On the capacity region of asynchronous channels

We consider asynchronous communication over discrete memoryless channels. The transmitter starts sending one block codeword of length N at an instant that is uniformly distributed within a certain time period A, which represents the level of asynchronism between the transmitter and the receiver. The receiver, by means of a sequential decoder, must isolate the message without knowing when the codeword transmission starts but being cognizant of the asynchronism level. Motivated by certain monitoring type of applications, we are interested in communication strategies that 1) operate with short codeword length with respect to the asynchronism level and 2) that guarantee quick decoding. In a recent work the authors showed that the communication rate - defined with respect to the decoder's reaction delay to the sent message - can be strictly positive unless A grows faster than e^Nα and α exceeding the synchronization threshold. The present work focuses on the regime where α is smaller than the synchronization threshold. The main contribution consists of simple expressions that give upper and lower bounds on the highest achievable rate for any α below the synchronization threshold. For random code constructions these bounds are tight.