Towards a Constant-Gap Sum-Capacity Result for the Gaussian Wiretap Channel with a Helper

TL;DR

This paper proposes a new signal-scale alignment approach using the linear deterministic model to achieve a constant-gap sum capacity for the Gaussian wiretap channel with a helper, overcoming limitations of previous interference alignment methods.

Contribution

It introduces a signal-scale alignment technique based on the linear deterministic model to obtain constant-gap sum capacity results for specific channel gains.

Findings

Achieves constant-gap sum capacity for certain channel parameters.

Demonstrates limitations of real interference alignment for constant-gap results.

Transfers deterministic model results to the Gaussian model.

Abstract

Recent investigations have shown that the sum secure degrees of freedom of the Gaussian wiretap channel with a helper is $\tfrac{1}{2}$. The achievable scheme for this result is based on the real interference alignment approach. While providing a good way to show degrees of freedom results, this technique has the disadvantage of relying on the Khintchine-Groshev theorem and is therefore limited to {\it almost all channel gains}. This means that there are infinitely many channel gains, where the scheme fails. Furthermore, the real interference alignment approach cannot be used to yield stronger constant-gap results. We approach this topic from a signal-scale alignment perspective and use the linear deterministic model as a first approximation. Here we can show a constant-gap sum capacity for certain channel gain parameters. We transfer these results to the Gaussian model and discuss the results.