Random Access Channel Coding in the Finite Blocklength Regime

TL;DR

This paper introduces a novel random access channel coding scheme that adapts to an unknown number of transmitters, achieving optimal performance with a simple threshold rule and finite blocklength analysis.

Contribution

It proposes a new RAC model where neither transmitters nor receiver know active users, and demonstrates a single-threshold coding scheme that attains MAC optimal performance.

Findings

Achieves first-order optimal performance for RAC in finite blocklength.

Uses a single threshold rule instead of multiple thresholds for different user counts.

Demonstrates that the scheme attains the same dispersion as the MAC.

Abstract

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.