The optimal burst-error correcting capability of the codes generated by ƒ(x) = (xp + 1)(xq + 1)/(x + 1)

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6 Scopus citations

Abstract

Considerable attention has been devoted in the literature to the possible use of f{hook}(X) = (Xp + 1)(Xq + 1)/(X + 1), where (p, q) = 1, as a generator polynomial of burst-correcting cyclic codes, owing to the extremely simple hardware implementation of both encoder and decoder, and the flexibility in choosing suitable codes. The problem of finding a relation among p, q and a certain b, such that the code generated by f{hook}(X) corrects error bursts of length b or less, has been solved in a number of ways. A complete optimal solution is presented here; i.e., it is shown how the maximum possible value of b can be determined when p and q are given. In most cases, the values obtained from the presented solution outperform those known hitherto. For b > 28 and for relatively long blocks, the presented codes are more efficient than the most efficient codes known. The probability is also found of detecting error bursts whose length exceeds the maximum correctable.

Original languageEnglish
Pages (from-to)303-314
Number of pages12
JournalInformation and control
Volume39
Issue number3
DOIs
StatePublished - 1 Jan 1978
Externally publishedYes

ASJC Scopus subject areas

  • General Engineering

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