Soft Decision Decoding of Reed Solomon Codes

Abstract

Reed Solomon codes form a well known family of multilevel cyclic block codes which meet the Singleton bound. As random symbol error correcting codes they are particularly useful in conditions where errors occur in bursts. For the AWGN channel, however, they suffer relative to other codes such as convolutional codes, at least at moderate bit error rates (around 10⁻⁵ to 10⁻⁶). Much of this disadvantage results from the lack of a generally applicable method for soft decision decoding.

This paper reports on progress in applying soft decision decoding to Reed Solomon codes. Any algebraic approach to soft decision decoding must address a number of problems such as the relationship of the soft decision values to the field over which the code is defined, the calculation of Euclidean distances and the provision of an algorithm to find the maximum likelihood codeword. In this paper it is proposed that the algebraic problems may be eased by defining the code as a subfield subcode of a code defined over a larger field and by a specially devised mapping of symbol values onto detected bit values. In the absence of any known algorithm, the performance of soft decision decoded RS codes has been studied by the application of trellis decoding methods. Viterbi decoding has been used to limit the complexity of trellis decoding and the performance of a reduced search method has been assessed. It has been found that useful coding gains can be achieved at moderate bit error rates from (15, 13) and (15, 11) codes, using a method in which only the best B paths are updated at each incoming symbol, with B having values of 16 or 32.