The Geometry of Uncoded Transmission for Symmetric Continuous Log-Concave Distributions
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Date
2022-03-02
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Conference Paper
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yes
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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.
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International Zurich Seminar on Information and Communication (IZS 2022). Proceedings
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29 - 33
Publisher
ETH Zurich
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International Zurich Seminar on Information and Communication (IZS 2022)
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03529 - Lapidoth, Amos / Lapidoth, Amos
02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.
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Is part of: https://doi.org/10.3929/ethz-b-000534535