Suboptimum decoding using Kullback principle

Abstract

Several successive decodings of cascaded codes become possible in principle without information loss if the decoding task is extended to determine a posterior probability distribution on the codewords. Kullback principle of cross-entropy minimization is considered as a means of implementing it. Its practical use, however, demands some kind of simplification. We propose to look for the posterior distribution in separable form with respect to the information symbols, which leads to decoding output of same form as its input. As an illustration of these ideas, we considered decoding an iterated product of parity-check codes which results in a vanishingly small error probability provided the channel signal-to-noise ratio is larger than some threshold. Interpreting a single linear code as a kind of product of its parity checks, the same ideas lead to a simple and efficient algorithm.