In this paper two symbol-level soft-decision decoding algorithms for Reed-Solomon codes, derived form the ordered statistics (OS) and from the generalized minimum-distance (GMD) decoding methods, are presented and analyzed. Both the OS and the GMD algorithms are based on the idea of producing a list of candidate code words, among which the one having the larger likelihood is selected as output. We propose variants of the mentioned algorithms that allow to finely tune the size of the list in order to obtain the desired decoding complexity. The method proposed by Agrawal and Vardy for computing the error probability of the GMD algorithm is extended to our decoding methods. Examples are presented where these algorithms are applied to singly-extended Reed-Solomon codes over GF(16) used as outer codes in a 128-dimensional coded modulation scheme that attains good performance, with manageable decoding complexity.

The authors present a method for computing the probability of undetected error for hybrid ARQ over the Gilbert-Elliott channel (Gilbert, E.N., Bell Syst. Tech. J., vol.39, p.1253-65, 1960; Elliott, E.O., Bell Syst. Tech. J., vol.42, p.1977-97, 1963). The method described by Elliott is extended to the case where the code is used for error detection and error correction simultaneously (hybrid ARQ, type-I). This analytical approach to the evaluation of the probability of undetected error allows the throughput to be calculated as a function of the code rate and length, and systems to be designed that maximize the throughput, given the channel parameters and the desired undetected error probability.

This correspondence presents performance analysis of symbol-level soft-decision decoding of q-ary maximum-distance-separable (MDS) codes based on the ordered statistics algorithm. The method we present is inspired by the one recently proposed by Agrawal and Vardy (2000), who approximately evaluate the performance of generalized minimum-distance decoding. The correspondence shows that in our context, the method allows us to compute the exact value of the probability that the transmitted codeword is not one of the candidate codewords. This leads to a close upper bound on the performance of the decoding algorithm. Application of the ordered statistics algorithm to MDS codes is not new. Nevertheless, its advantages seem not to be fully explored. We show an example where the decoding algorithm is applied to singly extended 16-ary Reed-Solomon (RS) codes in a 128-dimensional multilevel coded-modulation scheme that approaches the sphere lower bound within 0.5 dB at the word error probability of 10/sup -4/ with manageable decoding complexity.

The authors propose and analyze a reduced complexity ordered statistics decoding algorithm for maximum-distance separable (MDS) codes. The proposed algorithm provides a high degree of flexibility in the maximum number of candidate code words tested by the algorithm which yields different trade-offs between complexity and performance between orders of reprocessing. An upper bound to the error probability is calculated by extending the method proposed by D. Agrawal and A.Vardy (IEEE Trans. Inf. Theory, vol.46, p.60-83, 2000) for generalized-minimum-distance decoding. We present an application to singly-extended Reed-Solomon codes over GF(16) in a 128-dimensional multilevel coded modulation scheme that approaches the sphere lower bound within about 0.5 dB for a word error rate of 10/sup -4/ with manageable decoding complexity.

The authors describe a multilevel coded modulation scheme that has been designed for being implemented on FPGA. The goal of the design is to obtain good performance while keeping decoding delay and computational complexity as low as possible. This goal is obtained by a two-level scheme, where the partition chain of the 8-dimensional Gosset lattice is associated to a combination of 16-ary convolutional and block codes, at the first and second level respectively. The motivations behind the design choices are illustrated and the implementation on FPGA is presented. The authors conclude by analyzing the performance of the system and by showing experimental results.