Applications of Algebraic Soft-Decision Decoding of Reed–Solomon Codes

Abstract

Efficient soft-decision decoding of Reed–Solomon codes is made possible by the Koetter–Vardy (KV) algorithm which consists of a front-end to the interpolation-based Guruswami–Sudan list decoding algorithm. This paper approaches the soft-decision KV algorithm from the point of view of a communications systems designer who wants to know what benefits the algorithm can give, and how the extra complexity introduced by soft decoding can be managed at the systems level. We show how to reduce the computational complexity and memory requirements of the soft-decision front-end. Applications to wireless communications over Rayleigh fading channels and magnetic recording channels are proposed. For a high-rate (RS 9225,239) Reed–Solomon code, 2–3 dB of soft-decision gain is possible over a Rayleigh fading channel using 16-quadrature amplitude modulation. For shorter codes and at lower rates, the gain can be as large as 9 dB. To lower the complexity of decoding on the systems level, the redecoding architecture is explored which uses only the appropriate amount of complexity to decode each packet. An error-detection criterion based on the properties of the KV decoder is proposed for the redecoding architecture. Queuing analysis verifies the practicality of the redecoding architecture by showing that only a modestly sized RAM buffer is required.