Probabilistic capacity and optimal coding for asynchronous channel

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 was introduced in [1]. The paper unveiled 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. In this paper, the runlength limited code is shown not to be optimal for this channel model. An upper bound on the rate loss is given for the constraint that the transmitter and receiver clocks cannot be out of synchronization for a fixed maximum time. The probabilistic capacity of the asynchronous channel is determined and the result is used to design an optimal code. The relation between coding in constrained channels and random number generation is also discussed.