Novel Reduced-State BCJR Algorithms

The Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm is an exact efficient algorithm to computer the marginal posterior distributions of state variables and pairs of consecutive state variables of a trellis structure. Due to its overwhelming complexity, reduced-complexity variations such as the M-BCJR algorithm have been developed. In this paper, we propose improvements upon the conventional M-BCJR algorithm based on modified active state-selection criteria. We propose selecting the active states based on estimates of the fixed-lag smoothed distributions of the state variables. We also present Gaussian approximation techniques for the low-complexity estimation of these fixed-lag smoothed distributions. The improved performance over the M-BCJR algorithm is shown via computer simulations.