Reduced-complexity multi-interpolator algebraic soft-decision Reed-Solomon decoder

Abstract

Algebraic soft-decision decoding (ASD) of Reed-Solomon (RS) codes can achieve significant coding gain with polynomial complexity. Among ASD algorithms, the low-complexity Chase (LCC) algorithm can achieve better performance-complexity tradeoff. This algorithm tests 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">η</sup> vectors, and larger η leads to higher coding gain. One major step of the LCC decoding is the interpolation, and its latency grows exponentially with η. To reduce the latency, multiple interpolators can be used to test the vectors in parallel. However, they lead to large area requirement. This paper proposes to interpolate over the points in the test vectors in a different order. By making use of the properties of the interpolation points in the rearranged order, novel schemes are developed to simplify and share computations among the interpolators. From complexity analysis, the proposed interpolation scheme can achieve higher speed and reduce the area requirement by 30% for a (255, 239) RS code with η = 5 when 4-parallel interpolation is employed. The proposed interpolation architecture is incorporated into the LCC decoder and further optimizations are carried out. For the same RS code, the proposed decoder can achieve 16% speedup with 11% less area than the previous design.