Adaptive Maximum-Likelihood Decoding Algorithms for Linear Block Codes

This correspondence represents two new soft decision decoding algorithms that promise to reduce complexity and at the same time achieve the maximum likelihood decoding (MLD) performance. The first method is an Adaptive Two-Stage Maximum Likelihood Decoder [1] that first estimates a minimum sufficient set and performs decoding within the smaller set to reduce complexity and at the same time achieves MLD performance. The second scheme is an Iterative Reliability based decoder [2] that takes advantage of Adaptive Belief Propagation (ABP) [5] to update the reliabilities and then performs Order Statistics Decoding (OSD) or Box and Match Algorithm (BMA) to the new log likelihood ratios (LLRs). The updated reliability values reduce the number of errors in the most reliable positions (MPRs) therefore allowing for a smaller OSD or BMA to be used in the next step of decoding, thus reducing complexity and at the same time achieving close to MLD performance.