  Consider a random access communication scenario over a channel whose
operation is defined for any number of possible transmitters. As in the model
recently introduced by Polyanskiy for the Multiple Access Channel (MAC) with a
fixed, known number of transmitters, the channel is assumed to be invariant to
permutations on its inputs, and all active transmitters employ identical
encoders. Unlike the Polyanskiy model, in the proposed scenario, neither the
transmitters nor the receiver knows which transmitters are active. We refer to
this agnostic communication setup as the Random Access Channel (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 $n_t$ 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 $n_i, i \leq t$, 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 $2^k -
1$ simultaneous threshold rules, the proposed scheme uses a single threshold
rule and achieves the same dispersion.
