Capacity Region of Finite State Multiple-Access Channel with Delayed State Information at the Transmitters

A single-letter characterization is provided for the capacity region of finite-state multiple access channels. The channel state is a Markov process, the transmitters have access to delayed state information, and channel state information is available at the receiver. The delays of the channel state information are assumed to be asymmetric at the transmitters. We apply the result to obtain the capacity region for a finite-state Gaussian MAC, and for a finite-state multiple-access fading channel. We derive power control strategies that maximize the capacity region for these channels

Random Access Channel Coding in the Finite Blocklength Regime

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. Inspired by the model recently introduced by Polyanskiy for the Multiple Access Channel (MAC) with a fixed, known number of transmitters, we assume that the channel is invariant to permutations on its inputs, and that all active transmitters employ identical encoders. Unlike Polyanskiy, we consider a scenario where neither the transmitters nor the receiver know which transmitters are active. We refer to this agnostic communication setup as the Random Access Channel, or 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.Comment: Presented at ISIT18', submitted to IEEE Transactions on Information Theor