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.

翻译：针对复合块衰落窃听信道，我们利用多二次数域构造了多级格码。具体而言，我们在整数环 $\mathcal{O}_K$ 上特化了 $π_A$ 构造，并利用在 $K$ 中完全分裂的有理素数，通过中国剩余定理（CRT）分解为小残数字母表（特别是二进制），从而支持多级译码。所得嵌套格符合代数构造A框架，结合离散高斯整形和平坦因子界，为合法接收者提供通用可靠性，并在窃听者复合集上均匀实现强保密性。