 让我们将修改后的累积分布函数定义为

F¯(X)=∑和<X磷(和)+12磷(X)符号小于X加上符号概率的一半X. 函数的价值F¯(X)是对应于的步骤的中点X的累积分布函数。
图 1.15 累积分布由于概率为正，F(X)≠F(是)如果X≠是. 因此它是功能。可以确定X给定F¯(X)仅通过查看累积分布函数图。因此，价值F¯(X)可以用来编码X.

一般来说，F¯(X)是一个实数。这意味着我们需要无限数量的比特来表示F¯(X)，这将导致代码效率低下。假设我们四舍五入F¯(X)并且只使用第一个l(X)位，表示为⌊F¯(X)⌋l(X). 根据四舍五入的定义，我们有

F¯(X)−⌊F¯(X)⌋l(X)≤12l(X)
如果l(X)=[日志⁡1磷(X)]+1，然后，

12l(X)<磷(X)2=F¯(X)−F(X−1)
这意味着⌊F¯(X)⌋l(X)位于对应的步骤内X，和l(X)位足以描述X. 任何码字对应的区间都是有长度的2−l(X). 从（1.55）我们看到这个区间小于对应的台阶高度的一半X. 由于我们使用l(X)=[日志⁡1磷(X)]+1位来表示X，此代码的预期长度为

R¯=∑X磷(X)l(X)=∑X磷(X)([日志⁡1磷(X)]+1)<H(X)+2
因此，Shannon-Fano-Elias 编码方案在熵的两个比特内实现了码字长度。

数学代写|信息论作业代写information theory代考|Arithmetic Coding

正如我们从示例 1.14 中看到的，只有当符号的概率是 2 的负幂时，Huffiman 码才是最优的。这是因为所有前缀代码都在位级别工作。有两种方法可以查看它。
(a) 前缀码尝试使用长度为整数的码字匹配符号的自身信息。长度匹配可以归因于比自身信息更长或更短的码字。当且仅当自身信息是整数位时，精确匹配是可能的。
(b) 如果我们考虑使用二叉树生成的前缀码，则树分支之间的决策总是占用一位。这与分支的概率是否为0.5/0.5或者0.9/0.1. 在后一种情况下，理论上只需要0.15位

(−日志⁡2(0.9))选择第一个分支和3.32位(−日志⁡2(0.1))选择第二个分支，使平均代码长度0.467位(0.9×0.15+0.1×3.32). Huffiman 代码仍然需要一个位来进行每个决定。

算术编码没有这个限制。它的工作原理是用 0 到 1 之间的实数间隔来表示要编码的文件。消息中的连续符号会根据该符号的概率减小该间隔。更可能的符号将范围缩小得更少，因此向消息中添加的位更少。

数学代写|信息论作业代写information theory代考|The Lempel-Ziv Algorithm

霍夫曼编码需要符号概率。但大多数现实生活场景并没有提前提供符号概率（即来源的统计数据未知）。原则上，可以在足够长的时间段内观察源的输出并估计符号概率。然而，这对于实时应用来说是不切实际的。此外，霍夫曼编码对于一个符号的出现不会改变后续符号的概率的 DMS 源是最佳的。霍夫曼编码不是具有内存的源的最佳选择。例如，考虑书面文本的压缩问题。我们知道许多字母成对或成组出现，例如’q – 在 ‘, ‘ 吨−H‘, ‘一世=n−G’ 等等。使用字母表中字母的统计相互依赖性以及它们各自的出现概率可能会更有效。这种方案是由 Lempel 和 Ziv 在 1977 年提出的。他们的源编码算法不需要源统计。它是一种变定长信源编码算法，属于通用信源编码算法类。

Lempel-Ziv 通用编码背后的逻辑如下。通过将一系列 0 和 l 编码为一些先前的此类字符串（前缀字符串）加上一个新位，可以压缩任意位序列。然后，通过将新位添加到先前使用的前缀字符串而形成的新字符串成为未来字符串的潜在前缀字符串。这些可变长度的块称为短语。短语列在存储现有短语及其位置的字典中。在编码新短语时，我们指定字典中现有短语的位置并附加新字母。通过以下示例，我们可以更好地理解 Lempel-Ziv 算法的工作原理。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|信息论作业代写information theory代考|Information Measures for Continuous

Posted on 2022年5月28日2022年5月28日 by statistics-lab

如果你也在怎样代写信息论information theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的信息论information theory及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|Information Measures for Continuous

数学代写|信息论作业代写information theory代考|Random Variables

The definitions of mutual information for discrete random variables can be directly extended to continuous random variables. Let $X$ and $Y$ be random variables with joint probability density function (pdf) $p(x, y)$ and marginal pdfs $p(x)$ and $p(y)$. The average mutual information between $X$ and $Y$ is defined as follows.

