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Conference on Information Sciences and Systems

A new outer bound for the gaussian interference channel with confidential messages

Xiang He, Aylin Yener

Published Mar 1, 2009• 40 citations
Publisher

Abstract

In this work, we derive new outer bounds for the two-user interference channel with confidential messages. An upper bound is found for the sum rate. When the interfering link of the first user is greater than 1, a new upper bound on 2R1+ R2is obtained by studying a special form of the three-user interference channel. The bounds are then compared with known bounds for the symmetric interference channel under strong interference regime. In particular, examples are presented to showcase for channel parameters where positive secrecy rates are known to be achievable, the new bounds improve upon the known outer bounds on the secrecy capacity region. It is shown that, in some cases, the 2R1+R2bound also improves the bound on the sum rate.

DOI
10.1109/ciss.2009.5054738

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In this work, we derive new outer bounds for the two-user interference channel with confidential messages. An upper bound is found for the sum rate. When the interfering link of the first user is greater than 1, a new upper bound on 2R1+ R2is obtained by studying a special form of the three-user interference channel. The bounds are then compared with known bounds for the symmetric interference channel under strong interference regime. In particular, examples are presented to showcase for channel parameters where positive secrecy rates are known to be achievable, the new bounds improve upon the known outer bounds on the secrecy capacity region. It is shown that, in some cases, the 2R1+R2bound also improves the bound on the sum rate.
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The many-to-one interference channel has received interest by virtue of embodying the essence of an interference network while being more tractable than the generalK-user interference channel. In this paper, we introduce information theoretic secrecy to this model and consider the many-to-one interference channel with confidential messages, in which each receiver, in particular, the one subject to interference, is also one from which the interfering users' messages need to be kept secret from. We derive the achievable secrecy sum rate for this channel using nested lattice codes, as well as an upper bound on the secrecy sum rate for all possible channel gain configurations. We identify several nontrivial cases where the gap between the upper bound and the achieved secrecy sum rate is only a function of the number of the usersK, and is uniform over all possible channel gain configurations in each case. In addition, we identify the secure degrees of freedom for this channel and show it to be equivalent to its degrees of freedom, i.e., the secrecy in high SNR comes for free.
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.
In this paper, inner and outer bounds on the capacity region of two-user interference channels with two confidential messages have been proposed. By adding secure multiplex coding to the error correction method in [15] which achieves the best achievable capacity region for interference channel up to now, we have shown that the improved secure capacity region compared with [2] now is the whole Han-Kobayashi region. In addition, this construction not only removes the rate loss incurred by adding dummy messages to achieve security, but also change the original weak security condition in [2] to strong security. Then the equivocation rate for a collection of secret messages has also been evaluated, when the length of the message is finite or the information rate is high, our result provides a good approximation for bounding the worst case equivocation rate. Our results can be readily extended to the Gaussian interference channel with little efforts.
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.