New approaches to reduced-complexity decoding

Abstract We examine new approaches to the problem of decoding general linear codes under the strategies of full or bounded hard decoding and bounded soft decoding. The objective is to derive enhanced new algorithms that take advantage of the major features of existing algorithms to reduce decoding complexity. We derive a wide range of results on the complexity of many existing algorithms. We suggest a new algorithm for cyclic codes, and show how it exploits all the main features of the existing algorithms. Finally, we propose a new approach to the problem of bounded soft decoding, and show that its asymptotic complexity is significantly lower than that of any other currently known general algorithm. In addition, we give a characterization of the weight distribution of the average linear code and thus show that the Gilbert-Varshamov bound is tight for virtually all linear codes over any symbol field.