Construction $\pi_A$ over Multiquadratic Fields for Compound Block-Fading Wiretap Channels

TL;DR

This paper develops multilevel lattice codes from multiquadratic number fields for secure communication over compound block-fading wiretap channels, enabling reliable and secret transmission.

Contribution

It specializes Construction π_A over the ring of integers of multiquadratic fields, using CRT decomposition for multistage decoding and universal secrecy.

Findings

Achieves universal reliability for legitimate receiver.

Provides strong secrecy against eavesdropper set.

Enables multistage decoding with binary residue alphabets.

Abstract

We construct multilevel lattice codes from multiquadratic number fields for the compound block-fading wiretap channel. More precisely, we specialize Construction $\pi_A$ 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.