Definition $1.8$ The Average Mutual Information between two continuous random variables $X$ and $Y$ is defined as
$$
I(X ; Y)=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} p(x) p(y \mid x) \log \frac{p(y \mid x) p(x)}{p(x) p(y)} d x d y
$$
It should be pointed out that the definition of average mutual information can be carried over from discrete random variables to continuous random variables, but the concept and physical interpretation cannot. The reason is that the information content in a continuous random variable

is actually infinite, and we require infinite number of bits to represent a continuous random variable precisely. The self information, and hence the entropy, is infinite. To get around the problem we define a quantity called the differential entropy.
Definition 1.9 The Differential Entropy of a continuous random variable $X$ is defined as
$$
h(X)=-\int_{-\infty}^{\infty} p(x) \log p(x) d x
$$
Again, it should be understood that there is no physical meaning attached to the above quantity. We carry on with extending our definitions further.

Definition 1.10 The Average Conditional Entropy of a continuous random variable $X$ given $Y$ is defined as
$$
h(X \mid Y)=-\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} p(x, y) \log p(x \mid y) d x d y
$$
The average mutual information can be expressed as
$$
I(X ; Y)=h(X)-h(X \mid Y)=h(Y)-h(Y \mid X)
$$
Following is the list of some properties of differential entropy:

$h(a X)=h(X)+\log |a|$.
If $X$ and $Y$ are independent, then $h(X+Y) \geq h(X)$. This is because $h(X+Y) \geq h(X+Y \mid Y)=$ $h(X \mid Y)=h(X)$.

数学代写|信息论作业代写information theory代考|Relative Entropy

An interesting question to ask is how similar (or different) are two probability distributions? Relative entropy is used as a measure of distance between two distributions.

Definition 1.11 The Relative Entropy or Kullback Leibler (KL) Distance between two probability mass functions $p(x)$ and $q(x)$ is defined as
$$
D(p | q)=\sum_{x \in X} p(x) \log \left(\frac{p(x)}{q(x)}\right)
$$
It can be interpreted as the expected value of $\log \left(\frac{p(x)}{q(x)}\right)$.
Example 1.9 Consider a Gaussian distribution $p(x)$ with mean and variance given by $\left(\mu_{1}, \sigma_{1}^{2}\right)$, and another Gaussian distribution $q(x)$ with mean and variance given by $\left(\mu_{2}, \sigma_{2}^{2}\right)$. Using (1.33), we can find the KL distance between two Gaussian distributions as

$$
D(p | q)=\frac{1}{2}\left[\frac{\sigma_{1}^{2}}{\sigma_{2}^{2}}+\left(\frac{\mu_{2}-\mu_{1}}{\sigma_{2}}\right)^{2}-1-\log {2}\left(\frac{\sigma{1}^{2}}{\sigma_{2}^{2}}\right)\right]
$$
The distance becomes zero when the two distributions are identical, i.e., $\mu_{1}=\mu_{2}$ and $\sigma_{1}^{2}=\sigma_{2}^{2}$. It is interesting to note that when $\mu_{1} \neq \mu_{2}$, the distance is minimum for $\sigma_{1}^{2}=\sigma_{2}^{2}$. This minimum distance is given by
$$
D_{\min }(p | q)=\frac{1}{2}\left(\frac{\mu_{2}-\mu_{1}}{\sigma_{2}}\right)^{2}
$$
Also, the KL distance is infinite if either $\sigma_{1}^{2} \rightarrow 0$ or $\sigma_{2}^{2} \rightarrow 0$, that is, if either of the distributions tends to the Dirac delta.
The average mutual information can be seen as the relative entropy between the joint distribution, $p(x, y)$, and the product distribution, $p(x) p(y)$, i.e.,
$$
I(X ; Y)=D(p(x, y) | p(x) p(y))
$$
We note that, in general, $D(p | q) \neq D(q | p)$. Thus, even though the relative entropy is a distance measure, it does not follow the symmetry property of distances. To overcome this, another measure, called the Jensen Shannon distance, is sometimes used to define the similarity between two distributions.

Definition $1.12$ The Jensen Shannon Distance between two probability mass functions $p(x)$ and $q(x)$ is defined as
$$
J S D(p | q)=\frac{1}{2} D(p | m)+\frac{1}{2} D(q | m)
$$
where $m=\frac{1}{2}(p+q)$.
DID YOU If the base of the logarithm is 2 , then, $0 \leq J S D(p | q) \leq 1$. Note that Jensen Shannon distance is
KNOW sometimes referred to as Jensen Shannon divergence or Information Radius in literature.

