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1、Chapter 4：Channel and Channel Capacity,The goal to achieve,The understanding of the goal and content how Info. Theory studies the channel Understand the basic classification of the channel and grasp the basic description method of the channel Grasp the concept of channel capacity/Channel capacity pr
2、ice function, as well as relations between this concept and mutual info., channel input probability distribution, channel transfer function Can calculate the channel capacity/The channel capacity price function (symmetrical discrete channel, additive Gauss noise channel without memory ) of simple ch
3、annel Understand the function of the channel capacity/Capacity price function in communications system research,Definition question,Entropy Entropy rate function in lossless source coding theorem Mutual info. Channel Capacity function in source coding theorem,Review nature of mutual info. function :
4、 Nature.1,Relationship between mutual info. and channel input probability distribution Nature 1: I (X; Y) is a convex function of the channel input probability distribution p (x).,Review nature of mutual info. function : Nature.2,Relationship between Info. content and channel transition probability
5、distribution Nature 2: I (X; Y) is a concave function of channel transition probability distributes p (y/X).,Review nature of mutual info. function : Nature.3,Relationship between Info. content and channel input mark relevancy Nature 3: The channel input is discrete and without memory,Review nature
6、of mutual info. function : Nature.4,Relationship between Info. content and channel input mark relevancy Nature 4: The channel has no memory,Review nature of mutual info. function : Nature.5,Deduction of nature 3 and nature 4 : The channel input and the channel themselves are all discrete and without
7、 memory.,Channel and Channel Capacity,Outline classification and description of the channel The discrete channel without memory and its the capacity Continual channel and its capacity Capacity price function C(F),4.1: Outline,The content of Info. Theory researching on the channel Whats channel？ The
8、function of channel The goal of researching the channel,5.1:Outline1,Content that the Info. Theory studies on the channel: Channel modeling: describe with two appropriate input/outputs stochastic processes Channel capacity various means of taking fully advantage of the channel capacity under dissimi
9、lar condition,5.1:Outline2,What is channel? The channel is a carrier which transmits messages a passage which signal passes through. The information is abstract, the channel then is concrete. For instance: If two people converse, the air is the channel; If the two call each other, the telephone line
10、 is the channel; If we watch the television, listen to the radio, the space to receive and send is the channel.,5.1:Outline3,The function of channel The channel mainly be used in transmitting and storing data the info. system, but in communications system mainly be used in transmitting.,5.1:Outline4
11、,the goal to research channel Realize validity and reliability of intelligence transmission Validity: Fully use the channel capacity Reliability: Reduces the error rate through the channel coding Studying the channel in the communications system is mainly to describe, measure, analyze different type
12、s of channel, calculate their capacity, namely, the limit transmission capacity, and analyze their characteristic.,The communication technology mainly researches The physical rule which the signal follows while transmitting in the channel, namely transmission characteristic The Info. Theory mainly r
13、esearches info. transmission question (hypothesis is that the transmission characteristics are known),4.2:Classification and description of the channel,Classification Description,4.2: Classification and description of channel1,classification project physics transmission medium type; mathematics desc
14、ription way description way of signal and disturbance; parameter type of the channel itself changeable and permanent parameter; user type single user and multi-user;,4.2: Classification and description of channel2,4.2: Classification and description of channel3,4.2: Classification and description of
15、 channel4,4.2: Classification and description of channel5,4.2: Classification and description of channel6,Description of channel The channel may quote three groups of variables to describe: Channel input probability space： Channel output probability space： Channel probability shift matrix： P Namely：
16、 P ， It can be simplified： .,4.2: Classification and description of channel7,其中： 而 而,4.2: Classification and description of channel8,When K=1，degenerates to the single message (mark) channel; Further when n=m=2， degenerates to the binary single message channel. If it satisfied symmetry, namely constitutes most commonly used binary single message symmetrical channel BSC: A
