Providing Secrecy With Structured Codes: Tools and Applications to Two-User Gaussian Channels

TL;DR

This paper demonstrates that structured codes, specifically nested lattice codes, can be effectively used to achieve positive secrecy rates in two-user Gaussian channels, outperforming random codes at high SNR and enabling large secrecy rates with sufficient power.

Contribution

It introduces a method to compute secrecy rates using nested lattice codes and proves their advantage over Gaussian random codes in various two-user Gaussian channels.

Findings

Structured codes achieve positive secure degrees of freedom in non-degraded channels.

Nested lattice codes outperform Gaussian random codes at high SNR.

Large secrecy rates are achievable with structured codes and enough power.

Abstract

Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured codes are useful for providing secrecy, and show how to compute the secrecy rate when structured codes are used. In particular, we solve the problem of bounding equivocation rates with one important class of structured codes, i.e., nested lattice codes. Having established this result, we next demonstrate the use of structured codes for secrecy in two-user Gaussian channels. In particular, with structured codes, we prove that a positive secure degree of freedom is achievable for a large class of fully connected Gaussian channels as long as the channel is not degraded. By way of this, for these channels, we establish that structured codes outperform Gaussian random codes at high SNR. This class of channels include the two-user multiple access wiretap channel, the two-user interference channel with confidential messages and the two-user interference wiretap channel. A notable consequence of this result is that, unlike the case with Gaussian random codes, using structured codes for both transmission and cooperative jamming, it is possible to achieve an arbitrary large secrecy rate given enough power.