数学代写|信息论作业代写information theory代考|Huffman Coding

We will now study an algorithm for constructing efficient source codes for a DMS with source symbols that are not equally probable. A variable length encoding algorithm was suggested by Huffiman in 1952 , based on the source symbol probabilities $P\left(x_{i}\right), i=1,2, \ldots, L$. The algorithm is optimal in the sense that the average number of bits required to represent the source symbols is a minimum provided the prefix condition is met. The steps of the Huffman coding algorithm are as follows:
(i) Arrange the source symbols in decreasing order of their probabilities.
(ii) Take the bottom two symbols and tie them together as shown in Fig. 1.11. Add the probabilities of the two symbols and write it on the combined node. Label the two branches with a ‘ $l$ ‘ and a ‘ 0 ‘ as depicted in Fig. 1.11.
(iii) Treat this sum of probabilities as a new probability associated with a new symbol. Again pick the two smallest probabilities, tie them together to form a new probability. Each time we perform the combination of two symbols we reduce the total number of symbols by one. Whenever we tie together two probabilities (nodes) we label the two branches with $\mathrm{a}$ ‘ 1 ‘ and $\mathrm{a} \mathrm{} ~ 0$ ‘.

(iv) Continue the procedure until only one probability is left (and it should be 1 if your addition is right!). This completes the construction of the Huffman tree.
(v) To find out the prefix codeword for any symbol, follow the branches from the final node back to the symbol. While tracing back the route, read out the labels on the branches. This is the codeword for the symbol.
The algorithm can be easily understood using the following example.

信息论代写

数学代写|信息论作业代写information theory代考|Random Variables

离散随机变量的互信息定义可以直接推广到连续随机变量。让X和是是具有联合概率密度函数的随机变量 (pdf)p(X,是)和边缘pdfp(X)和p(是). 之间的平均互信息X和是定义如下。

定义1.8两个连续随机变量之间的平均互信息X和是定义为

一世(X;是)=∫−∞∞∫−∞∞p(X)p(是∣X)日志⁡p(是∣X)p(X)p(X)p(是)dXd是
需要指出的是，平均互信息的定义可以从离散随机变量推广到连续随机变量，但概念和物理解释不能。原因是信息内容在一个连续的随机变量中

实际上是无限的，我们需要无限多的比特来精确地表示一个连续的随机变量。自我信息，因此熵，是无限的。为了解决这个问题，我们定义了一个称为微分熵的量。
定义 1.9 连续随机变量的微分熵X定义为

H(X)=−∫−∞∞p(X)日志⁡p(X)dX
同样，应该理解的是，上述数量没有物理意义。我们继续进一步扩展我们的定义。

定义 1.10 连续随机变量的平均条件熵X给定是定义为

H(X∣是)=−∫−∞∞∫−∞∞p(X,是)日志⁡p(X∣是)dXd是
平均互信息可以表示为

一世(X;是)=H(X)−H(X∣是)=H(是)−H(是∣X)
以下是微分熵的一些性质的列表：

H(一个X)=H(X)+日志⁡|一个|.
如果X和是是独立的，那么H(X+是)≥H(X). 这是因为H(X+是)≥H(X+是∣是)= H(X∣是)=H(X).

数学代写|信息论作业代写information theory代考|Relative Entropy

一个有趣的问题是两个概率分布有多相似（或不同）？相对熵用于衡量两个分布之间的距离。

定义 1.11 两个概率质量函数之间的相对熵或 Kullback Leibler (KL) 距离p(X)和q(X)定义为

D(p|q)=∑X∈Xp(X)日志⁡(p(X)q(X))
可以理解为期望值日志⁡(p(X)q(X)).
例 1.9 考虑一个高斯分布p(X)均值和方差由下式给出(μ1,σ12), 和另一个高斯分布q(X)均值和方差由下式给出(μ2,σ22). 使用 (1.33)，我们可以找到两个高斯分布之间的 KL 距离为

D(p|q)=12[σ12σ22+(μ2−μ1σ2)2−1−日志⁡2(σ12σ22)]
当两个分布相同时，距离变为零，即μ1=μ2和σ12=σ22. 有趣的是，当μ1≠μ2, 距离最小σ12=σ22. 这个最小距离由下式给出

D分钟(p|q)=12(μ2−μ1σ2)2
此外，KL 距离是无限的，如果σ12→0或者σ22→0，也就是说，如果任何一个分布都倾向于狄拉克三角洲。
平均互信息可以看作是联合分布之间的相对熵，p(X,是)，以及产品分布，p(X)p(是)， IE，

一世(X;是)=D(p(X,是)|p(X)p(是))
我们注意到，一般来说，D(p|q)≠D(q|p). 因此，即使相对熵是距离度量，它也不遵循距离的对称性。为了克服这个问题，有时使用另一种称为 Jensen Shannon 距离的度量来定义两个分布之间的相似性。

