Linear Block Codes

Abstract

Chapter 2 gives a brief review of linear block codes. The goal is to provide the essential background material for the development of trellis structure and trellis-based decoding algorithms for linear block codes in the later chapters. We mainly present the basic concepts of encoding and decoding of linear block codes and state some facts without derivations or proofs. Since in most present digital data communication systems, information is coded in binary digits, ‘0’ or ‘1’, we discuss only linear block codes with symbols from the binary field GF(2). First, linear block codes are defined and described in terms of generator and parity-check matrices. Second, coset partition of a linear block code is discussed, which is needed in analyzing the code trellis structure and construction. Third, the concepts of minimum distance, weight distribution and distance profile are presented, which are needed in the later chapters for presenting decoding algorithms and their error performances. Finally, the concepts of hard-decision, soft-decision, and maximum likelihood decoding are presented.