System of and method for decoding trellis codes

Systems and related methods are described for (1) determining one or more state probabilities for one or more states in a trellis representation; (2) determining an estimate of or extrinsic output for one or more bits using a trellis representation; (3) determining a branch metric for a branch in a trellis representation; (4) performing a MAX*2->1 operation; (5) performing a MAX*2p->1 operation, where p is an integer of two or more, through a hierarchical arrangement of MAX*2->1 operations; and (6) computing forward state probabilities in a forward mode of operation and computing backward state probabilities in a backward mode of operation. Combinations of the foregoing are also described.