# Preserving Confidentiality in The Gaussian Broadcast Channel Using Compute-and-Forward

## TL;DR

This paper introduces a novel coding scheme combining nested lattices, cooperative jamming, and compute-and-forward decoding to securely transmit messages over a Gaussian broadcast channel with multiple receivers and helpers, achieving optimal secure degrees of freedom.

## Contribution

It presents a new secure transmission scheme that works at any finite SNR and achieves the optimal sum secure degrees of freedom for the K-receiver Gaussian broadcast channel.

## Key findings

- Achieves secure communication at any finite SNR.
- Attains the optimal sum secure degrees of freedom of 1.
- Utilizes a novel combination of lattice coding, jamming, and compute-and-forward decoding.

## Abstract

We study the transmission of confidential messages across a wireless broadcast channel with K>2 receivers and K helpers. The goal is to transmit all messages reliably to their intended receivers while keeping them confidential from the unintended receivers. We design a codebook based on nested lattice structure, cooperative jamming, lattice alignment, and i.i.d. coding. Moreover, we exploit the asymmetric compute-and-forward decoding strategy to handle finite SNR regimes. Unlike previous alignment schemes, our achievable rates are attainable at any finite SNR value. Also, we show that our scheme achieves the optimal sum secure degrees of freedom of 1 for the K-receiver Gaussian broadcast channel with K confidential messages and K helpers.