%0 Journal Article
%T Waiting Time Distributions for Pattern Occurrence in a Constrained Sequence
%A Valeri Stefanov
%A Wojciech Szpankowski
%J Discrete Mathematics & Theoretical Computer Science
%D 2007
%I Discrete Mathematics & Theoretical Computer Science
%X 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.
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/635