A Design Criterion for the Rayleigh Fading Wiretap Channel Based on ℓ1-Norm Theta Functions

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Authors

Date

2025

Department

Department of Mathematics and Systems Analysis

Major/Subject

Mcode

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Language

en

Pages

25

Series

SIAM Journal on Applied Algebra and Geometry, Volume 9, issue 3, pp. 682-706

Abstract

It is shown that the correct decoding probability of an eavesdropper and error probability of a legitimate receiver in a Rayleigh fading wiretap channel with lattice coset coding are both bounded above by the theta function in the ℓ1-norm of the dual code lattices. Motivated by this, we investigate the ℓ1-norm theta functions of sublattices of ℤ and their duals and prove that the lattice ℤ minimizes the theta function among all scalings of ℤ along the coordinate axes. In the small -range, the ℓ1-norm theta function of a lattice is governed by the cross-polytope packing density. Thus, a method is developed to algorithmically find locally critical lattice packings of the -dimensional cross-polytope. Using this method, we are able to construct a four-dimensional lattice having a cross-polytope packing density of Δ ≈0.824858 and kissing number 30, improving on the best known translational packing density of the cross-polytope in dimension four.

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Keywords

1-norm pound theta functions, Cross-polytope packings, Wireless communications, Wiretap codes

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DOI

10.1137/24M1658784

Citation

Miller, N 2025, 'A Design Criterion for the Rayleigh Fading Wiretap Channel Based on ℓ1-Norm Theta Functions', SIAM Journal on Applied Algebra and Geometry, vol. 9, no. 3, pp. 682-706. https://doi.org/10.1137/24M1658784

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https://urn.fi/URN:NBN:fi:aalto-202601021019

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[article-cris] Perustieteiden korkeakoulu / SCI