Shu Lin

A low-weight trellis-based iterative soft-decision decoding algorithm for binary linear block codes

This paper presents a new low-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The algorithm is devised based on a set of optimality conditions and the generation of a sequence of candidate codewords for an optimality test. The initial candidate codeword is generated by a simple decoding method. The subsequent candidate codewords, if needed, are generated by a chain of low-weight trellis searches, one at a time. Each search is conducted through a low-weight trellis diagram centered around the latest candidate codeword and results in an improvement over the previous candidate codewords that have been already tested. This improvement is then used as the next candidate codeword for a test of optimality. The decoding iteration stops whenever a candidate codeword is found to satisfy a sufficient condition on optimality or the latest low-weight trellis search results in a repetition of a previously generated candidate codeword. A divide-and-conquer technique is also presented for codes that are not spanned by their minimum-weight codewords. The proposed decoding algorithm has been applied to some well-known codes of lengths 48, 64, and 128. Simulation results show that the proposed algorithm achieves either practically optimal error performance for the example codes of length 48 and 64 or near optimal error performance for the (128, 29, 32) RM code with a significant reduction in computational decoding complexity.

The least stringent sufficient condition on the optimality of suboptimally decoded codewords

The number of iterations of an iterative optimal or suboptimal decoding scheme for binary linear block codes without any effect on its error performance can be reduced by testing a sufficient condition on the optimality of a candidate codeword. The least stringent sufficient condition on the optimality of a decoded codeword is investigated under the assumption that the available information on the code is restricted to (1) the minimum weight or the distance profile and (2) for a given positive integer h, h or fewer already generated candidate codewords. The least stringent sufficient conditions of optimality for 1/spl les/h/spl les/3 are presented. Cond/sub 1/ is the same as the one given by Taipale and Pursley (1991), Cond/sub 2/ is less stringent than the one given by Kaneko, Nishijima, Inazumi and Hirasawa (see IEEE Trans. Inform. Theory, vol.IT-40, no.3, p.320, 1994), and Cond/sub 1/ and Cond/sub 2/ are derived from Cond/sub 3/ as special cases. These conditions can be used effectively to save computer simulation time for evaluating the error probability for maximum likelihood decoding.

The structure and complexity of subtrellis diagrams for low weight codewords of binary linear block codes

This paper investigates the structure and complexity of low-weight subtrellises for binary linear block codes. The state and branch complexities of low-weight subtrellises for Reed-Muller (RM) codes and some extended permuted BCH (EBCH) codes are given.