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DMTCS
2007

Waiting Time Distributions for Pattern Occurrence in a Constrained Sequence

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Waiting Time Distributions for Pattern Occurrence in a Constrained Sequence
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.
Valery T. Stefanov, Wojciech Szpankowski
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where DMTCS
Authors Valery T. Stefanov, Wojciech Szpankowski
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