New Observations on Interference Channels under Strong and Very Strong Interference

The capacity region of a class of discrete memoryless interference channels is established. The setup is similar to the class of deterministic interference channels studied by El Gamal and Costa. However, we relax certain conditions that were imposed by El Gamal and Costa. The capacity region of this class of interference channels also includes the capacity region of the discrete memoryless interference channels with strong interference. Finally, we extend the result to the case where both transmitters have a common message to transmit.

This paper studies the capacity of a class of discrete memoryless interference channels (DMICs), where interference is defined analogous to that of a Gaussian interference channel with one-sided weak interference. The sum-rate capacity of this class of channels is determined. As with the Gaussian case, the sum-rate capacity is achieved by letting the transceiver pair subject to interference communicate at a rate such that its message can be decoded at the unintended receiver using single user detection. It is also established that this class of DMICs is equivalent in capacity region to certain degraded interference channels. This allows the construction of capacity outer-bounds using the capacity regions of associated degraded broadcast channels. The same technique is then used to determine the sum-rate capacity of DMICs with mixed interference as defined in this paper. The obtained capacity bounds and sum-rate capacities are used to resolve the capacities of several new DMICs.

This work proposes a new coding scheme for the discrete memoryless two-user interference channel whose receivers can cooperate to decode their desired messages. The coding scheme is built upon Han-Kobayashi rate splitting and superposition coding at the transmitters, noisy network coding, and non-unique joint decoding at the receivers. As a case study the general achievable region leads to an inner bound for the Gaussian interference channel whose receivers cooperate through rate-limited orthogonal channels. It is shown that this inner bound is equivalent to the one-round quantize-bin-and-forward inner bound established by Wang and Tse, thereby showing that noisy network coding achieves within 1 bit/s/Hz to the capacity region when the interference is strong, and achieves within 1 bit/s/Hz to the capacity region of the Gaussian compound multiple access channel with conferencing decoders regardless of channel parameters.

The second-order asymptotics of the Gaussian interference channel in the strictly very strong interference regime are considered. The rates of convergence to a given point on the boundary of the (first-order) capacity region are determined. These rates are expressed in terms of the average probability of error and variances of selected modified information densities which coincide with the dispersion of the (single-user) Gaussian channel. Interestingly, under the strictly very strong interference assumption, the intuition that receivers can decode messages from non-intended transmitters carries over to the second-order analysis.

The N +1 user, 1 ×N single-input multiple-output (SIMO) Gaussian interference channel where each transmitter has a single antenna and each receiver has N antennas is studied. The sum capacity within O(1) is characterized for the symmetric case where all direct links have the same signal-to-noise ratio (SNR) and all undesired links have the same interference-to-noise ratio (INR). The gap to the exact capacity is a constant which is independent of SNR and INR. To get this result, we first generalize the deterministic interference channel introduced by El Gamal and Costa to model interference channels with multiple antennas. We derive the capacity region of this deterministic interference channel. Based on the insights provided by the deterministic channel, we characterize the generalized degrees of freedom (GDOF) of Gaussian case, which directly leads to the O(1) capacity approximation. On the achievability side, an interesting conclusion is that the GDOF regime where treating interference as noise is found to be optimal in the two-user interference channel, does not appear in the N + 1 user, 1 × N SIMO case. On the converse side, new multiuser outer bounds emerge out of this work that do not follow directly from the two-user case. In addition to the GDOF region, the outer bounds identify a strong interference regime where the capacity region is established.

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.

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.

A Gaussian interference channel (IC) with a relay is considered. The relay is assumed to operate over an orthogonal band with respect to the underlying IC, and the overall system is referred to as IC with an out-of-band relay (IC-OBR). The system can be seen as operating over two parallel interference-limited channels: The first is a standard Gaussian IC and the second is a Gaussian relay channel characterized by two sources and destinations communicating through the relay without direct links. We refer to the second parallel channel as OBR Channel (OBRC). The main aim of this work is to identify conditions under which optimal operation, in terms of the capacity region of the IC-OBR, entails either signal relaying and/or interference forwarding by the relay, with either a separable or nonseparable use of the two parallel channels, IC, and OBRC. Here, “separable” refers to transmission of independent information over the two constituent channels. For a basic model in which the OBRC consists of four orthogonal channels from sources to relay and from relay to destinations (IC-OBR Type-I), a condition is identified under which signal relaying and separable operation is optimal. This condition entails the presence of a relay-to-destinations capacity bottleneck on the OBRC and holds irrespective of the IC. When this condition is not satisfied, various scenarios, which depend on the IC channel gains, are identified in which interference forwarding and nonseparable operation are necessary to achieve optimal performance. In these scenarios, the system exploits the “excess capacity” on the OBRC via interference forwarding to drive the IC-OBR system in specific interference regimes (strong or mixed). The analysis is then turned to a more complex IC-OBR, in which the OBRC consists of only two orthogonal channels, one from sources to relay and one from relay to destinations (IC-OBR Type-II). For this channel, some capacity resuls are derived that parallel the conclusions for IC-OBR Type-I and point to the additional analytical challenges.

