Class Of Interference Channels Research Articles

Secure Degrees of Freedom in Networks with User Misbehavior

We investigate the secure degrees of freedom (s.d.o.f.) of three new channel models: broadcast channel with combating helpers, interference channel with selfish users, and multiple access wiretap channel with deviating users. The goal of introducing these channel models is to investigate various malicious interactions that arise in networks, including active adversaries. That is in contrast with the common assumption in the literature that the users follow a certain protocol altruistically and transmit both message-carrying and cooperative jamming signals in an optimum manner. In the first model, over a classical broadcast channel with confidential messages (BCCM), there are two helpers, each associated with one of the receivers. In the second model, over a classical interference channel with confidential messages (ICCM), there is a helper and users are selfish. By casting each problem as an extensive-form game and applying recursive real interference alignment, we show that, for the first model, the combating intentions of the helpers are neutralized and the full s.d.o.f. is retained; for the second model, selfishness precludes secure communication and no s.d.o.f. is achieved. In the third model, we consider the multiple access wiretap channel (MAC-WTC), where multiple legitimate users wish to have secure communication with a legitimate receiver in the presence of an eavesdropper. We consider the case when a subset of users deviate from the optimum protocol that attains the exact s.d.o.f. of this channel. We consider two kinds of deviation: when some of the users stop transmitting cooperative jamming signals, and when a user starts sending intentional jamming signals. For the first scenario, we investigate possible responses of the remaining users to counteract such deviation. For the second scenario, we use an extensive-form game formulation for the interactions of the deviating and well-behaving users. We prove that a deviating user can drive the s.d.o.f. to zero; however, the remaining users can exploit its intentional jamming signals as cooperative jamming signals against the eavesdropper and achieve an optimum s.d.o.f.

An Achievable Region for the Cognitive Interference Relay Channel

In this paper, the causal cognitive interference relay channel (CCIRC) is considered. The CCIRC is obtained from the classic cognitive interference channel by introducing a full-duplex relay that has causal and noisy access to the transmitted signals and aids the communication between the two users. For this channel model, a simple upper bound on the capacity is initially established. Then, we derive an achievable rate region that jointly applies cooperative Han–Kobayashi rate splitting, block Markov encoding, superposition coding, Marton’s binning encoding, and backward decoding. In particular, these bounds are derived for both discrete memoryless model and Gaussian channel. Further, both our theoretical and numerical results indicate that the derived achievable rate region encompasses all known available results in the literature.

On the DoF Region of the MIMO Gaussian Two-User Interference Channel With an Instantaneous Relay

This paper studies inner and outer bounds on the degrees of freedom (DoF) region of the multi-antenna two-user Gaussian interference channel with an instantaneous relay (IR) or relay without delay. It is assumed that the two transmitters and the two receivers have $\mathop {\mathrm {\mathsf {M}}}\nolimits$ antennas, while the IR receives through $\mathop {\mathrm {\mathsf {N_{r}}}}\nolimits$ antennas and transmits through $\mathop {\mathrm {\mathsf {N_{t}}}}\nolimits$ antennas. In the proposed achievable scheme, which generalizes a known one for the case $\mathop {\mathrm {\mathsf {M}}}\nolimits = \mathop {\mathrm {\mathsf {N_{r}}}}\nolimits = \mathop {\mathrm {\mathsf {N_{t}}}}\nolimits$ to any $(\mathop {\mathrm {\mathsf {M}}}\nolimits, \mathop {\mathrm {\mathsf {N_{r}}}}\nolimits, \mathop {\mathrm {\mathsf {N_{t}}}}\nolimits)$ , the IR performs memoryless linear operations on its received signal so as to neutralize interference at the receivers, and the beamforming matrices used by the IR and the transmitters are jointly designed. This joint design strictly outperforms known achievable schemes. Two outer bounds are derived. An information theoretic outer bound is obtained by giving the receivers or the IR genie side information, so that the DoF region of the resulting enhanced channel is known; this converse is valid for any type of processing at the IR and shows the optimality of the proposed achievable scheme for some $(\mathop {\mathrm {\mathsf {M}}}\nolimits, \mathop {\mathrm {\mathsf {N_{r}}}}\nolimits, \mathop {\mathrm {\mathsf {N_{t}}}}\nolimits)$ . A linear processing outer bound is obtained when the IR is restricted to performs linear operations, without any memoryless restriction, on its received signal and shows the optimality of the proposed achievable scheme among all linear processing schemes at the IR. As a result of independent interest, the DoF region of the classical multi-antenna two-user Gaussian interference channel without relay when the channel matrices can have any structure is also derived, which generalized available DoF region results that were derived under certain assumptions on the structure of the channel matrices.

