Two-user Interference Channel Research Articles

Topological Content Delivery With Feedback and Random Receiver Cache

We study the problem of content delivery in two-user interference channels with altering topology, random available cache at the receivers, and delayed channel knowledge at the transmitter. We establish a new set of outer-bounds on the achievable rates when each receiver has access to a random fraction of the message intended for the other receiver, and when each transmitter is aware of which part of its own message is known to the unintended receiver. The outer-bounds reveal the significant potential rate boost associated with even a small amount of side-information at each receiver. The key in deriving the bounds is to quantify the baseline entropy that will always become available to the unintended receiver given the altering topology and the already available side-information. We will also present matching achievable rates in certain scenarios and outline the challenges in more general settings.

Adding Common Randomness Can Remove the Secrecy Penalty in GDoF

In communication networks secrecy constraints usually incur an extra limit in capacity or generalized degrees-of-freedom (GDoF), in the sense that a penalty in capacity or GDoF is incurred due to the secrecy constraints. Over the past decades a significant amount of effort has been made by the researchers to understand the limits of secrecy constraints in communication networks. In this work, we focus on how to remove the secrecy penalty in communication networks, i.e., how to remove the GDoF penalty due to secrecy constraints. We begin with three basic settings: a two-user symmetric Gaussian interference channel with confidential messages, a symmetric Gaussian wiretap channel with a helper, and a two-user symmetric Gaussian multiple access wiretap channel. Interestingly, in this work we show that adding common randomness at the transmitters can totally remove the penalty in GDoF or GDoF region of the three settings considered here. The results reveal that adding common randomness at the transmitters is a powerful way to remove the secrecy penalty in communication networks in terms of GDoF performance. Common randomness can be generated offline before the real-time message communication. The role of the common randomness is to jam the information signal at the eavesdroppers, without causing too much interference at the legitimate receivers. To accomplish this role, a new method of Markov chain-based interference neutralization is proposed in the achievability schemes utilizing common randomness. From the practical point of view, we need to minimize the amount of common randomness used for removing the secrecy penalty in terms of GDoF performance. With this motivation, for most of the cases we characterize the minimal GDoF of common randomness to remove secrecy penalty, based on our derived converses and achievability.

Distributed Interference Management: A Broadcast Approach

Effective interference management in the multiuser interference channel strongly hinges on the channel state information’s availability at the transmitters (CSIT). In a broad range of emerging large-scale and distributed networks (e.g., the Internet of Things), acquiring the CSIT is prohibitive due to the extensive information exchange that it imposes. As a result, the interference management approaches that rely on the CSIT lose their effectiveness in such circumstances. This article focuses on the two-user interference channel and proposes a broadcast approach to interference management. Its hallmark is that the transmitters, unlike the receivers, are entirely oblivious to instantaneous channel states. Each transmitter splits its message into multiple superimposed encoded information layers, where each layer is adapted to a given possible state for the combined states of all channels. Depending on the relative gain between the direct and interfering channels, each receiver opportunistically decodes a subset of both transmitters’ received layers. An average achievable rate region is delineated, serving as an inner bound on the Gaussian interference channel’s average capacity region in the absence of CSIT. Finally, an upper bound on the gap between the achievable sum-rate and the sum-rate capacity is established.

Sliding-Window Superposition Coding: Two-User Interference Channels

A low-complexity coding scheme is developed to achieve the rate region of maximum likelihood decoding for interference channels. As in the classical rate-splitting multiple access scheme by Grant, Urbanke, and Whiting, the proposed coding scheme uses superposition of multiple codewords with successive cancellation decoding, which can be implemented using standard point-to-point encoders and decoders. Unlike rate-splitting multiple access, which is not rate-optimal for multiple receivers, the proposed coding scheme transmits codewords over multiple blocks in a staggered manner and recovers them successively over sliding decoding windows, achieving the single-stream optimal rate region as well as the more general Han–Kobayashi inner bound for the two-user interference channel. The feasibility of this scheme in practice is verified by implementing it using commercial channel codes over the two-user Gaussian interference channel.

Common Throughput Maximization for UAV-Enabled Interference Channel With Wireless Powered Communications

This paper studies an unmanned aerial vehicle (UAV)-enabled two-user interference channel for wireless powered communication networks (WPCNs), in which two UAVs wirelessly charge two low-power Internet-of-things (IoT)-devices on the ground and collect information from them. We consider two scenarios when both UAVs cooperate in energy transmission and/or information reception via interference coordination and coordinated multi-point (CoMP), respectively. For both scenarios, the UAVs' controllable mobility is exploited via trajectory design to not only enhance the wireless power transfer (WPT) efficiency in the downlink, but also mitigate the co-channel interference for wireless information transfer (WIT) in the uplink. In particular, the objective is to maximize the uplink common (minimum) throughput of the two IoT-devices over a finite UAV mission period, by jointly optimizing the trajectories of both UAVs and the downlink/uplink wireless resource allocation, subject to the maximum flying speed and collision avoidance constraints at UAVs, as well as the individual energy neutrality constraints at IoT-devices. Under both scenarios of interference coordination and CoMP, we first obtain the optimal solutions to the two common-rate maximization problems in well structures for the special case with sufficiently long UAV mission duration. Next, we obtain high-quality solutions for the practical case with finite UAV mission duration by using the alternating optimization and successive convex approximation (SCA).

