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On synchronizable and PSK-synchronizable block codes | IEEE Journals & Magazine | IEEE Xplore
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On synchronizable and PSK-synchronizable block codes


Abstract:

A (finite) code is called synchronizable ofMth order if, and only if, there exists a least positive integerMsuch that the knowledge of the lastMletters of any message suf...Show More

Abstract:

A (finite) code is called synchronizable ofMth order if, and only if, there exists a least positive integerMsuch that the knowledge of the lastMletters of any message suffices to determine a separation of code words. This condition is less constraining than the comma-free restriction. Sections I-IV is a description of a way of selecting a synchronizable block codeC_{\sigma , n}for a given alphabet with\deltaletters and a given code-word length n. It is proved thatC_{\sigma , n}is maximal in the sense that it contains as many words as possible; and an expression is given for the number of words inC_{\sigma , n}.^{1}Sections V-VIII is a description of a construction of phase-shift-keying synchronizable codes. In the PSK case the letters themselves cannot be identified by the receiver. Only the differences between successive letters can be detected. Thus, if the sequenceX_{1},X_{2}, \cdots , X_{l}is transmitted, then the observed sequence in the receiver isX_{2} - X_{1}, X_{3}- X_{2}, \cdots , X_{i+1}- X_{i}, \cdots , X_{l} - X_{l-1}. The letters are assumed to be the integers mod\delta; andX_{i+1} - X_{i}is taken mod\delta. This situation occurs in the reading of phase-modulated signals. The construction of these codes (calledK_{\sigma , n}) is based onC_{\sigma , n}.
Published in: IEEE Transactions on Information Theory ( Volume: 10, Issue: 4, October 1964)
Page(s): 351 - 356
Date of Publication: 06 January 2003

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