Some Useful Coding Techniques for Binary Communication Systems

Abstract

An introduction to coding theory and a discussion of specific coding techniques are given as applied to digital communication systems. The place of coding in a communication system is illustrated and the various approaches to coding are discussed. The information theory concepts required are presented along with the First and Second Fundamental Theorems of Shannon, The relation between Shannon’s theorems and coding for the noisy and noiseless channel is discussed. For the noiseless channel the techniques of Shannon, Fano, Huffman, Gilbert-More, Karp and others are discussed. For the noisy channel, the techniques of Hamming, Slepian, Elias, Cowell, Bose-Chaudhuri, Reed-Muller, Fire, and Wozencraft are presented. The relationships between the various codes are given and the advantages and disadvantages of each indicated. Numerous examples illustrating the use of the codes are given and areas of further research outlined