Abstract

We present a geometric picture for optimal single-letter uncoded
transmission for source-channel duals, where the source and
distortion measure are dual to the channel and cost function. In
particular, we investigate an additive noise channel with the
conditional channel distribution and capacity-achieving input
distribution both being symmetric, continuous log-concave
densities. We show that under these assumptions, a Gaussian source
transmitted over an additive Gaussian channel is the only possible
choice for optimal single-letter uncoded transmission. We explain
the uniqueness of Gaussian uncoded transmission through a
homothetic property for the channel input and output typical sets,
and illustrate the geometry of single-letter uncoded transmission
as opposed to communication based on the classical source-channel
separation principle.

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Scientist, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan
/ \     []  \|    |_|   / \/    Web: https://moser-isi.ethz.ch/

Last modified: Wed Jan 5 12:28:54 CET 2022