Finite-Support Capacity-Approaching Distributions for AWGN Channels

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 minimumcardinality finite-support capacity-achieving PMFs.

Amplitude-Constrained Gaussian Wiretap Channel: Computation of the Optimal Input Distribution

“…To the best of our knowledge, there are no existing prior works that focus on generating numerical examples of secrecycapacity-achieving distribution for the Gaussian wiretap channel in the regime where P X is not available analytically. However, there is extensive prior work on generating examples of the capacity-achieving distribution for the point-to-point channel, which is a special case of the wiretap channel when σ 2 = ∞; The interested reader is referred to [14]- [16] for examples of such implementations.…”

Efficiently Computable Converses for Finite-Blocklength Communication

“…Such channels are of practical interest, and it is known that the optimal input distribution has finitesupport [16] given some fixed quantization bins {q i }. Dynamic Assignment Blahut-Arimoto [17], [18] can be used to find the optimal X and input distribution when restricting the input of a channel to be finite-support. Modifying the algorithm for AWGN channel with amplitude constraint from [17] to account for output quantization and performing alternating optimization with {q i } gives a choice of X and {q i }.…”

“…Dynamic Assignment Blahut-Arimoto [17], [18] can be used to find the optimal X and input distribution when restricting the input of a channel to be finite-support. Modifying the algorithm for AWGN channel with amplitude constraint from [17] to account for output quantization and performing alternating optimization with {q i } gives a choice of X and {q i }. Setting |Y| = 8 and the amplitude constraint to 10 yields an optimized X of cardinality 8 as shown in Fig.…”