A VLSI architecture for interpolation in soft-decision list decoding of Reed-Solomon codes

Abstract

The Koetter-Vardy algorithm is an algebraic soft-decision decoder for Reed-Solomon codes which is based on the Guruswami-Sudan list decoder. There are three main steps: 1) multiplicity calculation, 2) interpolation and 3) root finding. The Koetter-Vardy algorithm is challenging to implement due to the high cost of interpolation. We propose a VLSI architecture for interpolation that uses a transformation of the received word to reduce the number of iterations of the interpolation algorithm. We also show how the memory requirements can be reduced and an important operation, the Hasse derivative, can be efficiently implemented in VLSI.