Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix

TL;DR

This paper introduces an iterative SISO decoding algorithm for Reed-Solomon codes that adapts the parity check matrix to improve convergence and performance, outperforming traditional hard decision decoding.

Contribution

The novel approach reduces a submatrix of the parity check matrix to a sparse form for each iteration, enhancing decoding efficiency and accuracy.

Findings

Significant gain over hard decision decoding

Favorable comparison with other soft decision methods

Adaptive matrix reduction improves convergence

Abstract

An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS code. The novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the SPA is applied at each iteration. The proposed algorithm can be geometrically interpreted as a two-stage gradient descent with an adaptive potential function. This adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and, therefore, significantly improves the performance. Simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding (HDD) and compare favorably with other popular soft decision decoding methods.