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.
Highlights
The capacity of wireless networks, as evident from recent Degrees of Freedom (DoF) [2] and Generalized Degrees of Freedom (GDoF) [3] studies, depends rather strongly on the underlying assumptions about the availability of channel state information at the transmitter(s) (CSIT)
Even if we set practical concerns aside, there is another motivation for the emphasis on robustness — if the benefits of structured codes are lost under finite precision CSIT, perhaps this removes some of the obstacles that have made progress difficult in network information theory, and opens the door to a comprehensive and robust network information theory of wireless networks, based on optimality of random codes that are much better understood
Motivated by robustness concerns that are paramount in secure communications, in this work we study the robust GDoF of secure communication over a 2 user Z interference channel
Summary
The capacity of wireless networks, as evident from recent Degrees of Freedom (DoF) [2] and Generalized Degrees of Freedom (GDoF) [3] studies, depends rather strongly on the underlying assumptions about the availability of channel state information at the transmitter(s) (CSIT). What we find, using Aligned Images bounds and sum-set inequalities [35], is that the limitations imposed on structured codes by finite precision CSIT, are both strong and fundamental. Since the Z-interference channel is a canonical setting that has been extensively studied under a variety of assumptions, let us note that there are three essential distinguishing aspects of our work: 1) robustness, 2) information theoretic optimality in the GDoF sense, and 3) security. It is the combination of these 3 aspects that makes our setting uniquely challenging and allows us to explore the limitations of aggregate decoding for structured jamming under channel uncertainty.
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