On the Capacity Region of the Broadcast, the Interference, and the Cognitive Radio Channels

As the main basic building blocks of the interference networks, in this paper the broadcast channel, the classical interference channel (CIC), and the cognitive radio channel (CRC) are considered. New capacity outer bounds are established for these channels. These outer bounds are all derived based on a novel unified framework. Using the derived outer bounds, some new capacity results are proved for the CIC and the CRC; a mixed interference regime is identified for the two-user CIC, where decoding interference at one receiver and treating interference as noise at the other one is sum-rate optimal. In addition, a noisy interference regime is derived for the one-sided CIC. Our new capacity theorems for the CIC contain the previously obtained results regarding the Gaussian channel as special cases. For the CRC, a full characterization of the capacity region for a class of more-capable channels is derived. Moreover, it is shown that the derived outer bounds are useful to study channels with one-sided receiver side information wherein one of the receivers has access to the nonintended message; capacity bounds are also discussed in details for such scenarios. Our results lead to new insights regarding the nature of information flow in the basic interference networks.

The Sum-Capacity of the Ergodic Fading Gaussian Cognitive Interference Channel

This paper characterizes the sum-capacity of the ergodic fading Gaussian overlay cognitive interference channel (EGCIFC), a time-varying channel with two source-destination pairs in which a primary/licensed transmitter and a secondary/cognitive transmitter share the same spectrum and where the cognitive transmitter has noncausal knowledge of the primary user's message. The throughput/sum-capacity is characterized under the assumption of perfect knowledge of the instantaneous fading states at all terminals, which are assumed to form an ergodic process. A genie-aided outer bound on the sum-capacity is developed and then matched with an achievable scheme, thereby completely characterizing the sum-capacity of the EGCIFC. The power allocation policy that maximizes the sum-capacity is derived. It is shown that the sum-capacity achieving scheme for an EGCIFC is “separable” in all regimes (i.e., coding across fading states is not necessary), as opposed to the classical interference channel. Extensions to the whole capacity region are discussed. As a capacity achieving scheme for the EGCIFC under certain channel gain conditions, and as a topic of independent interest, the ergodic capacity of a point-to-point multiple-input-single-output channel with per-antenna power constraints and with perfect channel state information at all terminals is also derived.

Collaborative Wireless Energy and Information Transfer in Interference Channel

This paper studies the simultaneous wireless information and power transfer (SWIPT) in a multiuser wireless system, in which distributed transmitters send independent messages to their respective receivers, and at the same time cooperatively transmit wireless power to the receivers via energy beamforming. Accordingly, from the wireless information transmission (WIT) perspective, the system of interest can be modeled as the classic interference channel, while it also can be regarded as a distributed multiple-input multiple-output (MIMO) system for collaborative wireless energy transmission (WET). To enable both information decoding (ID) and energy harvesting (EH) in SWIPT, we adopt the low-complexity time switching operation at each receiver to switch between the ID and EH modes over scheduled time. Based on this hybrid model, we aim to characterize the achievable rate-energy (R-E) trade-offs in the multiuser SWIPT system under various transmitter-side collaboration schemes. Specifically, to facilitate the collaborative energy beamforming, we propose a new signal splitting scheme at the transmitters, where each transmit signal is generally composed of an information signal component and an energy signal component for WIT and WET, respectively. With this new scheme, first, we study the two-user SWIPT system and derive the optimal mode switching rule at the receivers and the corresponding transmit signal optimization to achieve various R-E trade-offs over the fading channel. We also compare the R-E performance of our proposed scheme with transmit energy beamforming and signal splitting against two existing schemes with partial or no cooperation of the transmitters, and show remarkable gains over these baseline schemes. Finally, the general case of SWIPT systems with more than two users is studied, for which we propose and compare two practical transmit collaboration schemes.

On the Capacity Region of the Two-User Interference Channel With a Cognitive Relay

This paper considers a variation of the classical two-user interference channel where the communication of two interfering source-destination pairs is aided by an additional node that has a priori knowledge of the messages to be transmitted, which is referred to as the cognitive relay. For this interference channel with a cognitive relay (ICCR), novel outer bounds and capacity region characterizations are derived. In particular, for the class of injective semi-deterministic ICCRs, a sum-rate upper bound is derived for the general memoryless ICCR and further tightened for the linear deterministic approximation (LDA) of the Gaussian noise channel at high SNR, which disregards the noise and focuses on the interaction among the users' signals. The capacity region of the symmetric LDA is completely characterized except for the regime of moderately weak interference and weak links from the CR to the destinations. The insights gained from the analysis of the LDA are then translated back to the symmetric Gaussian noise channel (GICCR). For the symmetric GICCR, an approximate characterization (to within a constant gap) of the capacity region is provided for a parameter regime where capacity was previously unknown. The approximately optimal scheme suggests that message cognition at a relay is beneficial for interference management as it enables simultaneous over the air neutralization of the interference at both destinations.

