On asynchronous capacity and dispersion

Recently Tchamkerten et al. proposed a mathematical formulation of the problem of joint synchronization and error-correction in noisy channels. A variation of their formulation in this paper considers a strengthened requirement that the decoder estimate both the message and the location of the codeword exactly. It is shown that the capacity region remains unchanged and that the strong converse holds. The finite blocklength regime is investigated and it is demonstrated that even for moderate blocklengths, it is possible to construct capacity-achieving codes that tolerate exponential level of asynchronism and experience only a rather small loss in rate compared to the perfectly synchronized setting; in particular, the channel dispersion does not suffer any degradation due to asynchronism.