Overview

In this chapter, we are dealing with the theory of error-control block codes. The treatment here will concentrate on the basic principles of encoding and decoding binary linear block codes.

Consider the coded digital communication system model shown in Figure 3.1.

Figure 3.1: Model of a coded digital communication system.

A sequence of q-ary digits called the information vector U = [ u ₀ u ₁ . . . u _{k ?1}] is fed into a block encoder. The block encoder adds redundancy digits to U and produces an encoded vector V = [ v ₀ v ₁ . . . v _{n ?1}] called a channel codeword. A set of q ^k q-ary vectors (codewords) of length n defines a block code. In most applications, q = 2 and the block code is binary in nature. The modulator transforms the encoded vector into a modulated signal vector which is suitable for transmission through the analog channel. Typical channels are telephone lines, high-frequency radio links, microwave links, satellite links, semi-conductor memories, and magnetic tapes. Because the channel is usually subject to noise disturbance, the channel output may be differed from the channel input. At the receiving end, the demodulator performs an inverse operation and produces a received vector R = [ r ₀ r ₁ . . . r _{n ?1}]. Subject to noise disturbance, the received vector R may...