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Algebraic properties of BCH codes useful for decoding

Cardoso Da Rocha, Valdemar and Honary, Bahram and Bate, Steve D. (1989) Algebraic properties of BCH codes useful for decoding. International Journal of Satellite Communications, 7 (3). pp. 225-229. ISSN 1099-1247

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Abstract

In this paper theorems are presented which allow the simplified decoding of (n, k, δ) BCH codes in certain cases of practical interest. Such results are in a way implicit in the theory of BCH codes, but so far have not appeared explicitly in the literature. It is shown that any t0 errors, 1 ⩽ t0 ⩽ δ-1, can be detected by using any set of only t0 consecutive coefficients of the syndrome polynomial. The correction of any t0 errors, 1 ⩽ t0 ⩽ [(δ-1)/2], can be performed by using any set of 2t0 consecutive coefficients of the syndrome polynomial, where [x] means the integer part of x. Similar results are derived for punctured BCH codes. In this case sets of t0 or 2t0 consecutive coefficients, respectively, for detecting or correcting t0 errors, are selected from the δ-1-p higher-order coefficients of the modified syndrome polynomial, where p is the number of digits punctured from a code word. These results hold true even when the punctured digits are not consecutive.

Item Type: Article
Journal or Publication Title: International Journal of Satellite Communications
Uncontrolled Keywords: Error detection and correction ; BCH codes ; Decoding ; Punctured codes ; Cyclic codes
Subjects:
Departments: Faculty of Science and Technology > School of Computing & Communications
ID Code: 60809
Deposited By: ep_importer_pure
Deposited On: 18 Dec 2012 16:07
Refereed?: Yes
Published?: Published
Last Modified: 30 Aug 2017 13:56
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/60809

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