NDLI: Filterbank Decompositions for (Non)-Systematic Reed–Solomon Codes With Applications to Soft Decoding

Content Provider	IEEE Xplore Digital Library
Author	Van Meerbergen, G. Moonen, M. De Man, H.
Copyright Year	1991
Abstract	This paper focuses on Reed-Solomon (RS) codes, which are the most widespread classical error correcting codes. Recently, we have shown that an finite-impulse response (FIR) critically subsampled filterbank representation can be derived for some RS codes. However, this work only addresses RS codes with a non-coprime codeword and dataword length, seriously limiting its practical usability. In this paper, an alternative purely algebraic method is presented to construct such a filterbank. Apart from providing additional insight into the algebraic structure of (non-systematic) RS codes, this method is suited to eliminate the non-coprimeness constraint mentioned before. Using this filterbank decomposition, a RS code is broken into smaller subcodes that can subsequently be used to build a soft-in soft-out (SISO) RS decoder. It is shown how any RS code, written as an FIR filterbank, can be SISO decoded using the filterbank based decoder. Owing to the importance of systematic RS codes, it is shown that any systematic RS code can be decoded using the FIR filterbank decomposition. This leads to better decoding performance in addition with a slightly lower complexity. A further extension towards systematic RS codes is also presented in this paper resulting in an infinite-impulse response critically subsampled filterbank representation.
Sponsorship	IEEE Signal Processing Society
Starting Page	5681
Ending Page	5694
Page Count	14
File Size	1371616
File Format	PDF
ISSN	1053587X
Volume Number	55
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Filter bank Decoding Finite impulse response filter Redundancy Error correction codes Laboratories OFDM modulation Error correction Usability Source coding soft-in soft-out (SISO) decoding Critical subsampling filterbanks Reed–Solomon (RS) codes
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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