  With the emergence of machine-driven communi- cation, there is a renewed
interest in the design of random multiple access schemes for networks with
large number of active devices. Many of the recently proposed access paradigms
are enhancements to slotted ALOHA. One of the popular schemes, irregular
repetition slotted ALOHA (IRSA), is based on an analogy between multiple access
with successive interference cancellation and message-passing decoding on
bipartite graphs. Most of the results on IRSA and its variants focus on the
collision channel and they ignore physical limitations such as transmit power
constraints and additive Gaussian noise at the physical layer. As such, naive
extensions of IRSA to the Gaussian multiple access channel are not power
efficient in the low signal-to-noise- ratio regime. This work introduces a
novel paradigm whereby devices adapt their rates and/or transmit powers based
on their chosen repetition profiles. The receiver performs maximal ratio
combining over all the replicas prior to decoding a message. Numerical results
for finite number of users show that the proposed scheme can provide
substantial improvements in terms of power efficiency and average rate over
standard IRSA.
