Wireless Communications

6Channel Coding

Abstract

A communication system designer has a limited resource of energy at hand; but where he should invest this resource? Part of the energy must be invested in digital modulation in order to implement effective transmission over a physical channel. The transmission reliability on AWGN channels improves with the symbol energy invested for signaling, in the form of the Q function. However, the reliability return is even more effective if part of the energy is invested on code structures, with the resulting error probability dropping much faster than that defined by the Q function. Code structures, once added to the information sequence, no longer solely belong to the encoder or the decoder. But rather, these structures should be regarded as the feature of the entire received signal and should be exploited for information-symbols retrieval. Channel coding is implemented through various algebraic structures, which can be in the form of parity-check matrix as used in linear block codes, Galois field structures as used in cyclic codes, filter structures as used in convolutional codes, or constellation structures as used in trellis coded modulation. Each code structure is well justified in its own right. Then, what is the best structure? How to share the energy between modulation and coding, and how to find a good structure for coding and decoding are two challenges to the designer.

6.1 Introduction and philosophical discussion

Coding and digital modulation are ...