Reduced-Complexity BCJR Algorithm for Turbo Equalization

We propose novel techniques to reduce the complexity of the well-known Bahl–Cocke–Jelinek–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 for deriving reduced-complexity techniques, we describe three reduced-complexity algorithms, each of them being particularly effective over one of the three different classes of channels (minimum-phase, maximum-phase, and mixed-phase channels) affected by intersymbol interference. The proposed algorithms do not explore all paths on the trellis describing the channel memory, but they work only on the most promising ones, which are chosen according to the maximum a posteriori criterion. Moreover, some optimization techniques for 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 compare them with other solutions in the literature.