定义1.12两个概率质量函数之间的 Jensen Shannon 距离p(X)和q(X)定义为

Ĵ小号D(p|q)=12D(p|米)+12D(q|米)
在哪里米=12(p+q).
DID YOU 如果对数的底是 2 ，那么，0≤Ĵ小号D(p|q)≤1. 请注意，Jensen Shannon 距离
在文献中有时称为 Jensen Shannon 散度或信息半径。

数学代写|信息论作业代写information theory代考|Huffman Coding

我们现在将研究一种算法，用于为具有不等可能的源符号的 DMS 构建有效的源代码。Huffiman 在 1952 年提出了一种基于源符号概率的可变长度编码算法。磷(X一世),一世=1,2,…,大号. 在满足前缀条件的情况下，表示源符号所需的平均比特数是最小值，该算法是最优的。霍夫曼编码算法的步骤如下：
(i) 以它们的概率的降序排列源符号。
(ii) 如图 1.11 所示，将底部的两个符号绑在一起。将两个符号的概率相加，并将其写在组合节点上。用’标记两个分支l’和一个’0’，如图1.11所示。
(iii) 将此概率总和视为与新符号相关联的新概率。再次选择两个最小的概率，将它们连接在一起形成一个新的概率。每次我们执行两个符号的组合时，我们都会将符号的总数减一。每当我们将两个概率（节点）联系在一起时，我们将两个分支标记为一个’1′ 和一个 0 ‘.

(iv) 继续这个过程，直到只剩下一个概率（如果你的加法正确，它应该是 1！）。这样就完成了 Huffman 树的构建。
(v) 要找出任何符号的前缀码字，请沿着从最终节点到符号的分支。一边追溯路线，一边读出树枝上的标签。这是符号的代码字。
使用以下示例可以很容易地理解该算法。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|信息论作业代写information theory代考|Source Coding

Posted on 2022年5月28日2022年5月28日 by statistics-lab

如果你也在怎样代写信息论information theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的信息论information theory及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|Source Coding

数学代写|信息论作业代写information theory代考|Introduction to Information Theory

DVD disk or streamed directly to our smart phones. Email and web addresses are commonly visible on business cards. Most of the people today prefer to send emails and e-cards to their friends rather than the regular snail mail. Stock quotes and cricket scores can be checked using the mobile phone. ‘Selfies’ can be captured and uploaded on social media sites with just a click of a button.

DID YOU 2 Information has become a key to success (it has always been the key to success, but in today’s KNOW $=$ world it is the key). And behind all this exchange of information lie the tiny l’s and 0 ‘s (the omnipresent bits) that hold the information by the mere way they sit next to one another. Yet the present day’s information age owes primarily to a seminal paper published in 1948 that laid the foundation of the wonderful field of Information Theory-a theory that was initiated by one man, the American Electrical Engineer Claude E. Shannon, whose ideas appeared in the article “The Mathematical Theory of Communication” in the Bell System Technical Journal (1948). In its broadest sense, information is interpreted to include the messages occurring in any of the standard communications media, such as telephone, radio, or television, and the signals involved in electronic computers, electromechanical systems, and other data-processing devices. The theory is even applicable to the signals appearing in the nerve networks of humans and other animals.

The chief concern of information theory is to discover mathematical laws governing systems designed to communicate or manipulate information. It sets up quantitative measures of information and of the capacity of various systems to transmit, store, and otherwise process information. Some of the problems treated are related to finding the best methods of using various available communication systems and the best methods for separating the wanted information, or signal, from the extraneous information, or noise. Another problem is the setting of upper bounds on what it is possible to achieve with a given information-carrying medium (often called an information channel). While the results are chiefly of the interest to communication engineers, some of the concepts have been adopted and found useful in fields like psychology and linguistics. The notion of mutual information has also found applications in population based gene mapping, whose aim is to find DNA regions (genotypes) responsible for particular traits (phenotypes).

数学代写|信息论作业代写information theory代考|Uncertainty and Information

Any information source produces an output that is random in nature. If the source output had no randomness, i.e., the output were known exactly, there would be no need to transmit it! There exist both analog and discrete information sources. Actually, we live in an analog world, and most sources Understanding the concep are analog sources, for example, speech, temperature fluctuations, etc. The of information. discrete sources are man made sources, for example, a source (say, a man) that generates a sequence of letters from a finite alphabet (while typing email).
Before we go on to develop a mathematical measure of information, let us develop an intuitive feel for it. Read the following sentences:
(A) Tomorrow, the sun will rise from the East.
(B) The phone will ring in the next one hour.
(C) It will snow in Delhi this winter.

