On soft-decision iterative algebraic decoding algorithms for non-binary codes

摘要

In this paper, we consider an iterative decoding algorithm by using algebraic decoding for non-binary codes. In the decoding algorithms, algebraic decodings are carried out with respect to successively chosen input words, called the search centers. The search center is the sum of the hard-decision sequence of received sequence and a chosen perturbation, called an error pattern. In conventional iterative decoding algorithms, such as GMD decoding, Chase II decoding algorithms and combining Chase II and GMD decoding algorithms (CGA), the generating methods of error patterns are quite simple. This fact is a cause for being unable to achieve good error performance with a relatively small iteration number of algebraic decodings. We present a new method for selecting sequences of error patterns for search centers of algebraic decoding in the iterative decoding algorithm by using an algebraic decoding for non-binary codes. The proposed method is more complicated. However, since a sequence of error patterns is generated beforehand for a given range of signal to noise ratios, the additional decoding complexity per iteration is to access a small read-only memory once. Over the AWGN channel using BPSK signaling, we show simulation results on the error performances of the iterative decoding algorithms whose search centers are given by the proposed method for Reed-Solomon codes. From the simulation results, the iterative decoding algorithm by the proposed method provides considerably better error performance than GMD and CGA decoding with the same number of iterations.