Random Access Channel Coding in the Finite Blocklength Regime

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