The three sentences carry different amounts of information. In fact, the first sentence hardly carries any information. It is a sure-shot thing. Everybody knows that the sun rises from the East and the Intuition probability of this happening again is almost unity ( ” Making predictions is risky, especially when it involves the future.” – N. Bohr). Sentence (B) appears to carry more information than sentence (A). The phone may ring, or it may not. There is a finite probability that the phone will ring in the next one hour (unless the maintenance people are at work again). The last sentence probably made you read it over twice. This is because it has never snowed in Delhi, and the probability of a snowfall is very low. It is interesting to note that the amount of information carried by the sentences listed above have something to do with the probability of occurrence of the events stated in the sentences. And we observe an inverse relationship. Sentence (A), which talks about an event which has a probability of occurrence very close to 1 carries almost no information. Sentence $(\mathrm{C})$, which has a very low probability of occurrence, appears to carry a lot of information (made us read it twice to be sure we got the information right!). The other interesting thing to note is that the length of the sentence has nothing to do with the amount of information it conveys. In fact, sentence (A) is the longest of the three sentences but carries the minimum information.
We will now develop a mathematical measure of information.

数学代写|信息论作业代写information theory代考|Average Mutual Information and Entropy

So far we have studied the mutual information associated with a pair of events $x_{i}$ and $y_{j}$ which are the possible outcomes of the two random variables $X$ and $Y$. We now want to find out the average mutual information between the two random variables. This can be obtained simply by weighting $I\left(x_{i} ; y_{j}\right)$ by the probability of occurrence of the joint event and summing over all possible joint events.
Definition 1.4 The Average Mutual Information between two random variables $X$ and $Y$ is given by
$$
\begin{aligned}
I(X ; Y) &=\sum_{i=1}^{n} \sum_{j=1}^{m} P\left(x_{i}, y_{j}\right) I\left(x_{i} ; y_{j}\right)=\sum_{i=1}^{n} \sum_{j=1}^{m} P\left(x_{i}, y_{j}\right) \log \frac{P\left(x_{i}, y_{j}\right)}{P\left(x_{i}\right) P\left(y_{j}\right)} \
&=\sum_{i=1}^{n} \sum_{j=1}^{m} P\left(x_{i}\right) P\left(y_{j} \mid x_{i}\right) \log \frac{P\left(y_{j} \mid x_{i}\right)}{P\left(y_{j}\right)} \
&=\sum_{j=1}^{m} \sum_{i=1}^{n} P\left(y_{j}\right) P\left(x_{i} \mid y_{j}\right) \log \frac{P\left(x_{i} \mid y_{j}\right)}{P\left(x_{i}\right)}
\end{aligned}
$$
For the case when $X$ and $Y$ are statistically independent, $I(X ; Y)=0$, i.e., there is no average mutual information between $X$ and $Y$. An important property of the average mutual information is that $I(X ; Y) \geq 0$, with equality if and only if $X$ and $Y$ are statistically independent.
Definition 1.5 The Average Self Information of a random variable $X$ is defined as
$$
H(X)=\sum_{i=1}^{n} P\left(x_{i}\right) I\left(x_{i}\right)=-\sum_{i=1}^{n} P\left(x_{i}\right) \log P\left(x_{i}\right)
$$
When $X$ represents the alphabet of possible output letters from a source, $H(X)$ represents the average information per source letter. In this case $H(X)$ is called the entropy. The entropy of $X$ can be interpreted as the expected value of $\log \left(\frac{1}{P(X)}\right)$. The term entropy has been borrowed from statistical mechanics, where it is used to denote the level of disorder in a system. It is interesting to see that the Chinese character for entropy looks like ！
We observe that since $0 \leq P\left(x_{i}\right) \leq 1, \log \left(\frac{1}{P\left(x_{i}\right)}\right) \geq 0$. Hence, $H(X) \geq 0$.

信息论代写

数学代写|信息论作业代写information theory代考|Introduction to Information Theory

DVD 光盘或直接流式传输到我们的智能手机。电子邮件和网址通常在名片上可见。今天的大多数人更喜欢向他们的朋友发送电子邮件和电子贺卡，而不是普通的蜗牛邮件。可以使用手机查看股票报价和板球比分。只需单击一个按钮，即可在社交媒体网站上捕获并上传“自拍”。

DID YOU 2 信息已成为成功的关键（它一直是成功的关键，但在今天的 KNOW=世界，它是关键）。在所有这些信息交换的背后，隐藏着微小的 l 和 0（无所不在的位），它们仅靠彼此相邻的方式来保存信息。然而，当今的信息时代主要归功于 1948 年发表的一篇开创性论文，该论文奠定了信息论这一奇妙领域的基础——这一理论由美国电气工程师克劳德·E·香农发起，他的想法出现在贝尔系统技术期刊（1948 年）中的文章“通信的数学理论”。在最广泛的意义上，信息被解释为包括在任何标准通信媒体（如电话、收音机或电视）中出现的消息，以及电子计算机、机电系统和其他数据处理设备中涉及的信号。

