Efficient architecture for generalized minimum-distance decoder 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. In addition, a simplified polynomial selection scheme is proposed to pass only one pair of locator and evaluator to succesive decoding steps. Efficient architectures are employed for the interpolation-based GMD decoder and detailed analysis is provided for the area requirement and decoding latency. With 15% less hardware requirement, the interpolation-based one-pass GMD decoder can reduce the decoding latency to 96% of the Kötter´s decoder for a (255, 239) RS code. In terms of speed-over-area ratio, our design is 22% more efficient.