Reduced-complexity BCJR algorithm for turbo equalization

We propose novel techniques to reduce the complexity of the well-known Bahl, Cocke, Jelinek, and Raviv (BCJR) algorithm when it is employed as a detection algorithm in turbo equalization schemes. In particular, by also considering an alternative formulation of the BCJR algorithm, which is more suitable than the original one for deriving reduced-complexity techniques, we describe three reduced-complexity algorithms, each of them particularly effective over one of the three different classes of channels affected by intersymbol interference (minimum-phase, maximum-phase, and mixed-phase channels). The proposed algorithms do not explore all paths on the trellis describing the channel memory, but they work only on the most promising ones, chosen according to the maximum a posteriori criterion. Moreover, some optimization techniques improving the effectiveness of the proposed solutions are described. Finally, we report the results of computer simulations showing the impressive performance of the proposed algorithms, and we compare them with other solutions in the literature.