Information-theoretic View to the Lower Bound of Mean Frame Synchronisation Time

The aim of the synchronisation process is to obtain sufficient amount of information to determine the exact position of the frame beginning within the received stream of bits. The redundancy, inherent to the received data or intentionally inserted for synchronisation purposes, is the source of this information. The aim of this paper is to connect the redundancy to the lower bound of the mean frame (or word) synchronisation time. Implemented is an approach analogous to the one in the classical Shannon's paper considering the maximum amount of text necessary to break a simple substitution cipher. An effort is made to include the influence of the channel errors and some illustrative simple examples are presented.