Soft and Hard Decision Decoding Performance

Abstract

In this chapter, we discuss the performance of codes under soft and hard decision decoding. Upper and lower bounds on hard and soft decision decoding are discussed. For hard decision decoding, evaluation of the performance of specific codes shows that full decoding produces better performance than the usual bounded distance decoder. An analysis of the upper and lower union bounds on the probability of error for maximum likelihood soft decision decoding shows that contrary to hard decision decoding above relative low values of SNR per information bit, the two bounds coincide. The implications of this observation is that the soft decision decoding performance may be determined for a linear code by the number of minimum Hamming weight codewords without the need to determine the weight distribution of the code. Numerical performance comparisons are made for a wide range of different codes. It is shown that the binomial weight distribution provides a good indicative performance for codes whose weight distribution is difficult to obtain.