Towards the goal of achieving better error correction performance in data storage systems, iterative soft decoding of low density parity check (LDPC) codes and soft-decision decoding of Reed-Solomon (RS) codes have started receiving increasing research attention. However, even with increased computing power, complexities of soft-decision decoding algorithms are still too high for real products which require high throughput and small hardware area. Another problem is that the performance gains of those approaches are smaller for magnetic recording channels than they are for memoryless additive white Gaussian noise (AWGN) channels. We propose a new soft-decision decoding algorithm (based on the Chase algorithm), which takes advantage of pattern reliability instead of symbol reliability or bit reliability. We also present a modified Viterbi algorithm that provides probable error patterns with corresponding reliabilities. Simulation results of the proposed algorithms over the partial response (PR) channel show attractive performance gains. The proposed algorithm dramatically reduces the number of iterations compared to the conventional Chase2 algorithm over the PR channel.

We propose a soft-decision decoding algorithm of Reed-Solomon (RS) codes using successive error-and-erasure decoding. Extensive simulations are conducted to show the possible performance gain of the proposed method. We derive a formula for performance estimation based on ordered statistics of symbol reliability, which matches well with the results of the simulation. The proposed method with almost the same average complexity as a conventional hard-decision decoder outperforms Koetter-Vardy (KV) algorithm and Chase2-GMD algorithm (CGA).

Reed-Solomon (RS) codes are defined in several different ways which are not exactly equivalent. Distinct algorithms for encoding and decoding of RS codes have been developed based on the different definitions. This paper clarifies the relationships among the several definitions of RS codes, especially focusing on the connection between non-binary BCH codes, which are not necessarily narrow-sense, and Generalized Reed- Solomon (GRS) codes. With the relationships, we introduce code space conversion which converts objects of a GRS code into corresponding objects of another GRS code with the same dimension. This transformation can be used for the flexible application of the decoder designed for a specific RS code. We show that the interpolation-based soft-decision RS decoders can be applied to non narrow-sense RS codes using code space conversion.