第4章 信道容量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 price 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 channel
§4.1: Outline

The content of Info. Theory researching on the channel What’s channel？
The function of channel The goal of researching the channel



§5.1:Outline－1
Nature 1: I (X; Y) is a convex function of the channel input probability distribution p (x).
I(X; Y)
p(x)
Review – nature of mutual info. function : Nature.2

Classification
Description

§4.2: Classification and description of channel－1

classification




project physics —— transmission medium type; mathematics description way —— description way of signal and disturbance; parameter type of the channel itself —— changeable and permanent parameter; user type ——single user and multi-user;

Studying the channel in the communications system is mainly to describe, measure, analyze different types of channel, calculate their capacity, namely, the limit transmission capacity, and analyze their characteristic.
§5.1:Outline－4


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

Relationship between Info. content and channel transition probability distribution
Nature 2: I (X; Y) is a concave function of channel transition probability distributes p (y/X).
§4.2: Classification and description
of channel－4
Constant 3〉Parameter type Changeable
§4.2: Classification and description
of channБайду номын сангаасl－5
二用户信道（点对点通信） 4 〉用户类型 多用户信道（通信网）

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 dissimilar condition

Mutual info. Channel Capacity function in chanel coding theorem
Review – nature of mutual info. function : Nature.1

Relationship between mutual info. and channel input probability distribution
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
§5.1:Outline－3

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.

The Info. Theory mainly researches －－ info. transmission question (hypothesis is that the transmission characteristics are known)
§4.2:Classification and description of the channel
§4.2: Classification and description
of channel－6

Description of channel

The channel may quote three groups of variables to describe:
space：[ X , p( x)]
channel
§4.2: Classification and description of
2
§4.2: Classification and description of channel－3
discrete memoryless continuous Signal Semi - discrete with memory Semi - continuous No interferen ce：can be ignored ； 2〉Signal interferen ce Passive thermal noise Linear superposit ion Active shot noise Impulse Noise Interferen ce With interferen ce Intermodul ation Multiplica tive Fading Inter - symbol interferen ce

The communication technology mainly
researches －－ The physical rule which the signal follows while transmitting in the channel, namely transmission characteristic
§5.1:Outline－2

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 is the channel; If we watch the television, listen to the radio, the space to receive and send is the channel.