Efficient Box and Match Algorithm for Reliability-Based Soft-Decision Decoding of Linear Block Codes

In this paper, efficient methods to improve the box and matching algorithm (BMA) are presented. Firstly, an efficient approach is introduced to terminate the decoding if a local optimal candidate satisfies a probabilistic sufficient condition. The false alarm probability associated with the use of the probabilistic sufficient condition is also derived. Secondly, by constructing a control band which is assumed error free, the matching capability of the BMA is enhanced. More precisely, the performance of BMA of order (i + 1) is nearly achieved with a small increase in complexity and no increase in memory with respect to the BMA of order i. A tight performance analysis is derived based on the theory of order statistics. An error floor associated either with false alarms or with errors in the control band is introduced, but this error floor can be controlled using the analysis in both cases. Simulation results show that the performance of the enhanced BMA for the decoding of the RS(255,239) code with BPSK signaling over an AWGN channel is about 0.1 dB away from that of maximum likelihood decoding at the word error rate (WER) 10^-3.