NDLI: New Scalable Decoder Architectures for Reed

Content Provider	IEEE Xplore Digital Library
Author	Yingquan Wu
Copyright Year	1972
Abstract	In this paper, we devise new scalable decoder architectures for Reed-Solomon (RS) codes, comprising three parts: error-only decoding, error-erasure decoding, and their decoding for singly extended RS codes. New error-only decoders are devised through algorithmic transformations of the inversionless Berlekamp-Massey algorithm (IBMA). We first generalize the Horiguchi-Koetter formula to evaluate error magnitudes using the error locator polynomial Λ(x) and the auxiliary polynomial B(x) produced by IBMA, which effectively eliminates the computation of error evaluator polynomial. We next devise an enhanced parallel inversionless Berlekamp-Massey algorithm (ePIBMA) that effectively takes advantage of the generalized Horiguchi-Koetter formula. The derivative ePIBMA architecture requires only 2t + 1 (t denotes the error correction capability) systolic cells, in contrast with 3t or more cells of the existing regular architectures based on IBMA or the Euclidean algorithm. Moreover, it may literally function as a linear-feedback-shift-register encoder. New error-erasure decoders are devised through algorithmic transformations of the inversionless Blahut algorithm (IBA). The proposed split parallel inversionless Blahut algorithm (SPIBA) yields merely 2t + 1 systolic cells, which is the same number as the error-only decoder ePIBMA. The task is partitioned into two separate steps, computing the complementary errorerasure evaluator polynomial followed by computing error-erasure locator polynomial, both utilizing SPIBA. Surprisingly, it has exactly the same number of cells and literally the same complexity and throughput as the proposed error-only decoder architecture ePIBMA; it employs 33% less hardware and at the same time achieves more than twice faster throughput, than the serial architecture IBA. we further propose a unified parallel inversionless Blahut algorithm (UPIBA) by incorporating the key virtues of the error-only decoder ePIBMA into SPIBA. The complexity and throughput of the rderivative UPIBA architecture are literally the same as ePIBMA and SPIBA, while performing almost equally efficiently as ePIBMA on error-only decoding and as SPIBA on error-erasure decoding. UPIBA also inherits the dynamic power saving feature of ePIBMA and SPIBA. Indeed, UPIBA renders highly attractive for on-the-fly implementation of error-erasure decoding. We finally demonstrate that the proposed decoders, i.e., ePIBMA, SPIBA, and UPIBA, can be magically migrated to decode singly extended RS codes, with negligible add-ons, except that an extra multiplexer is added to their critical paths. To the author's best knowledge, this is the first time that a high-throughput decoder for singly extended RS codes is explored.
Starting Page	2741
Ending Page	2761
Page Count	21
File Size	920541
File Format	PDF
ISSN	00906778
Volume Number	63
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
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 Computer architecture Heuristic algorithms Complexity theory Delays Hardware unified decoder Reed–Solomon codes singly extended Reed–Solomon codes inversionless Berlekamp-Massey algorithm inversionless Blahut algorithm Horiguchi-Koetter formula high-throughput decoder architecture
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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