Random Access Channel Coding in the Finite Blocklength Regime

The paper considers a random multiple access channel communication scenario with an unknown number of transmitters. The collection of active transmitters remains fixed during each epoch, but neither the transmitters nor the receiver know which subset of transmitters that is nor even the number of active transmitters. The receiver discerns from the channel output both the number of active transmitters (k) and their messages. The receiver takes more time to decode if the number of active transmitters is high, and it uses 1-bit feedback at fixed transmission times to inform all transmitters when it is ready to accept a new transmission. For a class of permutationinvariant channels, the central result of this work demonstrates the achievability of performance that is first-order optimal for the Multiple Access Channel (MAC) in operation during each coding epoch. In that class, the proposed scheme achieves the same dispersion using a single threshold rule as that achieved by prior multiple access schemes requiring 2 − 1 simultaneous threshold rules and a fixed number of transmitters.