Variable Length Coding over the Two-User Multiple-Access Channel

For discrete memoryless multiple-access channels, we propose a general definition of variable length codes with a measure of the transmission rates at the receiver side. This gives a receiver perspective on the multiple-access channel coding problem and allows us to characterize the region of achievable rates when the receiver is able to decode each transmitted message at a different instant of time. We show an outer bound on this region and derive a simple coding scheme that can achieve, in particular settings, all rates within the region delimited by the outer bound. In addition, we propose a random variable length coding scheme that achieve the direct part of the block code capacity region of a multiple-access channel without requiring any agreement between the transmitters.