信息论的主要关注点是发现管理旨在交流或操纵信息的系统的数学规律。它建立了信息和各种系统传输、存储和以其他方式处理信息的能力的定量测量。所处理的一些问题与寻找使用各种可用通信系统的最佳方法以及从无关信息或噪声中分离所需信息或信号的最佳方法有关。另一个问题是设定使用给定的信息承载媒介（通常称为信息通道）可能实现的目标的上限。虽然结果主要引起了通信工程师的兴趣，但其中一些概念已被采用并发现在心理学和语言学等领域很有用。

数学代写|信息论作业代写information theory代考|Uncertainty and Information

任何信息源都会产生本质上随机的输出。如果源输出没有随机性，即输出是完全已知的，就没有必要传输了！存在模拟和离散信息源。实际上，我们生活在一个模拟世界中，而大多数来源理解概念都是模拟来源，例如，语音、温度波动等信息。离散源是人造源，例如，从有限的字母表（在键入电子邮件时）生成一系列字母的源（例如，一个人）。
在我们继续开发信息的数学度量之前，让我们对它进行直观的感觉。阅读以下句子：
(A) 明天，太阳将从东方升起。
(B) 电话将在接下来的一小时内响起。
(C) 今年冬天德里会下雪。

这三个句子携带的信息量不同。事实上，第一句话几乎没有任何信息。这是肯定的事情。每个人都知道太阳从东方升起，这种再次发生的直觉概率几乎是统一的（“做出预测是有风险的，尤其是当它涉及到未来时。” – N. Bohr）。句子 (B) 似乎比句子 (A) 包含更多信息。电话可能响，也可能不响。电话在接下来的一小时内响铃的概率是有限的（除非维修人员再次上班）。最后一句话可能让你读了两遍。这是因为德里从来没有下过雪，下雪的概率很低。有趣的是，上面列出的句子所携带的信息量与句子中所述事件的发生概率有关。我们观察到一个反比关系。句子 (A) 谈论发生概率非常接近 1 的事件，几乎没有任何信息。句子(C)，它的发生概率非常低，似乎携带了很多信息（让我们阅读了两次以确保我们得到了正确的信息！）。另一个值得注意的有趣的事情是，句子的长度与它传达的信息量无关。事实上，句子 (A) 是三个句子中最长的，但携带的信息最少。
我们现在将开发一种信息的数学度量。

数学代写|信息论作业代写information theory代考|Average Mutual Information and Entropy

到目前为止，我们已经研究了与一对事件相关的互信息X一世和是j这是两个随机变量的可能结果X和是. 我们现在想要找出两个随机变量之间的平均互信息。这可以简单地通过加权来获得一世(X一世;是j)通过联合事件的发生概率和所有可能的联合事件的总和。
定义 1.4 两个随机变量之间的平均互信息X和是是（谁）给的

一世(X;是)=∑一世=1n∑j=1米磷(X一世,是j)一世(X一世;是j)=∑一世=1n∑j=1米磷(X一世,是j)日志⁡磷(X一世,是j)磷(X一世)磷(是j) =∑一世=1n∑j=1米磷(X一世)磷(是j∣X一世)日志⁡磷(是j∣X一世)磷(是j) =∑j=1米∑一世=1n磷(是j)磷(X一世∣是j)日志⁡磷(X一世∣是j)磷(X一世)
对于这种情况X和是是统计独立的，一世(X;是)=0，即之间没有平均互信息X和是. 平均互信息的一个重要性质是一世(X;是)≥0, 相等当且仅当X和是是统计独立的。
定义 1.5 随机变量的平均自信息X定义为

H(X)=∑一世=1n磷(X一世)一世(X一世)=−∑一世=1n磷(X一世)日志⁡磷(X一世)
什么时候X表示来自源的可能输出字母的字母表，H(X)表示每个源字母的平均信息。在这种情况下H(X)称为熵。的熵X可以解释为期望值日志⁡(1磷(X)). 熵这个术语是从统计力学中借来的，用来表示系统中的无序程度。有趣的是，熵的汉字看起来像！
我们观察到，因为0≤磷(X一世)≤1,日志⁡(1磷(X一世))≥0. 因此，H(X)≥0.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|信息论作业代写information theory代考|Preface to the Third Edition

Posted on 2022年5月28日2022年5月28日 by statistics-lab

如果你也在怎样代写信息论information theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的信息论information theory及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|Preface to the Third Edition

