NDLI: Fast Chase Decoding Algorithms and Architectures for Reed

Content Provider	IEEE Xplore Digital Library
Author	Yingquan Wu
Copyright Year	1963
Abstract	Chase decoding is a prevalent soft-decision decoding method for algebraic codes where an efficient bounded-distance decoder is available. Essentially, it repeatedly applies bounded-distance decoding upon combinatorially flipping certain least reliable bits (or patterns for nonbinary case). In this paper, we devise a one-pass Chase decoding algorithm of Reed-Solomon codes such that the desired error locator polynomial by flipping an error pattern is obtained in one pass (when operated in parallel) through utilizing the preceding results. This is effectively achieved through cumulative interpolation and linear-feedback-shift-register (LFSR) synthesis techniques. Furthermore, through converting the algorithm into the transform domain, exhaustive root search for each error locator polynomial is circumvented. Computationally, the new algorithm exhibits linear complexity , in attempting to determine a candidate codeword associated with each additionally flipped symbol/pattern; it compares favorably to quadratic complexity by straightforwardly utilizing hard-decision decoding, where and denote the code length and minimum distance, respectively. We also reveal a corrected algorithm for one-pass generalized minimum distance (GMD) decoding for Reed-Solomon codes from Koetter's original work. In addition, we devise a highly efficient one-pass Chase decoding algorithm for binary Bose-Chaudhuri-Hocquenghem (BCH) codes by taking advantage of a key characteristic of the Berlekamp algorithm. Finally, we present a systolic very large-scale integration (VLSI) decoder architecture through slightly compromising the proposed one-pass Chase decoding algorithm. It takes clock cycles to complete one iteration by flipping one error pattern. Both circuit and memory complexities are dictated by the dimension of flipping patterns; in particular, they are independent of the code length or the minimum distance , rendering it highly attractive for various applications.
Sponsorship	IEEE Information Theory Society
Starting Page	109
Ending Page	129
Page Count	21
File Size	8398338
File Format	PDF
ISSN	00189448
Volume Number	58
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Decoding Complexity theory Reed-Solomon codes Reliability Iterative decoding Transforms VLSI scalable architectures Berlekamp–Massey algorithm binary Bose–Chaudhuri–Hocquenghem (BCH) codes cumulative interpolation linear-feedback-shift-register (LFSR) synthesis one-pass Chase decoding algorithms one-pass generalized minimum distance (GMD) decoding transform domain Reed–Solomon codes soft-decision decoding
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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