Fast Chase Decoding Algorithms and Architectures for Reed-Solomon Codes

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 p...

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Veröffentlicht in:IEEE transactions on information theory Jg. 58; H. 1; S. 109 - 129
1. Verfasser: Wu, Yingquan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.01.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algebra
Algorithms
Applied sciences
Architecture
Berlekamp-Massey algorithm
binary Bose-Chaudhuri-Hocquenghem (BCH) codes
Coding, codes
Complexity
Complexity theory
cumulative interpolation
Decoders
Decoding
Errors
Exact sciences and technology
Information theory
Information, signal and communications theory
Iterative decoding
linear-feedback-shift-register (LFSR) synthesis
Locators
one-pass Chase decoding algorithms
one-pass generalized minimum distance (GMD) decoding
Polynomials
Reed-Solomon codes
Reliability
Signal and communications theory
soft-decision decoding
Telecommunications and information theory
transform domain
Transforms
VLSI scalable architectures
Berlekamp-Massey algorithm
Scalability
transform domain
Feedback regulation
Iterative method
Clock
Reed-Solomon codes
Locator
VLSI scalable architectures
linear-feedback-shift-register (LFSR) synthesis
Algorithm complexity
Linear complexity
Minimal distance
BCH code
Fast algorithm
Soft decision
Reed Solomon code
cumulative interpolation
Algebraic code
Berlekamp Massey algorithm
Decoding
Circuit architecture
Interpolation
Shift register
one-pass Chase decoding algorithms
binary Bose-Chaudhuri-Hocquenghem (BCH) codes
soft-decision decoding
one-pass generalized minimum distance (GMD) decoding
ISSN:0018-9448, 1557-9654
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Zusammenfassung: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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2165524