High signal-to-noise ratio asymptotics of entropy-constrained Gaussian channel capacity

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Adway Girish, Shlomo Shamai, Emre Telatar

Published: 2026, Last Modified: 24 Mar 2026CoRR 2026EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We study the input-entropy-constrained Gaussian channel capacity problem in the asymptotic high signal-to-noise ratio (SNR) regime. We show that the capacity-achieving distribution as SNR goes to infinity is given by a discrete Gaussian distribution supported on a scaled integer lattice. Further, we show that the gap between the input entropy and the capacity decreases to zero exponentially in SNR, and characterize this exponent.