We consider iterative soft-decision decoding algorithms in which bounded distance decodings are carried out with respect to successively selected input words, called search centers. Their error performances are degraded by the decoding failure of bounded distance decoding and the duplication in generating candidate codewords. To avoid those weak points, we present a new method of selecting sequences of search centers. For some BCH codes, we show the effectiveness by simulation results.

This letter deals with an iterative decoding algorithm (IDA) for product codes. In the IDA, a soft-input and output iterative bounded-distance and encoding-based decoding algorithm is used for the component codes. Simulation results over an AWGN channel with BPSK modulation is presented and show the effectiveness of the IDA.

In this paper, we consider linear subcodes of RMr,m whose bases are formed from the monomial basis of RMr,m by deleting ΔK monomials of degree r where ΔK < . For such subcodes, a procedure for computing the number of minimum weight codewords is presented and it is shown how to delete ΔK monomials in order to obtain a subcode with the smallest number of codewords of the minimum weight. For ΔK 3, a formula for the number of codewords of the minimum weight is presented. A (64,40) subcode of RM3,6 is being considered as an inner code in a concatenated coding system for NASA's high-speed satellite communications. For (64,40) subcodes, there are three equivalent classes. For each class, the number of minimum weight codewords, that of the second smallest weight codewords and simulation results on error probabilities of soft-decision maximum likelihood decoding are presented.

Recently, a trellis-based recursive maximum likelihood decoding (RMLD) algorithm has been proposed for decoding binary linear block codes. This RMLD algorithm is computationally more efficient than the Viterbi decoding algorithm. However, the computational complexity of the RMLD algorithm depends on the sectionalization of a code trellis. In general, minimization of the computational complexity results in non-uniform sectionalization of a code trellis. From implementation point of view, uniform sectionalization of a code trellis and regularity among the trellis sections are desirable. In this paper, we apply the RMLD algorithm to a class of codes which are transitive invariant. This class includes Reed-Muller (RM) codes, the extended and permuted BCH (EBCH) codes and their subcodes. For this class of codes, the binary uniform sectionalization of a code trellis results in the following regular structure. At each step of decoding recursion, the metric table construction procedure is applied uniformly to all the sections and the size and structure of each metric table are the same. This simplifies the implementation of the RMLD algorithm. Furthermore, for all RM codes of lengths 64 and 128 and EBCH codes of lengths 64 and 128 with relatively low rate, the computational complexity of the RMLD algorithm based on the binary uniform sectionalization of a code trellis is almost the same as that based on an optimum sectionalization of a code trellis.

This letter considers an iterative decoding algorithm for non-binary linear block codes in which erasure and error decoding is performed for input words given by the sums of a hard-decision received sequence and given test patterns. We have proposed a new selection method of test patterns for the iterative decoding algorithm. Simulation results have shown that the decoding algorithm with test patterns by the proposed selection method provides better error performance than a conventional iterative decoding algorithm with the same number of the error and erasure decoding iterations over an additive white Gaussian noise channel using binary phase-shift keying modulation.

A soft-decision recursive decoding algorithm (RDA) for the class of the binary linear block codes recursively generated using a u|u+v-construction method is proposed. It is well known that Reed-Muller (RM) codes are in this class. A code in this class can be decomposed into left and right components. At a recursive level of the RDA, if the component is decomposable, the RDA is performed for the left component and then for the cosets generated from the left decoding result and the right component. The result of this level is obtained by concatenating the left and right decoding results. If the component is indecomposable, a proposed iterative bounded-distance decoding algorithm is performed. Computer simulations were made to evaluate the RDA for RM codes over an additive white Gaussian-noise channel using binary phase-shift keying modulation. The results show that the block error rates of the RDA are relatively close to those of the maximum-likelihood decoding for the third-order RM code of length 26 and better than those of the Chase II decoding for the third-order RM codes of length 26 and 27, and the fourth-order RM code of length 28.

We consider a soft-decision iterative bounded distance decoding algorithm for binary linear block codes. In the decoding algorithm, bounded distance decodings are carried out with respect to successive input words, called the search centers. A search center is the sum of the hard-decision sequence of a received sequence and a sequence in a set of test patterns which are generated beforehand. This set of test patterns has influence on the error performance of the decoding algorithms as simulation results show. In this paper, we propose a construction method of a set of candidate test patterns and a selection method of test patterns based on an introduced measure of effectiveness of test patterns. For several BCH codes of lengths 127, 255 and 511, we show the effectiveness of the proposed method by simulation.

For binary linear block codes, we introduce "multiple GMD decoding algorithm. " In this algorithm, GMD-like decoding is iterated around a few appropriately selected search centers. The original GMD decoding by Forney is a GMD-like decoding around the hard-decision sequence. Compared with the original GMD decoding, this decoding algorithm provides better error performance with moderate increment of iteration numbers. To reduce the number of iterations, we derive new effective sufficient conditions on the optimality of decoded codewords.