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.
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.
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 ofkey rate splitting,one-time pad,stochastic encodingandsuperposition coding. 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 ofsecure generalized degrees of freedom. 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.
This paper considers the problem of secure communication over a 2-user Gaussian interference channel (GIC) with shared key of finite rate between the transmitter-receiver pair with strong secrecy constraint at the receiver. The main contributions of the paper lies in obtaining a novel achievable scheme which uses a combination of one-time pad, stochastic encoding and superposition based coding scheme, and outer bound on the secrecy capacity region of the 2-user GIC. The main novelty of the derivation of the outer bound lies in the selection of the side-information to be provided to the receiver and using the secrecy constraints at the receiver. The results highlight the role of secret key in the encoding of messages to enhance the system performance in interference limited scenarios.
In this paper, the role of unidirectional limited rate transmitter cooperation is studied for the two-user symmetric Z interference channel (Z-IC) with secrecy constraints at the receivers, in achieving two conflicting goals simultaneously: mitigating interference and ensuring secrecy. First, the problem is studied under the linear deterministic model. A novel scheme for partitioning the encoded messages and outputs based on the relative strengths of the signal and interference is proposed. The partitioning reveals the side information that needs to be provided to the receiver and facilitates the development of tight outer bounds on the secrecy capacity region. The achievable schemes for the deterministic model use a fusion of cooperative precoding and transmission of a jamming signal. The optimality of the proposed scheme is established for the deterministic model for all possible parameter settings. The insights obtained from the deterministic model are used to derive inner and outer bounds on the secrecy capacity region of the two-user Gaussian symmetric Z-IC. The achievable scheme for the Gaussian model uses stochastic encoding in addition to cooperative precoding and transmission of a jamming signal. For the Gaussian case, the secure sum generalized degrees of freedom (GDOF) is characterized and shown to be optimal for the weak/moderate interference regime. It is also shown that the secure sum capacity lies within 2 bits/s/Hz of the outer bound for the weak/moderate interference regime for all values of the capacity of the cooperative link. Interestingly, in the deterministic model, it is found that there is no penalty on the capacity region of the Z-IC due to the secrecy constraints at the receivers in the weak/moderate interference regimes. Similarly, it is found that there is no loss in the secure sum GDOF for the Gaussian case due to the secrecy constraint at the receiver, in the weak/moderate interference regimes. The results highlight the importance of cooperation in facilitating secure communication over the Z-IC.
In this work, the role of unidirectional limited rate transmitter cooperation is studied in the case of the 2-user Z interference channel (Z-IC) with secrecy constraints at the receivers, on achieving two conflicting goals simultaneously: mitigating interference and ensuring secrecy. First, the problem is studied under the linear deterministic model. The achievable schemes for the deterministic model use a fusion of cooperative precoding and transmission of a jamming signal. The optimality of the proposed scheme is established for the deterministic model for all possible parameter settings using the outer bounds derived by the authors in a previous work. Using the insights obtained from the deterministic model, a lower bound on the secrecy capacity region of the 2-user Gaussian Z-IC are obtained. The achievable scheme in this case uses stochastic encoding in addition to cooperative precoding and transmission of a jamming signal. The secure sum generalized degrees of freedom (GDOF) is characterized and shown to be optimal for the weak/moderate interference regime. It is also shown that the secure sum capacity lies within 2 bits/s/Hz of the outer bound for the weak/moderate interference regime for all values of the capacity of the cooperative link. Interestingly, in case of the deterministic model, it is found that there is no penalty on the capacity region of the Z-IC due to the secrecy constraints at the receivers in the weak/moderate interference regimes. Similarly, it is found that there is no loss in the secure sum GDOF for the Gaussian case due to the secrecy constraint at the receiver, in the weak/moderate interference regimes. The results highlight the importance of cooperation in facilitating secure communication over the Z-IC.
This paper derives outer bounds on the secrecy capacity region of the 2-user Z interference channel (Z-IC) with rate-limited unidirectional cooperation between the transmitters. First, the model is studied under the linear deterministic setting. The derivation of the outer bounds on the secrecy capacity region involves careful selection of the side information to be provided to the receivers and using the secrecy constraints at the receivers in a judicious manner. To this end, a novel partitioning of the encoded messages and outputs is proposed for the deterministic model based on the strength of interference and signal. The obtained outer bounds are shown to be tight using the achievable scheme derived by the authors in a previous work. Using the insight obtained from the deterministic model, outer bounds on the secrecy capacity region of the 2-user Gaussian Z-IC are obtained. The equivalence between the outer bounds for both the models is also established. It is also shown that secrecy constraint at the receiver does not hurt the capacity region of the 2-user Z-IC for the deterministic model in the weak/moderate interference regime. On the other hand, the outer bounds developed for the Gaussian case shows that secrecy constraint at the receiver can reduce the capacity region for the weak/moderate interference regime. The study of the relative performance of these bounds reveals insight into the fundamental limits of the 2-user Z-IC with limited rate transmitter cooperation.
This paper studies the value of limited rate cooperation between the transmitters for managing interference and simultaneously ensuring secrecy, in the two-user Gaussian symmetric interference channel (IC). First, the problem is studied in the symmetric linear deterministic IC (SLDIC) setting, and achievable schemes are proposed, based on interference cancelation, relaying of the other user's data bits, and transmission of random bits. In the proposed achievable scheme, the limited rate cooperative link is used to share a combination of data bits and random bits depending on the model parameters. Outer bounds on the secrecy rate are also derived, using a novel partitioning of the encoded messages and outputs depending on the relative strength of the signal and the interference. The partitioning helps to bound certain negative entropy terms, leading to a tractable outer bound. The inner and outer bounds are derived under all possible parameter settings. It is found that, for some parameter settings, the inner and outer bounds match, yielding the capacity of the SLDIC under transmitter cooperation and secrecy constraints. In some other scenarios, the achievable rate matches with the capacity region of the two-user SLDIC without secrecy constraints derived by Wang and Tse; thus, the proposed scheme offers secrecy for free, in these cases. Inspired by the achievable schemes and outer bounds in the deterministic case, achievable schemes and outer bounds are derived in the Gaussian case. The proposed achievable scheme for the Gaussian case is based on Marton's coding scheme and stochastic encoding along with dummy message transmission. One of the key techniques used in the achievable scheme for both the models is interference cancelation, which simultaneously offers two seemingly conflicting benefits: it cancels interference and ensures secrecy. Many of the results derived in this paper extend to the asymmetric case also. The results show that limited transmitter cooperation can greatly facilitate secure communications over two-user ICs.