Secure GDoF of the Z-channel with Finite Precision CSIT: How Robust are Structured Codes?

TL;DR

This paper investigates the robustness of structured codes for secure communication in interference channels when the transmitter's channel knowledge is imperfect, showing that their benefits vanish under finite precision CSIT.

Contribution

It proves that the GDoF advantages of structured codes are entirely lost with finite precision CSIT in a Z interference channel, providing the first such fundamental limitation result.

Findings

Structured codes' GDoF benefits are nullified under finite precision CSIT.

Secure GDoF region of the Z-channel is characterized.

Sum-set inequalities based on Aligned Images bounds are used for analysis.

Abstract

Under the assumption of perfect channel state information at the transmitters (CSIT), it is known that structured codes offer significant advantages for secure communication in an interference network, e.g., structured jamming signals based on lattice codes may allow a receiver to decode the sum of the jamming signal and the signal being jammed, even though they cannot be separately resolved due to secrecy constraints, subtract the aggregate jammed signal, and then proceed to decode desired codewords at lower power levels. To what extent are such benefits of structured codes fundamentally limited by uncertainty in CSIT? To answer this question, we explore what is perhaps the simplest setting where the question presents itself -- a Z interference channel with secure communication. Using sum-set inequalities based on Aligned Images bounds we prove that the GDoF benefits of structured codes are lost completely under finite precision CSIT. The secure GDoF region of the Z interference channel is obtained as a byproduct of the analysis.