Construction $\ddot{I}{€}_A$ over Multiquadratic Fields for Compound Block-Fading Wiretap Channels

Abstract

We construct multilevel lattice codes from multiquadratic number fields for the compound block-fading wiretap channel. More precisely, we specialize Construction $\ddot{I}{€}_A$ over the ring of integers ${\mathcal{O}}_K$ and exploit rational primes that split completely in $K$ to obtain a Chinese Remainder Theorem (CRT) decomposition into small residue alphabets, notably binary, which enables multistage decoding. The resulting nested lattices fit into the algebraic Construction A framework and, when combined with discrete Gaussian shaping and flatness-factor bounds, provide universal reliability for the legitimate receiver and strong secrecy uniformly over the eavesdropper compound set.

13 pages, 1 figure, Accepted for presentation at WCC2026