Complexity Reduction in SISO Decoding of Block Codes

Abstract

SISO decoding for block codes can be carried out based on a trellis representation of the code. However, the complexity entailed by such decoding is most often prohibitive and thus prevents practical implementation. This paper examines a new decoding scheme based on the soft-output Viterbi algorithm (SOVA) applied to a sectionalized trellis for linear block codes. The computational complexities of the new SOVA decoder and of the conventional SOVA decoder, based on a bit-level trellis, are theoretically analyzed and derived for different linear block codes. These results are used to obtain optimum sectionalizations of a trellis for SOVA. For comparisons, the optimum sectionalizations for Maximum A Posteriori (MAP) and Maximum Logarithm MAP (Max-Log-MAP) algorithms, and their corresponding computational complexities are included. The results confirm that the new SOVA decoder is the most computationally efficient SISO decoder, in comparisons to MAP and Max-Log-MAP algorithms. The simulation results of the bit error rate (BER) performance, assuming binary phase -- shift keying (BPSK) and additive white Gaussian noise (AWGN) channel, demonstrate that the performance of the new decoding scheme is not degraded. The BER performance of iterative SOVA decoding of serially concatenated block codes shows no difference in the quality of the soft outputs of the new decoding scheme and of the conventional SOVA.