Construction $π_A$ over Multiquadratic Fields for Compound Block-Fading Wiretap Channels
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910128874192896 |
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| author | Souza, Juliana G. F. Li, Conghui Ling, Cong |
| author_facet | Souza, Juliana G. F. Li, Conghui Ling, Cong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12703 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction $π_A$ over Multiquadratic Fields for Compound Block-Fading Wiretap Channels Souza, Juliana G. F. Li, Conghui Ling, Cong Information Theory 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. |
| title | Construction $π_A$ over Multiquadratic Fields for Compound Block-Fading Wiretap Channels |
| topic | Information Theory |
| url | https://arxiv.org/abs/2604.12703 |