A Method for Obtaining the Optimum Sectionalization of the RMLD Algorithm for Non-Linear Rectangular Codes

A recursive maximum likelihood decoding (RMLD) algorithm is more efficient than the Viterbi algorithm. The decoding complexity of the RMLD algorithm depends on the recursive sectionalization. The recursive sectionalization which minimizes the decoding complexity is called the optimum sectionalization. In this paper, for a class of non-linear codes, called rectangular codes, it is shown that a near optimum sectionalization can be obtained with a dynamic programming approach. Furthermore, for a subclass of rectangular codes, called C-rectangular codes, it is shown that the exactly optimum sectionalization can be obtained with the same approach. Following these results, an efficient algorithm to obtain the optimum sectionalization is proposed. The optimum sectionalizations for the minimum weight subcode of some Reed-Muller codes and of a BCH code are obtained with the proposed algorithm. key words: maximum likelihood decoding, recursive maximum likelihood decoding, rectangular code, optimum sectionalization, dynamic programming approach