On the Deterministic Sum-Capacity of the Multiple Access Wiretap Channel

TL;DR

This paper introduces a deterministic approximation approach for the two-user multiple access wiretap channel, achieving results beyond previous secure degrees of freedom by using signal-scale alignment and differentiating channel strengths.

Contribution

It presents a novel signal-scale alignment scheme that is independent of channel gain rationality and extends the s.d.o.f. bounds to more general channel conditions.

Findings

Achieves secrecy rates approaching s.d.o.f. for small channel gain differences.

Differentiates between users based on channel strength, influencing secrecy rates.

Extends s.d.o.f. bounds to a broader class of channel parameters.

Abstract

We study a deterministic approximation of the two-user multiple access wiretap channel. This approximation enables results beyond the recently shown $\tfrac{2}{3}$ secure degrees of freedom (s.d.o.f.) for the Gaussian multiple access channel. While the s.d.o.f. were obtained by real interference alignment, our approach uses signal-scale alignment. We show an achievable scheme which is independent of the rationality of the channel gains. Moreover, our result can differentiate between channel strengths, in particular between both users, and establishes a secrecy rate dependent on this difference. We can show that the resulting achievable secrecy rate tends to the s.d.o.f. for vanishing channel gain differences. Moreover, we extend the s.d.o.f. bound towards a general bound for varying channel strengths and show that our achievable scheme reaches the bound for certain channel gain parameters. We believe that our analysis is the first step towards a constant-gap analysis of the Gaussian multiple access wiretap channel.