On the Capacity of the Multiantenna Gaussian Cognitive Interference Channel

The capacity of the multiantenna Gaussian cognitive interference channel is studied. The cognitive interference channel is a variation of the classical two-users interference channel in which one of the transmitters, the cognitive transmitter, is also provided with the message of the second transmitter, the primary transmitter. We study the capacity of the multiple-input multiple-output Gaussian model, that is the channel in which the inputs are vectors and the outputs are obtained as linear combinations of the channel inputs plus an additive complex Gaussian noise. This channel models a wireless scenario in which transmitters and receivers have multiple antennas. For this channel, we derive capacity to within an additive gap, that is we show that inner and outer bounds to capacity lie to within a constant distance of each other. The gap between the inner and outer bounds depends on the number of antennas at the cognitive receiver and both bounds can be easily evaluated by considering jointly Gaussian inputs. We also derive capacity to within a constant multiplicative factor of two, that is we show that the ratio between inner and outer bound is at most two. The additive gap well-characterizes the capacity at high SNR, while the multiplicative gap is useful at low SNR. We also derive the exact capacity for a subset of the "strong interference" regime: in this subset, the primary transmitter can decode the cognitive message without loss of optimality. This new capacity result extends and generalizes previously known capacity results, in particular, the capacity in the "very strong interference" and the "primary decodes cognitive" regimes.

Interactive Interference Alignment

We study interference channels (IFCs) where the interaction among sources and destinations is enabled, e.g., both sources and destinations can talk to each other using full-duplex radios. The interaction can come in two ways. First is through in-band interaction where sources and destinations can transmit and listen in the same channel simultaneously, enabling interaction. Second is through out-of-band interaction where destinations talk back to the sources on an out-of-band channel, which is possible from white-space channels. The flexibility afforded by the interaction among sources and destinations allows for the derivation of interference alignment (IA) strategies that have desirable “engineering properties,” i.e., insensitivity to the rationality or irrationality of channel parameters, small block lengths, and finite SNR operations. We show that, for several classes of IFCs, the interactive IA scheme can achieve the optimal degrees of freedom. In particular, we show a simple scheme (having a finite block length for channels having no diversity) for three-user and four-user IFCs with full-duplex radios to achieve the optimal degrees of freedom even after accounting for the cost of interaction. On the technical side, we show using a Gröbner basis argument that, in a general network potentially utilizing cooperation and feedback, the optimal degrees of freedom under linear schemes of a fixed block length is the same for channel coefficients with a probability of 1. Furthermore, a numerical method to estimate this value is also presented. These tools have potentially wider utility in studying other wireless networks as well.

On the Capacity of the Interference Channel With a Cognitive Relay

The interference channel with a cognitive relay (IFC-CR) consists of the classical IFC with two independent source-destination pairs whose communication are aided by an additional node, referred to as the CR, that has a priori knowledge of both sources' messages. This a priori message knowledge is termed cognition and idealizes the relay learning the messages of the two sources from their transmissions over a wireless channel. This paper presents improved outer and inner bounds on the capacity region of the general memoryless IFC-CR that are shown to be tight for certain classes of channels. The new outer bound follows from arguments originally devised for broadcast channels, among which Sato's observation that the capacity region of channels with noncooperative receivers only depends on conditional marginal distributions of the channel output, not on their conditional joint distribution. A simplified expression for the inner bound is derived, which contains all previously proposed coding schemes. The new inner and outer bounds coincide for a class of channels satisfying some strong interference condition, i.e., for these channels there is no loss in optimality if both destinations decode both messages. This result parallels analogous results for the classical interference channel and for the cognitive interference channel and is the first known capacity result for the general IFC-CR. Numerical evaluations of the proposed inner and outer bounds are presented for the additive white Gaussian noise case.

