On the Search for a Sequence from a Predefined Set of Sequences in Random and Framed Data Streams

In this paper we present a statistical analysis of the search for a set of predefined sequences in non-equiprobable data streams, both random and framed, and derive a number of corresponding statistical parameters. Most importantly, we derive the probability of occurrence of some sequence from the set at any given position, from which all other statistical quantities of interest can be obtained. The presented analysis is based on descriptors called cross-bifices, which express similarities among sequences in the set. Based on the obtained results, we examine the problem of frame synchronization in synchronous transmission and derive parameters that could be used for the evaluation of the properties of frame-synchronization sequences. We introduce a survival probability of the search in a frame and a list-miss probability for the list synchronizer, which give exact bounds on the probability of correct frame synchronization when hard-correlation is used as a sequence detection metric.