信息论与编码英文课件 第7章 信道编码.ppt

Chapter 7 Channel Coding Theory  7.1 The characteristic of continuous source 7.2 The channel capacity of continuous source 7.3 Error Control and the fundamental of Channel encoding and decoding 7.4 Linear Block Code 7.5 Convolutional Code 7.1 The characteristic of continuous source 7.1.1 Continuous source 7.1.2 The entropy of continuous source 7.1.3 The maximum entropy of continuous source 7.1 The characteristic of continuous source 7.1.1 Continuous source In practical, the output of source is usually continuous signal, such as voice signal, television picture signal. Because they are continuous and random, the source is called continuous source, and the message source output can describe with stochastic process. For one continuous source , when a specific moment given, the value it takes is continuous, that means the time and amplitude are all continuous function. 7.1.2 The entropy of continuous source The simplest continuous source can be described with one-dimension random variables. Random variable exists non-negative function ( ). And it satisfies Then it is thought that has a continuous distribution, or is a continuous variable. is the probability density function, is the probability distribution function. Continuous variable satisfies: (1) (2) (3) is a monotone non-decreasing function. (4) is continuous from its left, that is. (5) Definition 7.1.1 For continuous source, if its probability density is, the entropy of the source is 7.1.3 The maximum entropy of continuous source Theorem 7.1.1 For source which is in its uniform probability distribution has a maximum output entropy. Proof: under the constraint condition to calculate the when reaches its maximum. Let , calculate its partial derivative and let it be zero, then After the simplification Solve the equation to get Because , there is . Then The defi