Efficient Generalized Minimum-distance Decoders of Reed-Solomon Codes

Generalized minimum distance (GMD) decoding of Reed–Solomon (RS) codes can correct more errors than conventional hard-decision decoding by running error-and-erasure decoding multiple times for different erasure patterns. The latency of the GMD decoding can be reduced by the Kötter’s one-pass decoding scheme. This scheme first carries out an error-only hard-decision decoding. Then all pairs of error-erasure locators and evaluators are derived iteratively in one run based on the result of the error-only decoding. In this paper, a more efficient interpolation-based one-pass GMD decoding scheme is studied. Applying the re-encoding and coordinate transformation, the result of erasure-only decoding can be directly derived. Then the locator and evaluator pairs for other erasure patterns are generated iteratively by applying interpolation. A simplified polynomial selection scheme is proposed to pass only one pair of locator and evaluator to successive decoding steps and a low-complexity parallel Chien search architecture is developed to implement this selection scheme. With the proposed polynomial selection architecture, the interpolation can run at the full speed to greatly increase the throughput. After efficient architectures and effective optimizations are employed, a generalized hardware complexity analysis is provided for the proposed interpolation-based decoder. For a (255, 239) RS code, the high-speed interpolation-based one-pass GMD decoder can achieve 53% higher throughput than the Kötter’s decoder with slightly more hardware requirement. In terms of speed-over-area ratio, our design is 51% more efficient. In addition, compared to other soft-decision decoders, the high-speed interpolation-based GMD decoder can achieve better performance-complexity tradeoff.