Gaussian Multiple and Random Access Channels: Finite-Blocklength Analysis

This paper presents finite-blocklength achievability bounds for the Gaussian multiple access channel (MAC) and random (RAC) under average-error maximal-power constraints. Using codewords uniformly distributed on a sphere maximum likelihood decoder, derived MAC bound each transmitter's rate matches MolavianJazi-Laneman (2015) in its first- second-order terms, improving remaining terms to $\frac12\frac{\log n}{n}+O \left(\frac 1 n \right)$ bits per use. The result then extends RAC model which neither encoders nor decoder knows of $K$ possible transmitters are active. In proposed rateless coding strategy, decoding occurs at time $n_t$ that depends decoder's estimate $t$ number active $k$. Single-bit feedback from all potential $n_i$, $i \leq t$, informs when stop transmitting. For this model, code achieves same first-, second-, third-order performance as best known operation.