A Random Coding Approach to Gaussian Multiple Access Channels With Finite Blocklength

Contrary to the common use of random coding and typicality decoding for the achievability proofs in information theory, the tightest achievable rates for point-to-point Gaussian channels build either on geometric arguments or composite hypothesis testing, for which direct generalization to multi-user settings appears challenging. In this paper, the authors provide a new perspective on the procedure of handling input cost constraints for tight achievability results. In particular, they show with a proper choice of input distribution and using a change of measure technique, tight bounds can be achieved via the common random coding argument and a modified typicality decoding.