We investigate the secure degrees of freedom (s.d.o.f.) of two new channel models: broadcast channel with combating helpers and interference channel with selfish users. 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. The goal of introducing these channel models is to investigate various malicious interactions that arise in networks, including active adversaries. 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.

This study investigates the capacity region of a three-user cognitive radio network with two primary users and one cognitive user. A three-user cognitive interference channel (C-IFC) is proposed by considering a three-user interference channel (IFC) where one of the transmitters has cognitive capabilities and knows the messages of the other two transmitters in a non-causal manner. First, two inner bounds on the capacity region of the three-user C-IFC are obtained based on using the schemes which allow all receivers to decode all messages with two different orders. Next, two sets of conditions are derived, under which the capacity region of the proposed model coincides with the capacity region of a three-user C-IFC in which all three messages are required at all receivers. Under these conditions, referred to as strong interference conditions, the capacity regions for the proposed three-user C-IFC are characterised. Moreover, the Gaussian three-user C-IFC is considered and the capacity results are derived for the Gaussian case. Some numerical examples are also provided.

This paper explores the relationship between two ideas in the network information theory: edge removal and strong converses. Edge removal properties state that if an edge of small capacity is removed from a network, the capacity region does not change too much. Strong converses state that, for rates outside the capacity region, the probability of error converges to 1 as the blocklength goes to infinity. Various notions of edge removal and strong converse are defined, depending on how edge capacity and error probability scale with blocklength, and relations between them are proved. Each class of strong converse implies a specific class of edge removal. The opposite directions are proved for deterministic networks. Furthermore, a technique based on a novel, causal version of the blowing-up lemma is used to prove that for discrete memoryless networks, the weak edge removal property—that the capacity region changes continuously as the capacity of an edge vanishes—is equivalent to the exponentially strong converse—that outside the capacity region, the probability of error goes to 1 exponentially fast. This result is used to prove exponentially strong converses for several examples, including the discrete two-user interference channel with strong interference, with only a small variation from traditional weak converse proofs.

In this paper, we introduce discrete memoryless Interference Channel (IFC) with two relays as two interfering transmitter-receiver pairs that are aided by two relays. We propose two different coding strategies for this channel. In the first strategy, we assume that each relay tries to mainly help one of the transmitter-receiver pairs through signal relaying and interference cancellation, while in the second strategy we assume that each relay tries to help both transmitter-receiver pairs. In our coding schemes, we employ rate-splitting, generalized block Markov coding, superposition coding and Gel'fand-Pinsker binning to cancel parts of the interference known to be experienced at the receivers. The derived achievable rate regions can be specialized to new achievable rate regions for discrete memoryless IFC with a relay. Under special conditions, the derived achievable rate regions also reduce to some previously known ones.

The capacity of a network in which a multiple access channel (MAC) generates interference to a single-user channel is studied. An achievable rate region based on superposition coding and joint decoding is established for the discrete case. If the interference is strong, the capacity region is obtained for both the discrete memoryless channel and Gaussian channel. A boundary point of the capacity region is determined for a subclass of Gaussian channels with mixed interference.

In a multi-user channel, completion time refers to the number of channel uses required for users, each with some given fixed bit pool, to complete the transmission of all their data bits. This paper extends the information theoretic formulation of multi-access completion time to broadcast channel and interference channel, enabling us to obtain the so-called completion time region (CTR), which, analogous to capacity region, characterizes all possible trade-offs between users' completion times. Specifically, for Gaussian broadcast channel (GBC) and Gaussian interference channel (GIC) in the strong/very strong regime, the exact CTR is obtained. For GIC in the weak/mixed regime, an achievable CTR based on the Etkin-Tse-Wang scheme and an outer-bound are obtained.

In this overview paper, we introduce an application of stochastic orders in wireless communications. In particular, we show how to use stochastic orders to investigate the ergodic capacity results for fast fading Gaussian memoryless multiuser channels when only the statistics of the channel state information are known at the transmitters (CSIT). In general, the characterization of the capacity region of multiuser channels with only statistical CSIT is open. To attain our goal, in this work we resort to classifying the random channels through their probability distributions by which we can obtain the capacity results. To be more precise, we derive sufficient conditions to attain some information theoretic channel orders such as degraded and very strong interference by exploiting the usual stochastic order and exploiting the same marginal property. After that, we apply the developed scheme to Gaussian interference channels and Gaussian broadcast channels. We also extend the framework to channels with multiple antennas. Possible scenarios for channel enhancement under statistical CSIT are also discussed. Several practical examples such as Rayleigh fading and Nakagami-m fading, etc., illustrate the application of the derived results.