Secrecy function conjecture for formally unimodular packings

Let Γ\Gamma be a formally unimodular packing, and let ΞΓ(τ)\Xi_{\Gamma}(\tau) denote its secrecy function and ξΓ\xi_{\Gamma} its maximum value. Formally unimodular packing secrecy function conjecture. The secrecy function achieves its maximum at τ=1\tau=1, i.e.,

ξΓ=ΞΓ(1).\xi_{\Gamma}=\Xi_{\Gamma}(1).

This is the generalized packing version of the formally unimodular lattice conjecture. The source presents it as the basis for studying secrecy-optimal Construction A packings.

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Primary source

Maiara F. Bollauf, Hsuan-Yin Lin and Øyvind Ytrehus, “Formally Unimodular Packings for the Gaussian Wiretap Channel”, arXiv:2206.14171 (2023).

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