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

2026-04-14

AI Summary

This work addresses the challenge of simultaneously achieving reliable communication and strong information-theoretic security over compound block-fading wiretap channels. To this end, the authors propose a novel algebraic lattice code construction based on rings of integers in multiquadratic number fields. They extend Construction $\pi_A$ to multiquadratic fields for the first time, leveraging completely split rational primes and applying the Chinese Remainder Theorem to decompose the code into small alphabets—such as binary—enabling efficient multistage decoding. By integrating discrete Gaussian shaping with a careful analysis of flatness factors, the resulting nested lattice codes guarantee universal reliability for legitimate users while ensuring strong secrecy against any set of eavesdroppers in the information-theoretic sense.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Multiagent Systems: Agent Communication

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

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.

Problem

• compound block-fading wiretap channel
• strong secrecy
• reliable communication
• lattice codes
• multiquadratic fields

Innovation

• multiquadratic number fields
• Construction π_A
• Chinese Remainder Theorem
• nested lattices
• strong secrecy