Analysis of the synchronization properties of the t-codes

Abstract

The desirable synchronization properties of the T-Codes have been well documented ever since they were first reported [Titchener 1984]. Different T-Codes exhibit different levels of synchronization performance, even if they come from the same subgroup. The average synchronization delay (ASD) is a measure of synchronization performance. A theoretical method for calculating such delays was developed by Higgie [Higgie 1992], However, computational efficiency of the established theoretical algorithm could be improved, notably when suffix conditions are encountered during the decoding process. This thesis documents approaches which aim to improve that algorithm. Two main approaches were adopted. The first involved the consideration of power series in the context of solving sums in Higgie’s algorithm. The second was a tree algorithm developed to concisely and systematically characterize all the important bit sequences, ignoring the vast majority of all possible bit sequences. This algorithm has been implemented to produce ASD values which match the results obtained using the original method at much improved computational speeds. With this new method, computational efficiency has been improved by reducing the average time required per code set. It produces ASD results in approximately half the time required by the original method to generate comparable results.