A new SISO algorithm with application to turbo equalization
  In this paper we propose a new soft-input soft-output equalization algorithm, offering very good performance/complexity tradeoffs. It follows the structure of the BCJR algorithm, but dynamically constructs a simplified trellis during the forward recursion. In each trellis section, only the M states with the strongest forward metric are preserved, similar to the M-BCJR algorithm. Unlike the M-BCJR, however, the remaining states are not deleted, but rather merged into the surviving states. The new algorithm compares favorably with the reduced-state BCJR algorithm, offering better performance and more flexibility, particularly for systems with higher order modulations. 
Marcin Sikora and Daniel J. Costello Jr