Algebraic Soft-Decision Decoding of Reed-Solomon Codes with Erasures on Gaussian Channels

E.M.G Fernández,F.R Coutinho

doi:10.14209/jcis.2007.3

Abstract

The search for increasing the error performance of algebraic soft-decision decoding of high rate Reed-Solomon (RS) codes motivates the development of this work in an attempt to determine the ultimate error-correcting capabilities of algebraic soft-decision decoding of RS codes in Gaussian channels with erasures. It is shown through simulation that a significant performance improvement can be obtained when the unreliable bits received from channel output are declared as erased bits. An alternative method to construct the reliability matrix is developed through the mapping of the a posteriori channel probabilities in order to assign equal multiplicity for symbols with the same erased bits patterns. Conversely, it is also shown through simulation that trying to declare the unreliable symbols received from the channel as erasures does not lead to any performance gain and in some cases it would affect the decoder performance.

Highlights

In [9] the decoding radius when using algebraic soft-decisionR EED-SOLOMON codes [1] are among of the most important error correcting codes which are widely employed in many digital communications and data storage systems with applications ranging from digital data storage (CD and DVD), to satellite communication systems
Koetter and Vardy, in [5], In an attempt to improve the performance of algebraic softdecision decoding of finite length, high rate RS codes without increasing the decoding complexity, this paper presents an alternative method for constructing the reliability matrix based on the erasure of unreliable bits by considering them probable
Some background concepts on Reed-Solomon codes and algebraic soft-decision decoding of RS codes that are relevant to this paper are reviewed

Summary

Introduction

In [9] the decoding radius when using algebraic soft-decisionR EED-SOLOMON codes [1] are among of the most important error correcting codes which are widely employed in many digital communications and data storage systems with applications ranging from digital data storage (CD and DVD), to satellite communication systems. In 1999, Guruswami and Sudan showed in [2] how they surpassed the conventional error correction capacity of (n − k)/2 symbols through a polyno√mial-time list decoding algorithm that corrects up to n − nk symbol errors. To achieve this results they thought the decoding process as if it was a problem of constructing a bivariate polynomial that pass through all the points received from the channel with an arbitrary order or multiplicity m.

Methods

Results

Conclusion