Search Process and Probabilistic Bifix Approach

TL;DR

This paper develops a mathematical framework for analyzing search processes in non-uniform L-ary data, deriving probability distributions and statistical parameters for bifix indicators, with applications beyond telecommunications.

Contribution

It introduces a detailed probabilistic model for search processes and bifix indicators in arbitrary L-ary sequences, extending analysis tools for digital synchronization.

Findings

Derived probability distribution functions for search processes.

Analyzed the probabilistic nature of bifix indicators.

Outlined applications beyond telecommunication fields.

Abstract

An analytical approach to a search process is a mathematical prerequisite for digital synchronization acquisition analysis and optimization. A search is performed for an arbitrary set of sequences within random but not equiprobable L-ary data. This paper derives in detail an expression for probability distribution function, from which other statistical parameters - expected value and variance - can be obtained. The probabilistic nature of (cross-) bifix indicators is shown and application examples are outlined, ranging beyond the usual telecommunication field.