Secure Degrees of Freedom of Rank-Deficient BCCM and Rank-Deficient ICCM

The secure degrees of freedom (SDoF) of two-user rank-deficient multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and two-user rank- deficient MIMO interference channel with confidential messages (ICCM) are studied respectively in this paper. In the systems, each transmitter has $M$ antennas, and each receiver has $N$ antennas. We consider that each transmitter intends to send secure messages to the corresponding receiver, and another receiver can receive the messages but cannot decode them, which ensures that the messages are confidential. Comparing with previous studies on two-user broadcast channel and interference channel, we explore the case that channel matrices are rank-deficient, and the rank of channel matrices can take arbitrary value, $D \leq \text{min} (M,N)$ . For the two rank-deficient channels, BCCM and ICCM, we divide the problem into several regimes according to the different configurations of the rank of channel matrices and the number of antennas at each node. The outer bound of rank-deficient BCCM is inferred from information theoretic methods and the achievable schemes are given by zero forcing techniques. We derive the outer bound of rank-deficient ICCM by taking the minimum region of the three outer bounds, where the first outer bound is the result of rank-deficient interference channel model without secrecy constraints, the second outer bound is obtained by considering secrecy constraints, and the third outer bound is achieved by transmitters cooperation. Then we present the achievable schemes by combining zero-forcing, real interference alignment, and spatial alignment. Finally, we determine the exact SDoF of the rank-deficient BCCM and the rank-deficient ICCM.

Coding for Two-User Energy Harvesting Interference Channel

A two-user interference channel with energy harvesting transmitters, each equipped with a finite battery, is considered. Achievable rate regions (ARRs) considering independent and identically distributed Shannon strategies at both users and ignoring the memory in the battery state are obtained for both single-user decoding and joint decoding at the receivers. Explicit and implementable codes based on concatenation of a nonlinear trellis code (NLTC) with an outer low-density parity-check code are designed, and it is demonstrated that rate pairs close to the boundary of ARR can be obtained with this approach. Furthermore, an improved alternative decoding scheme which exploits the memory in the battery state is developed, and it is shown to be highly superior to the simple decoding approach via numerical examples. Superiority of the newly developed practical channel coding solutions over the previously known alternative approaches are illustrated via extensive set of examples as well.

Novel Outer Bounds and Capacity Results for the Interference Channel With Conferencing Receivers

In this paper, capacity bounds for the two-user interference channels with cooperative receivers via conferencing links of finite capacities are investigated. Capacity results known for these communication scenarios are limited to a very few special cases of the one-sided channels. One of the challenges in obtaining capacity limits of such cooperative networks is how to establish efficient capacity outer bounds for them. In this paper, by applying new techniques, novel capacity outer bounds are established for the interference channels with conferencing receivers. Using the outer bounds, several new capacity results are proved for interesting channels with unidirectional cooperation in strong and mixed interference regimes. A conferencing link (between receivers) may be utilized to provide a receiver with “information about its desired signal” or “information about its interfering signal”. It is demonstrated that both strategies can be helpful to achieve capacity. Finally, for the case of Gaussian interference channel with conferencing receivers, it is argued that our outer bound is strictly tighter than the previous one derived by Wang and Tse.

Improper Signaling for SISO Two-User Interference Channels With Additive Asymmetric Hardware Distortion

Hardware non-idealities are among the main performance restrictions for upcoming wireless communication systems. Asymmetric hardware distortions (HWD) happen when the impairments of the I/Q branches are correlated or imbalanced, which in turn generate improper additive interference at the receiver side. When the interference is improper, as well as in other interference-limited scenarios, improper Gaussian signaling (IGS) has been shown to provide rate and/or power efficiency benefits. In this paper, we investigate the rate benefits of IGS in a two-user interference channel (IC) with additive asymmetric HWD when interference is treated as noise. We propose two iterative algorithms to optimize the parameters of the improper transmit signals. We first rewrite the rate region as an pseudosignal-to-interference-plus-noise-ratio (PSINR) region and employ majorization minimization and fractional programming to find a suboptimal solution for the achievable user rates. Then, we propose a simplified algorithm based on a separate optimization of the powers and complementary variances of the users, which exhibits lower computational complexity. We show that IGS can improve the performance of the two-user IC with additive HWD. Our proposed algorithms outperform proper Gaussian signaling and competing IGS algorithms in the literature that do not consider asymmetric HWD.

