THE REDUNDANCY OF A SIMPLE SYNCHRONIZATION METHOD FOR VARIABLE LENGTH CODES

Abstract

Prefix insertion prior to the coded representation of every fixed length block of data provides a simple synchronization method for variable length coding. Unlike fixed length coding where the prefix appears with a set period, the appearance time of each prefix word in the variable length coded representation is a random variable. At the receiver a synchronization decision is made whenever a pattern within a threshold Hamming distance of the prefix is received. In this paper an expression is found for small synchronization error probabilities. This egression depends on the coded block length only through its average value L. The optimal value for the recognition threshold is found. The necessary and sufficient condition for an arbitrarily small synchronization error probability is shown to be that the prefix length grows as log L. The results are discussed from the viewpoint of data compression and source encoding.