Construction $π_A$ over Multiquadratic Fields for Compound Block-Fading Wiretap Channels
This work provides a novel algebraic framework for secure communication over fading channels, though it is an incremental extension of existing Construction A techniques.
The paper constructs multilevel lattice codes from multiquadratic number fields for compound block-fading wiretap channels, achieving universal reliability and strong secrecy through CRT decomposition into binary alphabets.
We construct multilevel lattice codes from multiquadratic number fields for the compound block-fading wiretap channel. More precisely, we specialize Construction $π_A$ 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.