Asynchronous Communication: Exact Synchronization, Universality, and Dispersion

Abstract

Recently, Tchamkerten and coworkers proposed a novel variation of the problem of joint synchronization and error correction. This paper considers a strengthened formulation that requires the decoder to estimate both the message and the location of the codeword exactly. Such a scheme allows for transmitting data bits in the synchronization phase of the communication, thereby improving bandwidth and energy efficiencies. It is shown that the capacity region remains unchanged under the exact synchronization requirement. Furthermore, asynchronous capacity can be achieved by universal (channel independent) codes. Comparisons with earlier results on another (delay compensated) definition of rate are made. 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. For the binary symmetric channel, a translation (coset) of a good linear code is shown to achieve the capacity-synchronization tradeoff.