Self-synchronizable codes for asynchronous communication

We introduce the asynchronous channel as a model for a continuous time asynchronous communication system. The asynchronous channel can be used as a model for information storage systems such as magnetic recording systems and CD players, or communication systems in which the transmitter and the receiver have no common clock. Let S(t) and V(t) be the input signal and the output signal of the channel respectively, which are related by V(t)=S(τ), where τ(t)=∫₀^t r(u)du and r(u) is a positive function of u, u≥0. We assume that S(0)=V(0), i.e., the input and the output are synchronized to start with. The asynchronous channel is noiseless in the sense that it only compresses or stretches the input signal in the time domain without changing its values. In our model, we assume that S(t) is a step function which takes values from a finite alphabet χ={0, 1, 2,..., p-1}. An interval on which S(t) takes a constant value is called a run, and the lengths of runs are called runlengths.