Delay in Cooperative Communications: Achieving Higher Multiplexing Gain in Gaussian Interference Channels With Full-Duplex Transmitters

Delay, guaranteeing causality, is inevitable in cooperative communication systems. Traditionally, delay granularity has been limited to one symbol; however, channel delay is in fact governed by channel memory and can be shorter. For example, the delay requirement in orthogonal frequency-division multiplexing, captured in the cyclic prefix, is typically much shorter than the symbol itself. This perspective is used to study the two-user Gaussian interference channel with full-duplex transmitters. By superimposing the signal from the other node onto its own signal, each transmitter cancels the interference at its receiver. Among other results, it is proved that under a mild condition, the maximum multiplexing gain of this channel is in fact two, rather than the limit of one, previously shown under the traditional constraint of causal delay. Further, the optimal power allocation among orthogonal sub-carriers, which maximizes the achievable sum-rate, is shown to be a generalization of the well-known water filling. Simulation results are included to demonstrate the improvement in the achievable sum-rate when full-duplex transmitters are used.

Positioning Optimization for Sum-Rate Maximization in UAV-Enabled Interference Channel

This letter studies an unmanned aerial vehicle (UAV)enabled two-user interference channel, in which two ground users send individual messages to their respective UAVs in the sky. By considering probabilistic line-of-sight (LoS) channel models, we jointly optimize the two UAVs' three-dimensional (3D) positioning locations and the two users' power control, to maximize their sumrate throughput. Although this problem is non-convex and difficult to solve in general, we obtain the optimal solution by decoupling the positioning optimization and power control. The optimal solution shows that if the signal-to-noise-ratio (SNR) ρ is high, then the two users should take turns to transmit at the maximum power in anonoff manner and each UAV is positioned exactly above the associated user. By contrast, if ρ is low and/or the two users' distance D is large, then the two users should transmit simultaneously at the maximum power, and each UAV should be positioned away from the two users for interference mitigation.

Robust Improper Signaling for Two-User SISO Interference Channels

It has been shown that improper Gaussian signaling (IGS) can improve the performance of wireless interference-limited systems when perfect channel-state information (CSI) is available. In this paper, we investigate the robustness of IGS against imperfect CSI on the transmitter side in a two-user single-input single-output (SISO) interference channel (IC) as well as in a SISO Z-IC, when interference is treated as noise. We assume that the true channel coefficients belong to a known region around the channel estimates, which we call the uncertainty region. Following a worst-case robustness approach, we study the rate-region boundary of the IC for the worst channel in the uncertainty region. For the two-user IC, we derive a robust design in closed form, which is independent of the phase of the channels by allowing only one of the users to transmit IGS. For the Z-IC, we provide a closed-form design for the transmission parameters by considering an enlarged uncertainty region and allowing both users to employ IGS. In both cases, the IGS-based designs are ensured to perform no worse than proper Gaussian signaling. Furthermore, we show, through numerical examples, that the proposed robust designs significantly outperform non-robust solutions.

Strong Converses are Just Edge Removal Properties

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.

Polar Coding Strategies for the Interference Channel With Partial-Joint Decoding

Existing polar coding schemes for the two-user interference channel follow the original idea of Han and Kobayashi, in which component messages are encoded independently and then mapped by some deterministic functions (i.e., homogeneous superposition coding). In this paper, we propose a new polar coding scheme for the interference channel based on the heterogeneous superposition coding approach of Chong, Motani, and Garg. We prove that fully joint decoding (the receivers simultaneously decode both senders’ common messages and the intended sender’s private message) in the Han–Kobayashi strategy can be simplified to two types of partial-joint decoding, which are friendly to polar coding with practical decoding algorithms. The proposed coding scheme requires less auxiliary random variables and no deterministic functions and can be efficiently constructed. Furthermore, we extend this result to interference networks and show that partial-joint decoding is a general method for designing heterogeneous superposition polar coding schemes in interference networks.

