arXiv subjects

Juliana G. F. Souza

Publications and source records attributed to Juliana G. F. Souza.

3 recordsLinked to original sources

arXiv2026

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

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.

cs.IT↗

arXiv2025

Multilevel lattice codes from Hurwitz quaternion integers

This work presents an extension of the Construction $π_A$ lattices proposed in \cite{huang2017construction}, to Hurwitz quaternion integers. This construction is provided by using an isomorphism from a version of the Chinese remainder theorem applied to maximal orders in contrast to natural orders in prior works. Exploiting this map, we analyze the performance of the resulting multilevel lattice codes, highlight via computer simulations their notably reduced computational complexity provided by the multistage decoding. Moreover it is shown that this construction effectively attain the Poltyrev-limit.

cs.IT↗

arXiv2025

Achieving uniform side information gain with multilevel lattice codes over the ring of integers

The index coding problem aims to optimise broadcast communication by taking advantage of receiver-side information to improve transmission efficiency. In this letter, we explore the application of Construction $π_A$ lattices to index coding. We introduce a coding scheme, named \textit{CRT lattice index coding}, using Construction $π_A$ over $\mathbb{Z}$ to address the index coding problem. It is derived an upper bound for side information gain of a CRT lattice index code and conditions for the uniformity of this gain. The efficiency of this approach is shown through theoretical analysis and code design examples.

cs.IT↗