Bounds on the Capacity Region for a Class of Interference Channels With Common Information

An approximate capacity result is demonstrated for a specific class of interference channels with common information (IC-CI). The class is the semideterministic interference channel of Telatar and Tse, and the outer bound herein generalizes their bound from the case where each transmitter sends only private information to the case where each transmitter sends both private and common information to its corresponding receiver. It is shown that our outer bound is within a quantifiable gap of the inner bound of Jiang-Xin-Garg, a generalization of the Han-Kobayashi region to the IC-CI. Moreover, this result reproduces both the Telatar-Tse result in the case of no common information and a constant-gap-to-capacity result for the Gaussian IC-CI.

On the capacity of the cognitive interference channel with a common cognitive message

AbstractIn this paper, the cognitive interference channel with a common message, a variation of the classical cognitive interference channel in which the cognitive message is decoded at both receivers, is studied. For this channel model, new outer and inner bounds are developed as well as new capacity results for both the discrete memoryless and the Gaussian case. The outer bounds are derived using bounding techniques originally developed by Sato for the classical interference channel, and Nair and El Gamal for the broadcast channel. A general inner bound is obtained combining rate‐splitting, superposition coding, and binning. Inner and outer bounds are shown to coincide in the ‘very strong interference’ and the ‘primary decodes cognitive’ regimes. The first regime consists of channels in which there is no loss of optimality in having both receivers decode both messages, whereas in the latter regime, interference pre‐cancellation at the cognitive receiver achieves capacity. Capacity for the Gaussian channel is shown to within a constant additive gap and a constant multiplicative factor. The first result well characterises the capacity at high signal‐to‐noise ratio, whereas the latter at low signal‐to‐noise ratio. Copyright © 2013 John Wiley & Sons, Ltd.

A New Outer Bound for a Class of Interference Channels with a Cognitive Relay and a Certain Capacity Result

The interference channel with a cognitive relay is a variation of the classical two-user interference channel in which a relay aids the transmission among the users. The relay is assumed to have genie-aided cognition: that is it has full, a-priori, knowledge of the messages to be transmitted. We obtain a new outer bound for this channel model and prove capacity for a class of channels in which the transmissions of the two users are non interfering. This capacity result improves on a previous result for the Gaussian case in which the capacity was proved to within a gap of 3 bits/s/Hz.

On the Capacity of the $K$-User Cyclic Gaussian Interference Channel

This paper studies the capacity region of a K-user cyclic Gaussian interference channel, where the kth user interferes with only the (k-1)th user (mod K ) in the network. Inspired by the work of Etkin, Tse, and Wang, who derived a capacity region outer bound for the two-user Gaussian interference channel and proved that a simple Han-Kobayashi power-splitting scheme can achieve to within one bit of the capacity region for all values of channel parameters, this paper shows that a similar strategy also achieves the capacity region of the K-user cyclic interference channel to within a constant gap in the weak interference regime. Specifically, for the K-user cyclic Gaussian interference channel, a compact representation of the Han-Kobayashi achievable rate region using Fourier-Motzkin elimination is first derived; a capacity region outer bound is then established. It is shown that the Etkin-Tse-Wang power-splitting strategy gives a constant gap of at most 2 bits in the weak interference regime. For the special three-user case, this gap can be sharpened to 1 ½ bits by time-sharing of several different strategies. The capacity result of the K-user cyclic Gaussian interference channel in the strong interference regime is also given. Further, based on the capacity results, this paper studies the generalized degrees of freedom (GDoF) of the symmetric cyclic interference channel. It is shown that the GDoF of the symmetric capacity is the same as that of the classic two-user interference channel, no matter how many users are in the network.

Layered Coding for Interference Channels With Partial Transmitter Side Information

A two-user interference channel is considered where each transmitter has access to a part of the information intended to the other destination. A primary objective is to maximize the information rates, by exploring the cooperation between the transmitters for interference mitigation, based on the partial side information. It is clear that full cooperation between the transmitters is not possible since each transmitter has only a part of the side information. With this insight, several “layered coding” schemes, consisting of binning and superposition at different stages, are developed. These schemes are are carefully built on coding strategies for the classical interference channel and node cooperation mechanisms. In particular, two layered coding schemes, which are based on a combination of MIMO broadcast coding and the Han-Kobayashi (HK) coding, are thoroughly studied : The first one, namely layered coding with binning, makes heavy use of the Gelfand-Pinsker binning and the HK coding and the second one, namely layered superposition coding, involves superposition coding over different tiers. Rate regions corresponding to the proposed schemes are derived. Then the application of these coding schemes are illustrated for the Gaussian case and numerical results corroborate that the proposed layered coding schemes yield substantial gains at high SNR.

