Quasi-Optimal Decoding of Linear Block Codes Using Soft Decision Detection

Abstract

A simple but effective decoding procedure, applicable to any (n,k) linear block code with symbols from GF(q), is described. The technique involves a transformation of the parity check equations which focuses the code's correction power on the soft symbol set while still retaining the capability to correct one symbol error from outside this set. The soft symbol set is defined to be the n-k least reliably detected code symbol positions whose parity check rowspaces are linearly independent. The process generates a number of error vector screening candidates, each a solution to the parity check equations, and the maximum-likelihood candidate is accepted. If P(opt) and P(qopt) are the decoder error rates for the optimal and quasi-optimal decoders respectively, then P(opt) < P(qopt) < P(opt) + P(se) where P(se) is the probability that the actual error vector is not included in the screening candidate set. Since P(se) can be shown to approach zero for a wide range of codes and operating conditions, the performance of this decoder can be quasi-optimal in these cases.