3
Block Codes
This chapter introduces the theory of block codes. Here we will describe mainly the features of block codes which correct the independent errors. The importance of considering this class of codes can be explained by its significance for practice and by the fact that analyses of these codes allows the main methods and results of coding theory to be shown.
3.1 Main Definitions
Let us consider in accordance with Shannon [1] the model of data transmission system represented in
Figure 3.1. A data source generates messages 
and a receiver needs to receive them correctly (with high reliability). The data source and the receiver are connected by a channel allowing transmitting symbols from an input alphabet (set) A transmitting in a sequential way. However, due to some noise in the channel the output sequence may differ from the input one. Moreover, in general the input alphabet A and the output alphabet B do not coincide. The probabilistic model of the channel is given by transition probabilities P(b|a) that an output sequence (of symbols) is b under condition that an input sequence was a. We restrict our consideration ...
