Open Access

Multirate Filter Bank Representations of RS and BCH Codes

EURASIP Journal on Wireless Communications and Networking20082008:478253

DOI: 10.1155/2008/478253

Received: 20 December 2007

Accepted: 12 September 2008

Published: 10 November 2008


This paper addresses the use of multirate filter banks in the context of error-correction coding. An in-depth study of these filter banks is presented, motivated by earlier results and applications based on the filter bank representation of Reed-Solomon (RS) codes, such as Soft-In Soft-Out RS-decoding or RS-OFDM. The specific structure of the filter banks (critical subsampling) is an important aspect in these applications. The goal of the paper is twofold. First, the filter bank representation of RS codes is now explained based on polynomial descriptions. This approach allows us to gain new insight in the correspondence between RS codes and filter banks. More specifically, it allows us to show that the inherent periodically time-varying character of a critically subsampled filter bank matches remarkably well with the cyclic properties of RS codes. Secondly, an extension of these techniques toward the more general class of BCH codes is presented. It is demonstrated that a BCH code can be decomposed into a sum of critically subsampled filter banks.

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Authors’ Affiliations

Deptartment of Electrical Engineering, Faculty of Engineering, ESAT, Katholieke Universiteit Leuven


© G. Van Meerbergen and M. Moonen. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.