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IEEE International Symposium on Information Theory (ISIT)

On the Secure Degrees of Freedom of the K-user Interference Channel with Delayed CSIT

Mohamed Seif, Ravi Tandon, Ming Li

Published Jun 1, 2018• 6 citations
Publisher

Abstract

In this paper, the K-user interference channel with confidential messages is considered with delayed channel state information at transmitters (CSIT). We propose a novel secure transmission scheme in which the transmitters carefully mix information symbols with artificial noises to ensure confidentiality. Achieving confidentiality is challenging due to the delayed nature of CSIT, and the distributed nature of the transmitters. Our scheme works over two phases: phase one in which each transmitter sends information symbols mixed with artificial noises, and repeats such transmission over multiple rounds. In the next phase, each transmitter uses delayed CSIT of the previous phase and sends a function of the net interference and artificial noises (generated in previous phase), which is simultaneously useful for all receivers. These phases are designed to ensure the decodability of the desired messages while satisfying the confidentiality constraints. The proposed scheme achieves a sum secure degrees of freedom (SDoF) of at least [1/2](√K-6). To the best of our knowledge, this is the first result on the K-user interference channel with confidential messages and delayed CSIT that achieves a SDoF which scales with K -.

DOI
10.1109/isit.2018.8437339

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In this paper, the K-user interference channel with confidential messages is considered with delayed channel state information at transmitters (CSIT). We propose a novel secure transmission scheme in which the transmitters carefully mix information symbols with artificial noises to ensure confidentiality. Achieving confidentiality is challenging due to the delayed nature of CSIT, and the distributed nature of the transmitters. Our scheme works over two phases: phase one in which each transmitter sends information symbols mixed with artificial noises, and repeats such transmission over multiple rounds. In the next phase, each transmitter uses delayed CSIT of the previous phase and sends a function of the net interference and artificial noises (generated in previous phase), which is simultaneously useful for all receivers. These phases are designed to ensure the decodability of the desired messages while satisfying the confidentiality constraints. The proposed scheme achieves a sum secure degrees of freedom (SDoF) of at least 1/2. To the best of our knowledge, this is the first result on the K-user interference channel with confidential messages and delayed CSIT that achieves a SDoF which scales with K -.
In this paper, the K-user interference channel with secrecy constraints is considered with delayed channel state information at transmitters (CSIT). We propose a novel secure retrospective interference alignment scheme in which the transmitters carefully mix information symbols with artificial noises to ensure confidentiality. Achieving positive secure degrees of freedom (SDoF) is challenging due to the delayed nature of CSIT, and the distributed nature of the transmitters. Our scheme works over two phases: Phase one, in which each transmitter sends information symbols mixed with artificial noises, and repeats such transmission over multiple rounds. In the next phase, each transmitter uses the delayed CSIT of the previous phase and sends a function of the net interference and artificial noises (generated in previous phase), which is simultaneously useful for all receivers. These phases are designed to ensure the decodability of the desired messages while satisfying the secrecy constraints. We present our achievable scheme for three models, namely: (1) K-user interference channel with confidential messages (IC-CM), and we show that 1 2 ( K − 6 ) SDoF is achievable; (2) K-user interference channel with an external eavesdropper (IC-EE); and (3) K-user IC with confidential messages and an external eavesdropper (IC-CM-EE). We show that for the K-user IC-EE, 1 2 ( K − 3 ) SDoF is achievable, and for the K-user IC-CM-EE, 1 2 ( K − 6 ) is achievable. To the best of our knowledge, this is the first result on the K-user interference channel with secrecy constrained models and delayed CSIT that achieves an SDoF which scales with K , square-root of number of users.
Secure degrees-of-freedom (SDoF) for multiple-input multiple-output (MIMO) interference channel with confidential messages and delayed channel state information at transmitter (CSIT) remains unclear, even for single-input single-output (SISO) case. In this paper, we propose an achievable SDoF for MIMO interference channel with confidential messages and delayed CSIT by designing a multi-phase achievable scheme. For the proposed scheme, we first establish a multi-phase transmission procedure with undetermined phase durations. In the next, the security and decoding conditions on feasible phase durations are derived. Finally, an achievable SDoF maximization problem with respect to phase durations is solved under security and decoding conditions. Due to effective coordination of interference, the proposed achievable SDoF can be 20% greater than the SDoF of MIMO wiretap channel with delayed CSIT, which removes one transmitter from the MIMO interference channel.
