Soft-decision Reed-Solomon decoding on partial response channels

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Abstract
We compare the performance of list-type soft-decision Reed-Solomon (RS) decoding algorithms to that of classical hard-decision RS decoding on partial response (PR) channels. The two soft-decision RS decoding approaches that we consider, the list-GMD and the Koetter-Vardy (see Proc. IEEE Int. Symp. Information Theory, (Sorrento, Italy), IEEE, June 2000) algorithm, are both based on Sudan's (1997) (polynomial) interpolation approach to polynomial-time list-decoding. The soft-decision RS decoders take as input symbol-based reliabilities which can be provided by a symbol-based BCJR algorithm. The symbol-based BCJR algorithm is an extension of the original BCJR algorithm and calculates the a posteriori probability (APP) of a block of l-bits. The complexity of the algorithm can be reduced when applied to a PR channel. We present a hybrid Viterbi-BCJR approach that can be used when only the reliability of the most-likely symbol is desired. The hybrid approach calculates the APP of the most reliable symbol without the need to run the complete forward and backward algorithm. We demonstrate through simulations that soft-decision RS decoding will lead to a lower probability of decoding error. Moreover, we show that using the symbol-based APPs will yield a lower symbol error rate (SER) than using the measures obtained by multiplying the bit reliabilities.

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