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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.
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