A new adaptive two-stage maximum-likelihood decoding algorithm for linear block codes

This work presents a maximum-likelihood (ML) decoding algorithm for linear block codes. In this algorithm, the optimal performance is achieved at low computational complexity through a two-stage processing. At the first stage, a minimum sufficient set S that includes the optimal solution is estimated. With the minimum sufficient set, the decoding complexity can be greatly reduced without performance degradation. At the second stage, ordered processing is performed within the estimated minimum sufficient set S to obtain the optimal solution. During the ordered processing, S is adoptively updated to minimize the computational complexity, and an effective stopping criterion is used to decide whether the optimal solution is found. Ordered processing not only helps to find the optimal solution quickly, but also enables simplified sub-optimal solutions with bounded block error rates. The proposed algorithm is also extended to decode block turbo codes. Finally, simulation results are given to show that this algorithm achieves optimal performance with a low average computational complexity.