Studies on recursive maximum likelihood decoding and suboptimum decoding algorithms for nonlinear subcodes of linear block codes

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(1) For the minimum weight subcodes of Reed-Muller (RM) codes and BCH codes, the computational complexity of the recursive maximum likelihood decoding is dominated by those for a few sections in upper levels. For these sections, to find only good metrics, the trellis structure is studied, mainly for RM codes. As a result, for the minimum weight subcodes of (64, 42) RM code, some regular structure similar to that for the (64, 42) RM code itself is found. For an iterative decoding using the recursive maximum likelihood decoding for the minimum weight subcode with the majority logic decoding for the initial candidate, the relation between the error probability and the decoding complexity is examined. If the number of the iteration and threshold are properly chosen, the decoding complexity is reduced to 80% at SNR 3dB.(2) For the local distance profile which is important for the performance evaluation, an algorithm for computing it using the invariant property for symbol position is devised. For a group of permutation under which the code is closed, choose a subcode which is also invariant. The set of cosets of the subcode in the code is partitioned into blocks in which every coset equally contributes the local distance profile. Then, the contribution of every representative coset is computed. For several codes for which their local distance profiles were unknown, the local distance profiles have been computed.(3) For a soft-input soft-output decoding, an iterative type decoding using the minimum distance codeword search is considered. Using the structure of Reed-Muller code, the computational complexity is reduced.(4) The above mentioned decoding methods are suitable for the inner code of the concatenated coding scheme. Good (64, 40) codes as the inner code are searched among the shortened MDS codes, and several good codes are found. Also, by permuting symbol ordering, the complexity of the recursive maximum likelihood decoding is shown to be small.