Variable-length coding for short packets over a multiple access channel with feedback

We consider a two-user discrete memoryless multiple access channel with a common stop-feedback signal from the receiver to both transmitters. The achievable regions are characterized using joint decoding and successive cancellation decoding and, it is shown that the achievable regions are significantly larger for variable-length stop-feedback codes compared to fixed-blocklength codes. This is analogous to the result by Polyanskiy et al. (2011) for the point-to-point channel. An important conclusion is the following. In the asymptotic case the capacity region can be achieved by joint decoding, but also by successive cancellation decoding and time-sharing. For the case of finite blocklength, joint decoding performs significantly better than successive cancellation decoding, even when aiming for the corners of the achievable regions.