We consider the K-user interference channel with confidential messages (IC-CM) with intersymbol interference (ISI). The main contribution of this paper is to show that sum-secure degrees of freedom (SDoF) can be made to linearly increase with the number of users K with no channel state information at the transmitters (CSIT). We demonstrate that this is true whenever the channel impulse response (CIR) lengths from the legitimate transmitters towards their respectively intended receivers are larger than those from the interfering transmitters towards the unintended receivers. To design this scheme, we use: a) the simple channel matrix structures of the received signal space to eliminate interference and allow decodability at the intended receivers. b) an injection of artificial noise into the transmitted signal from a strategically chosen small number of transmitters that act as cooperative jammers in order to preserve confidentiality of messages at unintended receivers. This is the first work showing that the SDoF of the K-user IC-CM with ISI can linearly increase with K, the number of users.
We consider the problem of K-user interference channel with confidential messages (IC-CM) with intersymbol interference (ISI). The main contribution of this paper is to show that sum-secure degrees of freedom (SDoF) can be made to linearly increase with the number of users K in the absence of channel state information at the transmitters (CSIT). The proposed scheme entails three main ingredients : a) leveraging the simple channel matrix structures resulting from the orthogonal frequency division multiplexing (OFDM) type transmission technique in order to eliminate interference and allow coherent decoding of each message at its respectively intended receiver. b) exploiting the inherent heterogeneity in channel impulse response (CIR) lengths between the transmitters and the receivers (which results from the wireless multipath propagation), and c) injection of artificial noise into the transmitted signal from a strategically chosen small number of transmitters J that act as cooperative jammers in order to preserve full confidentiality of the messages at the unintended receivers. This is the first work showing that the SDoF of the K-user IC-CM with ISI can linearly increase with the number of users without CSIT.
Secrecy Degrees of Freedom of the 2 ×\times× 2 ×\times× 2 Interference Channel With Delayed CSIT
We consider the two-hop interference channel with confidential messages (ICC), where each transmitter sends one confidential message to its intended destination through two trusted relays. We study the secrecy degrees of freedom (SDoF) of the considered 2 × 2 × 2 ICC with delayed channel state information at transmitters (CSIT). We settle the optimal SDoF of the considered network to be (1/2, 1/2). Thus, the considered network has a strictly larger sum SDoF than a two-user one-hop ICC with even full CSIT. Moreover, we study the SDoF of the network with limited Shannon feedback, that only one relay can obtain the delayed CSIT and output feedback from the destinations. The optimal SDoF is also shown to be (1/2, 1/2), revealing that only limited feedback can also bring SDoF gain. Our proposed achievable schemes in both cases are integrated forms of the retrospective interference alignment and artificial noise transmission.
This paper investigates the sum-secure degrees-of-freedom (SDoF) of three-user multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and delayed channel state information at the transmitter (CSIT). Specifically, we obtain non-trivial sum-SDoF upper and lower bounds. Firstly, we derive the sum-SDoF upper bound by means of statistical equivalence property, security constraints, and permutations. Then, for the sum-SDoF lower bound, we leverage the artificial noise transmission and interference re-transmission to design two transmission schemes, which have holistic and sequential higher-order symbol generation, respectively. For these two schemes, we propose the redundancy reduction approach for security analysis, by which the minimal duration of artificial noise transmission phase of the scheme is obtained. To eliminate the redundant equations in security analysis, this approach first identifies the constituent equations, and then analyzes the rank of assemble of them. As a result, both the proposed sum-SDoF upper and lower bounds are tighter than the existing sum-SDoF upper and lower bounds, respectively. Furthermore, the proposed lower bound showcases a three-user coding gain.