数学代写|信息论作业代写information theory代考|Introduction to the Course

The textbook is designed for the students of electrical/electronics engineering and computer science. The primary aim of this book is to arouse the curiosity of the students. This edition is prepared, keeping in mind, the current needs of students and instructors. The revised text is (hopefully) more fascinating-to-read, simple-to-understand, logical-to-follow and motivating-to-design. An attempt has been made to adhere to the original philosophy behind writing this book – it is to be a lively introduction to the topics dealing with Information Theory, Coding and Cryptography.This book is intended for final-year undergraduate students and first-year postgraduate students of the electrical engineering or the computer science programs. The book will help in forming a strong foundation for the broad areas of Information Theory, Coding and Cryptography. It emphasizes on the basic concepts, lays stress on the fundamental principles and motivates their application to practical problems. By design, the mathematical complexity of the book remains at a level well within the grasp of engineering college students. The book can also be used as a quick reference by practicing engineers.The main objectives of the revision are to update the material of the previous edition, to make it easier to teach and to add Learning Objectives in each chapter. Two new chapters have also been added: Chapter 6-Space Time Codes and Chapter 10-Physical Layer Security. In addition to these, several other interesting topics have been included, for example, Relative Entropy, Video Compression Standards, Parallel Gaussian Channels and Capacity region for Multiple Access Channels. While making these modifications, the main aim was to increase the utility-quotient of this book for the students and instructors.

数学代写|信息论作业代写information theory代考|Roadmap of Target Courses

This book is ideally suited for a full semester-long course at the post-graduate level. For an advanced undergraduate course, the following topics may be omitted: Relative Entropy, Rate Distortion Function, Channel capacity for MIMO systems, Capacity region for Multiple Access Channels, Bounds on Minimum Distance, Circuit Implementation of Cyclic Codes, Performance of RS codes over real channels, Nested Codes, Quasi-Orthogonal Space Time Block Codes, Turbo decoding, Interleaver Design for Turbo Codes, TCM for Fading Channels, Cooperative Jamming and Artificial Noise Forwarding. Certain portions of this book can also be used for short-term courses, quality-improvement programs and continuing education programs.

The third edition is student-centric, and follows the ‘Learning Objective/Levels of Difficulty (LO/LOD)’ approach. This is an educational process that emphasizes on developing engineering skills in student and testing the outcomes of the study of a course, as opposed to rote learning. Each of the 10 chapters follows a common organizational structure with a range of learning and assessment tools for instructors and students. The feedback received on the second edition has been constructively used to augment the book in different dimensions. Following are the specific improvements over the earlier editions.

数学代写|信息论作业代写information theory代考|Organisation of the Book

This edition of the book retains the original flavor. It has been divided into four logical parts which are as follows:

Chapter 0 in the book covers pre-requisites. It gives an introduction to Matrices and Probability Theory by providing important definitions relevant to the topics that have been introduced herein this chapter.
Part I: Information Theory and Source Coding
The first part consists of following two fundamental chapters:
Chapter 1 deals with information and its efficient representation. It introduces the important concepts of Source Coding, Huffman Coding, Shannon-Fano-Elias Coding, Arithmetic Coding, Lempel-Ziv Coding, Run Length Coding and the Rate Distortion Theory. Image and Video Compression techniques are also covered in this chapter.

Chapter 2 deals with Channel Capacity and Coding. The reader is introduced to various types of channel models. Information Capacity Theorem, Gaussian Channels, Channel capacity for MIMO systems, Capacity region for Multiple Access Channels and Random selection of codes are also discussed in detail. This chapter also motivates the need for Error Control Coding, which is covered in Part II.
Part II: Error Control Coding (Channel Coding)
This part consists of the following four interesting chapters:
Chapter 3 introduces the reader to the fascinating world of Linear Block Codes for Error Correction. Encoding and decoding of linear block codes are discussed in detail. Ideas related to Syndrome decoding, Perfect codes, Optimal linear codes and Maximum distance separable (MDS) Codes are presented in the chapter. Hamming Codes and Low Density Parity Check (LDPC) Codes are also discussed.

Chapter 4 deals with Cyclic Codes, a useful sub-class of linear block codes. This chapter introduces the Matrix description of cyclic codes, Quasi-cyclic codes, Shortened cyclic codes, Fire Codes, Golay Codes and the powerful Cyclic Redundancy Check (CRC) Codes. Circuit implementation of Cyclic Codes has also been discussed here.

Chapter 5 deals with Bose-Chaudhuri Hocquenghem (BCH) Codes, a useful sub-class of cyclic codes. The chapter builds the necessary mathematical background required to work with BCH codes. Reed Solomon (RS) Codes, an important sub-class of BCH codes, are also discussed, along with their performance over real channels.

Chapter 6 is a new chapter and introduces the reader to the intriguing world of Space-Time Codes. The chapter covers Real Orthogonal Design, Generalized Real Orthogonal Design, Complex Orthogonal Design, Generalized Complex Orthogonal Design and Quasi-orthogonal Space Time Block Codes. Space-Time Code design criteria and design targets are also discussed in this chapter.
Part III: Codes on Graph
This part consists of following two fascinating chapters that deal with codes with memory:
Chapter 7 discusses various aspects of Convolutional Codes, including the Polynomial description, Distance Notion, Generating Function and the Matrix description. Viterbi decoding of Convolutional Codes is discussed in detail. Turbo Codes, Turbo decoding and Interleaver Design for Turbo Codes are also covered in this chapter.

