Waiting time distributions for pattern occurrence in a constrained sequence

Valeri Stefanov, W. Szpankowski

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    7 Citations (Web of Science)


    A binary sequence of zeros and ones is called a (d, k)-sequence if it does not contain runs of zeros of length either less than d or greater than k, where d and k are arbitrary, but fixed, non-negative integers and d < k : Such sequences find an abundance of applications in communications, in particular for magnetic and optical recording. Occasionally, one requires that (d, k)-sequences do not contain a specific pattern w. Therefore, distribution results concerning pattern occurrence in (d, k)-sequences are of interest. In this paper we study the distribution of the waiting time until the r-th occurrence of a pattern w in a random (d, k)-sequence generated by a Markov source. Numerical examples are also provided.
    Original languageEnglish
    Pages (from-to)305-320
    JournalDiscrete Mathematics and Theoretical Computer Science
    Issue number1
    Publication statusPublished - 2007


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