The topological interference management (TIM) problem refers to the study of the$K$-user partially connected interference networks with no channel state information at the transmitters (CSIT), except for the knowledge of network topology. In this paper, we study the TIM problem with confidential messages (TIM-CM), where message confidentiality must be satisfied in addition to reliability constraints. In particular, each transmitted message must be decodable at its intended receiver and remain confidential at the remaining$(K-1)$receivers. Our main contribution is to present a comprehensive set of results for the TIM-CM problem by studying the symmetric secure degrees of freedom (SDoF). To this end, we first characterize necessary and sufficient conditions for feasibility of positive symmetric SDoF for any arbitrary topology. We next present two achievable schemes for the TIM-CM problem: For the first scheme, we use the concept of secure partition and, for the second one, we use the concept of secure independent sets. We also present outer bounds on symmetric SDoF for any arbitrary network topology. Using these bounds, we characterize the optimal symmetric SDoF of all$K=2$-user and$K=3$-user network topologies.

The classic wiretap channel (WTC) problem is concerned with a transmitter (Alice) that wants to send a message$W$to the intended receiver (Bob) while keeping it secret from a passive eavesdropper (Eve). However, under certain communication scenarios, the user may not be interested in hiding the entire message from the eavesdropper, but rather in hiding its most sensitive attributes. While classic wiretap coding is capable of hiding these salient message attributes, it may be too stringent and better communication rates may be achievable. Motivated by the above, in this paper, we introduce and study the latent variable wiretap channel (LV-WTC) problem. Under this setting, the transmitter is interested in sending the message$W$to the intended receiver while keeping a correlated latent variable$S$(which models privacy sensitive attributes) secret from the eavesdropper. We present a message splitting based achievable scheme for the LV-WTC problem, which adapts to the structure of the conditional distribution PS|Wto achieve higher rates compared to the classical WTC. Several open problems and future directions that originate from this new communication problem are also discussed.

The topological interference management (TIM) problem is a framework for studying partially connected interference networks with no channel state information at transmitters (CSIT), except network topology. TIM is a more pragmatic setting as CSIT is often available imperfectly, or may not be available at all. In this paper, we study the TIM problem with confidential messages, denoted in short by the secure TIM (STIM) problem. More specifically, we focus on the STIM problem for half-rate-feasible (HRF) networks. Half-rate-feasible networks are a class of partially connected interference networks whose sum degrees of freedom (DoF) have been characterized by K/2, without any secrecy constraints. The main contribution of this paper is as follows: We design achievable schemes for HRF networks subject to secrecy constraints, and present a lower bound on the secure degrees of freedom (SDoF). To this end, we first show the necessity of classifying HRF networks into two sub-categories based on some properties of the underlying network topology. As it turns out, the division of HRF networks into these sub-categories is critical for the design of secure transmission schemes. We then leverage the underlying topological properties along with ideas from secure interference alignment (SIA) in order to design achievable schemes for both subclasses of HRF networks.

We investigate the secure degrees of freedom (SDoF) of the multiple-input multiple-output (MIMO) wiretap channel with intersymbol interference (ISI) in the presence of a multi-antenna cooperative jammer. We focus on the practically relevant setting with no channel state information at the transmitters (CSIT). More specifically, the legitimate transmitter and the cooperative jammer only have statistical knowledge of the channel in terms of the effective number of ISI channel taps, i.e., channel impulse response (CIR) lengths, toward the legitimate receiver and the eavesdropper. Our main contribution is to show that in the absence of CSIT, positive SDoF can be achieved by carefully exploiting: 1) the heterogeneity of the CIR lengths toward both receivers and 2) the relative number of antennas at the four terminals. To achieve secrecy, we propose a scheme in which the transmitter strategically sends a mixture of information and artificial noise symbols in a way that exploits the heterogeneity of CIR lengths. Additionally, the cooperative jammer transmits artificial noise symbols in a way that completely masks all the information symbols that are received at the eavesdropping node. Under the proposed scheme, positive SDoF can be achieved, even when the number of antennas at the legitimate receiver is less than the number of antennas at the eavesdropper.

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.

We investigate secure degrees of freedom (SDoF) of a single-input single-output (SISO) wiretap channel with a single helper without channel state information at the transmitters (CSIT). Wireless communication systems inherently suffer from intersymbol interference (ISI) due to channel dispersion. In this paper, we propose a novel blind cooperative jamming scheme that exploits the ISI heterogeneity to achieve positive SDoF, even without any CSIT. In order to achieve positive SDoF, the proposed approach only requires statistical properties of the ISI channel. In particular, we show that if LB is the effective ISI channel multipath link length towards the legitimate receiver (Bob) and LE is the link length towards the eavesdropper (Eve), a positive SDoF of LB-LE is achievable. To the best of our 2(LB -1) knowledge, this is the first work that exploits ISI link length heterogeneity to achieve positive secure degrees of freedom.