Role of Shared Key for Secure Communication Over 2-User Gaussian Z-Interference Channel

Abstract

In this paper, the role of secret key with finite rate is studied to enhance the secrecy performance of the system when users are operating in interference limited scenarios. To address this problem, a 2-user Gaussian Z-interference channel with secrecy constraint at the receiver is considered. The paper proposes novel achievable schemes, where the schemes differ from each other based on how the key has been used in the encoding process. The first achievable scheme uses a combination of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">key rate splitting</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">one-time pad</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stochastic encoding</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">superposition coding</i> . In this scheme, one part of the key is used for one-time pad and the remaining part of the key is used for stochastic encoding. The encoding is performed such that the receiver experiencing interference can decode some part of the interference without violating the secrecy constraint. As a special case of the derived result, one can obtain the secrecy rate region when the key is completely used for one-time pad or part of the stochastic encoding. The second scheme uses the shared key to encrypt the message using one-time pad and in contrast to the previous case no interference is decoded at the receiver. The paper also derives outer bound on the sum rate and secrecy rate. The main novelty of deriving outer bound lies in the selection of side information provided to the receiver and using the secrecy constraint. The derived outer bounds are found to be tight for certain channel conditions and rate of the key. The scaling behaviour of key rate is also explored for different schemes using the notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">secure generalized degrees of freedom</i> . The optimality of different schemes are characterized for some specific cases. The developed results show the importance of key rate splitting in enhancing the secrecy performance of the system.