  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.
