Reduced-State BCJR-Type Algorithms

In this paper, we propose a technique to reduce the number of trellis states in BCJR-type algorithms, i.e., algorithms with a structure similar to that of the well-known algorithm by Bahl, Cocke, Jelinek, and Raviv (BCJR). This work is inspired by reduced-state sequence detection (RSSD). The key idea is the construction, during one of the recursions in the reduced-state trellis, of a “survivor map” to be used in the other recursion. In a more general setting, two distinct survivor maps could be determined in the two recursions and used jointly to approximate the a posteriori probabilities. Three examples of application to iterative decoding are shown: 1) coherent detection for intersymbol interference (ISI) channels; 2) noncoherent detection based on an algorithm recently proposed by the authors; and 3) detection based on linear prediction for Rayleigh fading channels. As in classical RSSD, the proposed algorithm allows significant state-complexity reduction with limited performance degradation.