Abstract :

We introduce the continuous time asynchronous channel as a model for time jitter in a communication system with no common clock between the transmitter and the receiver. We have obtained a simple characterization for an optimal zero-error self-synchronizable code for the asynchronous channel. The capacity of this channel is determined by both a combinatorial approach and a probabilistic approach. Our results unveil the somewhat surprising fact that it is not necessary for the receiver clock to re-synchronize with the transmitter clock within a fixed maximum time in order to achieve reliable communication. This means that no upper limit should be imposed on the runlengths of the self-synchronization code as in the case of runlength limited (RLL) codes which are commonly used in magnetic recording.