Capacity Bounds for Discrete-Time, Amplitude-Constrained, Additive White Gaussian Noise Channels

TL;DR

This paper derives improved analytic upper bounds on the capacity of amplitude-constrained AWGN channels, showing they are very close to the true capacity across various SNRs.

Contribution

It introduces a dual capacity expression to obtain tighter bounds for scalar and vector AWGN channels under amplitude constraints.

Findings

Scalar bound within 0.1 bits of capacity for all SNRs

Two-dimensional bound within 0.15 bits up to 4.5 dB SNR

Numerical evidence suggests bounds are tight across all SNRs

Abstract

The capacity-achieving input distribution of the discrete-time, additive white Gaussian noise (AWGN) channel with an amplitude constraint is discrete and seems difficult to characterize explicitly. A dual capacity expression is used to derive analytic capacity upper bounds for scalar and vector AWGN channels. The scalar bound improves on McKellips' bound and is within 0.1 bits of capacity for all signal-to-noise ratios (SNRs). The two-dimensional bound is within 0.15 bits of capacity provably up to 4.5 dB, and numerical evidence suggests a similar gap for all SNRs.