On the Average Complexity of Reed–Solomon List Decoders

The number of monomials required to interpolate a received word in an algebraic list decoder for Reed-Solomon codes depends on the instantaneous channel error, and not only on the decoder design parameters. The implications of this fact are that the decoder should be able to exhibit lower decoding complexity for low-weight errors and, consequently, enjoy a better average-case decoding complexity and a higher decoding throughput. On the analytical side, this paper studies the dependence of interpolation costs on instantaneous errors, in both hard- and soft-decision decoders. On the algorithmic side, it provides an efficient interpolation algorithm, based on the state-of-the-art interpolation algorithm, that enjoys reduced running times for reduced interpolation costs.