In this paper, the Voronoi region of the transmitted codeword is employed to improve the sphere bound on the maximum-likelihood decoding (MLD) performance of binary linear block codes over additive white Gaussian noise (AWGN) channels. We obtain the improved sphere bounds both on the frame-error probability and the bit-error probability. With the framework of the sphere bound proposed by Kasami et al., we derive the conditional decoding error probability on the spheres by defining a subset of the Voronoi region of the transmitted codeword, since the Voronoi regions of a binary linear block code govern the decoding error probability analysis over AWGN channels. The proposed bound improves the sphere bound by Kasami et al. and the sphere bound by Herzberg and Poltyrev. The computational complexity of the proposed bound is similar to that of the sphere bound by Kasami et al.

This paper treats weight distributions of the coset leaders of binary linear block codes. We first present a method for computing the weight distribution of the coset leaders of a given code using two tables each of which stores the weights of the coset leaders of a related code of the code. Then, the weight distributions of the coset leaders of the (N,K) Reed-Muller codes, binary primitive BCH codes, and their extended codes with N 128 and 29 N-K 42 that are obtained by using the computing method are given.

In this paper, soft decision decoding of linear block codes based on the reprocessing of several information sets is considered. These information sets are chosen according to the reliability measures of the received symbols and constructed from the most reliable information set, referred to as the most reliable basis. Each information set is then reprocessed by a multi-stage decoding algorithm until either the optimum error performance, or a desired level of error performance is achieved. General guidelines for the trade-offs between the number of information sets to be processed, the number of computations for reprocessing each information set, and the error performance to be achieved are provided. It is shown that with a proper selection of few information sets, low-complexity near-optimum soft decision decoding of relatively long block codes (64 N 128) can be achieved with significant reduction in computation complexity with respect to other known algorithms. This scheme, which generalizes the reprocessing of the most reliable basis with the ordered statistic algorithm proposed by Fossorier and Lin, is particularly efficient for codes with rate R 1/2.