NDLI: Algebraic Decoding of a Class of Binary Cyclic Codes Via Lagrange Interpolation Formula

Content Provider	IEEE Xplore Digital Library
Author	Yaotsu Chang Chong-Dao Lee
Copyright Year	1963
Abstract	In this paper, three algebraic decoding algorithms are proposed for the binary quadratic residue (QR) codes generated by irreducible polynomials. The polynomial relations among the syndromes and the coefficients of the error-locator polynomials have been computed with Lagrange interpolation formula (LIF). Unlike some previous QR decoders, which may take several iterations to decode a corrupted word, the iteration number of the first two algorithms is at most one. The processes in the first algorithm are the calculation of consecutive syndromes, inverse-free Berlekamp-Massey algorithm (IFBMA), and the Chien search. One of Orsini-Sala's results on the structure of general error-locator polynomials is generalized and applied to derive the second (respectively, third) algorithm that consists of the determination of general error-locator polynomial (respectively, classical error-locator polynomials) and the Chien search. Finally, the (17, 9, 5), (23, 12, 7), and (41, 21, 9) QR decoders are illustrated and their complexity analyses are given.
Sponsorship	IEEE Information Theory Society
Starting Page	130
Ending Page	139
Page Count	10
File Size	466793
File Format	PDF
ISSN	00189448
Volume Number	56
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Lagrangian functions Interpolation Polynomials Iterative decoding Error correction codes Instruction sets Councils Mathematics Error correction syndrome Decoding algorithm general error-locator polynomial Lagrange interpolation formula (LIF) quadratic residue (QR) code
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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