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arXiv · 2006.00344

Finite-Support Capacity-Approaching Distributions for AWGN Channels

Derek Xiao·Linfang Wang·Richard D. Wesel
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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.

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Derek Xiao, Linfang Wang, Richard D. Wesel. 2020-05-30. Finite-Support Capacity-Approaching Distributions for AWGN Channels. https://arxiv.org/abs/2006.00344

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