Consider a random access communication scenario over a channel whose
operation is defined for any number of possible transmitters. Inspired by the
model recently introduced by Polyanskiy for the Multiple Access Channel (MAC)
with a fixed, known number of transmitters, we assume that the channel is
invariant to permutations on its inputs, and that all active transmitters
employ identical encoders. Unlike Polyanskiy, we consider a scenario where
neither the transmitters nor the receiver know which transmitters are active.
We refer to this agnostic communication setup as the Random Access Channel, or
RAC. Scheduled feedback of a finite number of bits is used to synchronize the
transmitters. The decoder is tasked with determining from the channel output
the number of active transmitters (k) and their messages but not which
transmitter sent which message. The decoding procedure occurs at a time nt
depending on the decoder's estimate t of the number of active transmitters,
k, thereby achieving a rate that varies with the number of active
transmitters. Single-bit feedback at each time ni,i≤t, enables all
transmitters to determine the end of one coding epoch and the start of the
next. The central result of this work demonstrates the achievability on a RAC
of performance that is first-order optimal for the MAC in operation during each
coding epoch. While prior multiple access schemes for a fixed number of
transmitters require 2k−1 simultaneous threshold rules, the proposed
scheme uses a single threshold rule and achieves the same dispersion.Comment: Presented at ISIT18', submitted to IEEE Transactions on Information
Theor