Finite-Support Capacity-Approaching Distributions for AWGN Channels

TL;DR

This paper introduces the DAB algorithm to find small-support probability distributions that nearly achieve the capacity of AWGN channels under amplitude and power constraints, improving practical communication system design.

Contribution

The paper presents the DAB algorithm for identifying finite-support PMFs that approach AWGN channel capacity with minimal shaping loss, extending previous theoretical results.

Findings

PMFs with small support can nearly achieve AWGN capacity

DAB finds PMFs with support size close to theoretical limits

Finite-support distributions approach capacity within 1%

Abstract

In this paper, the Dynamic-Assignment Blahut-Arimoto (DAB) algorithm identifies finite-support probability mass functions (PMFs) with small cardinality that achieve capacity for amplitude-constrained (AC) Additive White Gaussian Noise (AWGN) Channels, or approach capacity to within less than 1% for power-constrained (PC) AWGN Channels. While a continuous Gaussian PDF is well-known to be a theoretical capacity-achieving distribution for the PC-AWGN channel, DAB identifies PMFs with small-cardinality that are, for practical purposes, indistinguishable in performance. We extend the results of Ozarow and Wyner that require a constellation cardinality of $2^{C+1}$ to approach capacity C to within the shaping loss. PMF's found by DAB approach capacity with essentially no shaping loss with constellation cardinality of $2^{C+1.2}$. For AC-AWGN channels, DAB characterizes the evolution of minimum-cardinality finite-support capacity-achieving PMFs.