An Algebraic Description Of Iterative Decoding Schemes

. Several popular, suboptimal algorithms for bit decoding of binary block codes such as turbo decoding, threshold decoding, and message passing for LDPC, were developed almost as a common sense approach to decoding of some specially designed codes. After their introduction, these algorithms have been studied by mathematical tools pertinent more to computer science than the conventional algebraic coding theory. We give an algebraic description of the optimal and suboptimal bit decoders and of the optimal and suboptimal message passing. We explain exactly how suboptimal algorithms approximate the optimal, and show how good these approximations are in some special cases. Key words. Iterative decoding, soft-output decoding, suboptimal decoding, bitoptimal decoding. AMS(MOS) subject classifications. 94B05, 94B25, 94B35, 94B60. 1. Introduction. We propose an entirely new approach to the problem of iterative decoding, which is algebraic in nature and derives the well known suboptimal algori..