Decoding interleaved Reed---Solomon codes beyond their joint error-correcting capability

Authors:
Antonia Wachter-Zeh;Alexander Zeh;Martin Bossert
Affiliations:
Institute of Communications Engineering, Ulm University, Ulm, Germany 89081 and Institut de recherche mathématique de Rennes (IRMAR), Université de Rennes 1, Rennes, France;Institute of Communications Engineering, Ulm University, Ulm, Germany 89081 and INRIA Saclay-Île-de-France, École Polytechnique ParisTech, Palaiseau Cedex, France;Institute of Communications Engineering, Ulm University, Ulm, Germany 89081
Venue:
Designs, Codes and Cryptography
Year:
2014

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Abstract

A new probabilistic decoding algorithm for low-rate interleaved Reed---Solomon (IRS) codes is presented. This approach increases the error correcting capability of IRS codes compared to other known approaches (e.g. joint decoding) with high probability. It is a generalization of well-known decoding approaches and its complexity is quadratic with the length of the code. Asymptotic parameters of the new approach are calculated and simulation results are shown to illustrate its performance. Moreover, an upper bound on the failure probability is derived.