  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.
