An adaptive two-stage algorithm for ML and sub-ML decoding of binary linear block codes

Two distinct codeword-searching procedures based on iterative bounded-distance decoding (BDD) are combined to form an adaptive two-stage maximum-likelihood (ML) decoder for binary linear block codes. During the first stage of the algorithm, a tight upper bound on an error likelihood metric ("discrepancy") is established iteratively for the ML codeword. Firststage processing requires sorting and storage. Adaptive switching to the second stage removes the sorting and storage requirements and allows to rule out redundant BDDs efficiently. Second-stage processing accounts for all codewords with discrepancy lower bound below the upper bound of the ML codeword and guarantees ML performance. In addition, the proposed two-stage algorithm is inherently tunable for controlled suboptimum operation. Under sub-ML operation, the overall scheme can be interpreted as a generalization of the Chase (1972) algorithm. Simulation studies for the (24,12,8) extended Golay and the (64,30,14) and (128,64,22) extended Bose-Chaudhuri-Hocquenghem (BCH) codes illustrate and support these theoretical developments.