Calculating the expected synchronisation delay for T-code sets

When variable-length encoding is used over a noisy communications channel, synchronisation problems typically arise following any sort of error. T-codes have been noted for their inherent self-synchronising behaviour following such a loss of synchronisation. Given a code set and associated source symbol probabilities, one measure of synchronisation performance is the expected synchronisation delay (ESD). The authors present a new analytic method for calculating the ESD for an arbitrary T-code set and associated information source. The method more closely reflects the construction of T-code sets than the earlier symbol-oriented asymptotic calculation of Titchener (1986), and yields better precision than Monte Carlo simulations, which have been typically used with large sets. The new algorithm further accommodates the generalised T-augmentation construction of Titchener (see IEE Proc. E, Digit Tech., vol.143, no.3, p.122-8, 1996)