信息论代写

数学代写|信息论作业代写information theory代考|Introduction to the Course

该教材是为电气/电子工程和计算机科学专业的学生设计的。本书的主要目的是激发学生的好奇心。本版本是在考虑学生和教师当前的需求的情况下编写的。修订后的文本（希望）更引人入胜，易于理解，符合逻辑并激发设计灵感。本书试图坚持最初的写作理念——它是对信息论、编码和密码学主题的生动介绍。本书适用于本科生和研究生一年级电气工程或计算机科学课程的学生。这本书将有助于为信息论的广泛领域奠定坚实的基础，编码和密码学。它强调基本概念，强调基本原理，并促使其应用于实际问题。通过设计，本书的数学复杂性保持在工程学院学生能够掌握的水平。本书也可以作为实践工程师的快速参考。修订的主要目的是更新上一版的材料，使教学更容易，并在每章中增加学习目标。还添加了两个新章节：第 6 章 – 时空代码和第 10 章 – 物理层安全性。除此之外，还包括其他几个有趣的主题，例如，相对熵、视频压缩标准、并行高斯通道和多路访问通道的容量区域。

数学代写|信息论作业代写information theory代考|Roadmap of Target Courses

这本书非常适合研究生阶段的完整学期课程。对于高级本科课程，可能会省略以下主题：相对熵、速率失真函数、MIMO 系统的信道容量、多路访问信道的容量区域、最小距离的界限、循环码的电路实现、RS 码的实际性能信道、嵌套码、准正交空时分组码、Turbo 解码、Turbo 码的交织器设计、衰落信道的 TCM、协作干扰和人工噪声转发。本书的某些部分也可用于短期课程、质量改进计划和继续教育计划。

第三版以学生为中心，遵循“学习目标/难度级别 (LO/LOD)”方法。这是一个教育过程，强调培养学生的工程技能并测试课程学习的结果，而不是死记硬背。10 章中的每一章都遵循一个共同的组织结构，为教师和学生提供一系列学习和评估工具。第二版收到的反馈已被建设性地用于在不同维度上扩充本书。以下是对早期版本的具体改进。

数学代写|信息论作业代写information theory代考|Organisation of the Book

本版保留原味。它分为四个逻辑部分，如下所示：

本书第 0 章介绍了先决条件。它通过提供与本章介绍的主题相关的重要定义来介绍矩阵和概率论。
第一部分：信息理论和源代码编码
第一部分包括以下两个基本章节：
第 1 章处理信息及其有效表示。它介绍了源编码、霍夫曼编码、香农-法诺-埃利亚斯编码、算术编码、Lempel-Ziv 编码、游程编码和速率失真理论的重要概念。本章还介绍了图像和视频压缩技术。

第 2 章处理信道容量和编码。向读者介绍了各种类型的通道模型。还详细讨论了信息容量定理、高斯信道、MIMO 系统的信道容量、多址信道的容量区域和码的随机选择。本章还提出了对错误控制编码的需求，这将在第二部分中介绍。
第二部分：差错控制编码（Channel Coding）
这部分包括以下四个有趣的章节：
第 3 章向读者介绍了用于纠错的线性分组码的迷人世界。详细讨论了线性块码的编码和解码。本章介绍了与综合症解码、完美码、最佳线性码和最大距离可分 (MDS) 码相关的思想。还讨论了汉明码和低密度奇偶校验 (LDPC) 码。

第 4 章讨论循环码，一种有用的线性块码子类。本章介绍循环码、准循环码、缩短循环码、Fire 码、Golay 码和强大的循环冗余校验 (CRC) 码的矩阵描述。此处还讨论了循环码的电路实现。

第 5 章讨论 Bose-Chaudhuri Hocquenghem (BCH) 码，这是一个有用的循环码子类。本章建立了使用 BCH 代码所需的必要数学背景。还讨论了 Reed Solomon (RS) 码，这是 BCH 码的一个重要子类，以及它们在真实信道上的性能。

第 6 章是新的一章，向读者介绍了时空码的迷人世界。本章涵盖实正交设计、广义实正交设计、复正交设计、广义复正交设计和准正交时空分组码。本章还讨论了空时码设计标准和设计目标。
第三部分：图上的代码
这部分包括以下两个引人入胜的章节，分别处理带有记忆的代码：
第 7 章讨论了卷积码的各个方面，包括多项式描述、距离概念、生成函数和矩阵描述。详细讨论了卷积码的维特比解码。本章还介绍了 Turbo 码、Turbo 解码和 Turbo 码的交织器设计。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写