Interference Channels With Correlated Receiver Side Information

The problem of joint source-channel coding in transmitting independent sources over interference channels with correlated receiver side information is studied. When each receiver has side information correlated with its own desired source, it is shown that source-channel separation is optimal. When each receiver has side information correlated with the interfering source, sufficient conditions for reliable transmission are provided based on a joint source-channel coding scheme using the superposition encoding and partial decoding idea of Han and Kobayashi. When the receiver side information is a deterministic function of the interfering source, source-channel separation is again shown to be optimal. In addition to these source-channel coding problems, a new channel model that generalizes the classical interference channel is introduced: the interference channel with message side information. Achievable rate regions are given and a single letter characterization of the capacity region for a special class of Z-interference channels is provided. Using this capacity result and the optimality of source-channel separation, we demonstrate that our sufficient conditions for reliable transmission when each receiver has side information correlated with the interfering source are also necessary for some special cases. As a by-product, the capacity region of a class of Z-channels with degraded message sets is also provided.

Inner and Outer Bounds for the Gaussian Cognitive Interference Channel and New Capacity Results

The capacity of the Gaussian cognitive interference channel, a variation of the classical two-user interference channel where one of the transmitters (referred to as cognitive) has knowledge of both messages, is known in several parameter regimes but remains unknown in general. In this paper we provide a comparative overview of this channel model as we proceed through our contributions: we present a new outer bound based on the idea of a broadcast channel with degraded message sets, and another series of outer bounds obtained by transforming the cognitive channel into channels with known capacity. We specialize the largest known inner bound derived for the discrete memoryless channel to the Gaussian noise channel and present several simplified schemes evaluated for Gaussian inputs in closed form which we use to prove a number of results. These include a new set of capacity results for the a) "primary decodes cognitive" regime, a subset of the "strong interference" regime that is not included in the "very strong interference" regime for which capacity was known, and for the b) "S-channel" in which the primary transmitter does not interfere with the cognitive receiver. Next, for a general Gaussian cognitive interference channel, we determine the capacity to within one bit/s/Hz and to within a factor two regardless of channel parameters, thus establishing rate performance guarantees at high and low SNR, respectively. We also show how different simplified transmission schemes achieve a constant gap between inner and outer bound for specific channels. Finally, we numerically evaluate and compare the various simplified achievable rate regions and outer bounds in parameter regimes where capacity is unknown, leading to further insight on the capacity region of the Gaussian cognitive interference channel.

Distributed power allocation in multi-user multi-channel cellular relay networks

In this paper, we consider the amplify-and-forward relaying transmission in the downlink of a multi-channel cellular network with one base station and multiple relay-destination pairs. Spatial reuse of the relaying slot by allowing simultaneous transmissions from the relays is adopted to avoid the spectral loss incurred by the half-duplex relays. The relays are modeled as rational agents engaging in a non-cooperative game. In order to maximize its individual rate, each relay node iteratively allocates its power across different subchannels based on local information, while treating the signals from the other users as additive noise. First, we propose a distributed algorithm based on best response that is applicable in any signal to interference plus noise ratio (SINR) regions. Then, by focusing on the low SINR region, we propose a modified iterative water-filling algorithm. The existence of Nash equilibrium (NE) is guaranteed and the sufficient condition to reach a NE iteratively is determined. Next, we consider medium to high SINR regions and propose a distributed algorithm based on the sub-optimal response, which can be shown to reduce to the classic Gaussian interference channel model, for which analytical sufficient conditions for the convergence to the unique NE can be readily obtained. Finally, we extend the analysis to a general network topology wherein the users having different channel conditions coexist. The results show that, in low SINR regions, the proposed modified iterative water-filling algorithm yields a higher average sum rate than two simplified algorithms, i.e., the equal power allocation scheme and the conventional time-division based protocol, while in medium to high SINR regions, the sub-optimal-response based algorithm outperforms these two simplified algorithms in terms of the average sum rate

The Capacity Region of a Class of Semideterministic Interference Channels

The capacity region of a class of discrete memoryless interference channels with common information is established. The setup is similar to the class of deterministic interference channels without common information studied by El Gamal and Costa, which was later extended to the class of deterministic interference channels with common information. In this paper, certain conditions that were originally imposed by El Gamal and Costa are relaxed and it is shown, by a specific example, that this new class of interference channels is strictly larger than the class of deterministic interference channels previously studied. In fact, the result of this paper is obtained by combining the class of deterministic interference channels with the class of discrete memoryless interference channels with strong interference. Hence, it also includes the capacity region of the class of discrete memoryless interference channels with strong interference as a special case.