The Capacity Region of the Symbol-Asynchronous Gaussian Multiple-Access Channel

In the information theory of the multiple-access channel, two types of synchronism are usually assumed among the transmitters, namely, frame and symbol synchronism. Frame synchronism refers to the ability of the users to start the transmission of their codewords in unison. The issue of symbol synchronism arises in continuous-time channels in which each codeword symbol modulates a fixed assigned waveform; the channel is symbol synchronous if the users cooperate so that their symbol epochs coincide at the receiver. In practice symbol synchronism is harder to achieve, yet the only reported progress so far has been in the removal of the assumption of frame synchronism. It is shown that if the transmitters are assigned the same waveform, symbol asynchronism has no effect on the two-user capacity region of the white Gaussian channel which is equal to the Cover-Wyner pentagon, whereas if the assigned waveforms are different (e.g., code division multiple access), the symbol-asynchronous capacity region is no longer a pentagon.