Enhancing the Correcting Radius of Interleaved Reed-Solomon Decoding using Syndrome Extension Techniques

Abstract

Reed-Solomon codes have become one of the most popular classes of error correcting codes, since they can be decoded very efficiently up to half their minimum distance using syndrome-based techniques. Modern interpolation-based decoding algorithms like the Sudan algorithm allow for decoding error patterns beyond half the minimum distance in polynomial time. Recently, a syndrome-based decoding algorithm has been proposed, which virtually extends a Reed-Solomon code into an Interleaved Reed-Solomon (IRS) code. This method is competitive to the classical Sudan algorithm. In this paper, a new method for decoding IRS codes is described, which combines the idea of syndrome extension and the idea of collaboratively decoding IRS codes to increase the decoding radius of low-rate IRS codes.