On the Secrecy Capacity of 2-user Gaussian Z-Interference Channel with Shared Key

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-IC with secrecy constraint at the receiver is considered. One of the fundamental problems here is how to use the secret key as a part of the encoding process. 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 one part of the key for one-time pad and remaining part of the key for wiretap coding. 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 wiretap coding. 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 an outer bound on the sum rate and secrecy rate of the transmitter which causes interference. The main novelty of deriving outer bound lies in the selection of side information provided to the receiver and using the secrecy constraint at the receiver. The derived outer bounds are found to be tight depending on the channel conditions and rate of the key. The scaling behaviour of key rate is also explored for different schemes using the notion of secure GDOF. The optimality of different schemes is characterized for some specific cases. The developed results show the importance of key rate splitting in enhancing the secrecy performance of the system when users are operating under interference limited environment.