Computing the probability of undetected error for shortened cyclic codes

TitleComputing the probability of undetected error for shortened cyclic codes
Publication TypeJournal Article
Year of Publication1992
AuthorsAgarwal, V. K., and A. Ivanov
JournalCommunications, IEEE Transactions on
Volume40
Pagination494 -499
Date Publishedmar.
ISSN0090-6778
Keywordsbit error probabilities, burst errors, channels, code block length, code generator polynomials, error detection codes, linear block codes, probability, recursive method, shortened cyclic codes, telecommunication channels, time complexity
Abstract

The authors present a general technique for computing P e for all possible shortened versions of cyclic codes generated by any given polynomial. The technique is recursive, i.e. computes Pe for a given code block length n from that of the code block length n-1. The proposed computation technique for determining Pe does not require knowledge of the code weight distributions. For a generator polynomial of degree r, and |g| nonzero coefficients, the technique yields Pe for all code block lengths up to length n in time complexity O(n|g |2r+|g|). Channels with variable bit error probabilities can be analyzed with the same complexity. This enables the performance of the code generator polynomials to be analyzed for burst errors

URLhttp://dx.doi.org/10.1109/26.135719
DOI10.1109/26.135719

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