Information-Theoretic Outer-Bounds from Sphere-Packing, Compactness, and Zero-One Laws

Ponniah, Jonathan; Xie, Liang-Liang

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https://hdl.handle.net/2142/130313 Copy

Description

Title

Information-Theoretic Outer-Bounds from Sphere-Packing, Compactness, and Zero-One Laws

Author(s)

• Ponniah, Jonathan
• Xie, Liang-Liang

Issue Date

2025-09-17

Keyword(s)

• Sphere-packing
• Relay-channel
• Zero-one laws
• Converses

Abstract

Information-theoretic outer-bounds are derived using sphere-packing arguments for the point-to-point channel and the relay channel. The arguments rely on novel applications of compactness and zero-one exponent laws to address issues of coordination and distortions to the codeword orbits caused by generic relay encoding functions. The capacity of the relay channel is I(Xs; Ŷr, Yd|Xr) for I(Ŷr; Yr|xr) < I(Xr; Yd) for some p(xs, xr)p(ŷr|yr, xr)p(yr, yd|Xs, xr), where the distribution falls into one of two regimes: a fine compression regime where H(Yr|Xs,Xr) > H(Yr|Ŷr,Xr) and a coarse compression regime where H(Yr|Xs,Xr) ≤ H(Yr|Ŷr,Xr). Both regimes support p(xs)p(xr)p(ŷr|yr, xr)p(yr, yd|xs, xr) which corresponds to simple compress-forward (no Wyner-Ziv). The coarse compression regime also supports p(xs, xr)p(ŷr|xr)p(yr, yd|xs, xr) which corresponds to partial decode-forward.

Publisher

Allerton Conference on Communication, Control, and Computing

Series/Report Name or Number

2025 61st Allerton Conference on Communication, Control, and Computing Proceedings

ISSN

2836-4503

Type of Resource

Text

Genre of Resource

Conference Paper/Presentation

Language

eng

Handle URL

https://hdl.handle.net/2142/130313&&

Copyright and License Information

Copyright 2025 is held by Jonathan Ponniah and Liang-Liang Xie.

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