A Unified Theory of Multiple-Access and Interference Channels via Approximate Capacity Regions for the MAC-IC-MAC

Approximate capacity regions are established for a class of interfering multiple access channels consisting of two multiple-access channels (MACs), each with an arbitrary number of transmitters, with one transmitter in each MAC causing interference to the receiver of the other MAC, a channel we refer to henceforth as the MAC-IC-MAC. For the discrete memory-less (DM) MAC-IC-MAC, two inner bounds are obtained that are generalizations of prior inner bounds for the two-user DM interference channel (IC) due to Chong et al. For the semi-deterministic MAC-IC-MAC, it is shown that single-user coding at the non-interfering transmitters and superposition coding at the interfering transmitter of each MAC achieves a rate region that is within a quantifiable gap of the capacity region, thereby extending such a result for the two-user semi-deterministic IC by Telatar and Tse. For the Gaussian MAC-IC-MAC, an approximate capacity region that is within a constant gap of the capacity region is obtained, generalizing such a result for the two-user Gaussian IC by Etkin et al. On contrary to the aforementioned approximate capacity results for the two-user IC, whose achievability requires the union of all admissible input distributions, our gap results on the semi-deterministic and the Gaussian MAC-IC-MAC are achievable by only a subset and one of all admissible coding distributions, respectively. The symmetric generalized degrees of freedom (GDoFs) of the symmetric Gaussian MAC-IC-MAC with more than one user per cell, which is a function of the interference strength (the ratio of INR to SNR at high SNR, both expressed in dB) and the numbers of users in each cell, are V-shaped with flat shoulders. An analysis based on signal-level partitions shows that the non-interfering transmitters utilize the signal-level partitions at the receiver where they are intended that cannot be accessed by the interfering transmitters (due to the restriction of superposition coding), thereby improving the sum symmetric GDoF of up to one degree of freedom per cell under a range of SINR exponent levels, which in turn becomes wider as the number of transmitters in each cell increases. Consequently, time-sharing between interfering and non-interfering transmitters is GDoF-suboptimal in general, as is time-sharing between the two embedded MAC-Z-MACs.

Adding a Helper Can Totally Remove the Secrecy Constraints in a Two-User Interference Channel

In many communication channels, secrecy constraints usually incur a penalty in capacity, as well as generalized degrees-of-freedom (GDoF). In this paper, we show an interesting observation that adding a helper can totally remove the penalty in sum GDoF for a two-user symmetric Gaussian interference channel. For the interference channel where each transmitter sends a message to an intended receiver without secrecy constraints, the sum GDoF is a well-known “W” curve, characterized by Etkin–Tse–Wang in 2008. If the secrecy constraints are imposed on this interference channel, where the message of each transmitter must be secure from the unintended receiver (eavesdropper), then a GDoF penalty is incurred and the secure sum GDoF is reduced to a modified “W” curve, derived by Chen recently. In this paper, we show that, by adding a helper into this interference channel with secrecy constraints, the secure sum GDoF turns out to be a “W” curve, which is the same as the sum GDoF of the setting without secrecy constraints. The proposed scheme is based on the cooperative jamming and a careful signal design such that the jamming signal of the helper is aligned at a specific direction and power level with the information signals of the transmitters, which allows us to totally remove the penalty in GDoF due to the secrecy constraints. Furthermore, the estimation approaches of noise removal and signal separation due to the rational independence are used in the secure rate analysis.

Stable Throughput Region of the Two-User Interference Channel

We consider the two-user interference channel where two independent pairs communicate concurrently and investigate its stable throughput region. First, the stability region is characterized for the general case, i.e., without any specific consideration on the transmission and reception structures. Second, we explore two different interference harnessing strategies at the receiver: treating interference as noise and successive interference cancellation. Furthermore, we provide conditions for the convexity of the stability region and for which a certain receiver strategy leads to broader stability region. The impact of multiple transmit antennas on the stability region is briefly discussed. Finally, we study the effect of random access on the stability region of the two-user interference channel.

Interference Cancellation Through Interference Forwarding in Relay-Assisted Systems

Interference forwarding and multiuser (MU) codes are potential solutions to manage moderate interference. In particular, MU codes based simplified Han-Kobayashi (SHK) scheme is known to achieve sum-rate within one bit of outer bound for a two-user interference channel. However, if each user has its own quality-of-service requirements, it is unknown whether the SHK scheme performs better compared to that of single-user (SU) codes. We investigate whether the SHK scheme with full-duplex decode-and-forward relay can achieve better diversity gain than SU codes for altruistic and selfish modes. In the altruistic mode, the interfering transmitter lets the interference-limited receiver operate at the interference-free diversity order, and in selfish mode, the interfering transmitter optimizes its receiver's diversity order. In both modes, the SHK scheme is shown to provide better diversity gain region (DGR) than the SU codes based transmission scheme only if the interference is weak and the multiplexing gain of the interference is high. Moreover, if the self-interference is not eliminated, relay based SHK protocol cannot operate in selfish mode and also, the multiplexing gain region where the relay based SHK scheme achieves better DGR than other schemes reduces.

The Degrees of Freedom of the Interference Channel With a Cognitive Relay Under Delayed Feedback

This paper studies the interference channel with a cognitive relay under delayed feedback. Three types of delayed feedback are studied: delayed channel state information at the transmitter, delayed output feedback, and delayed Shannon feedback. Outer bounds are derived for the degrees of freedom (DoF) region of the two-user multiple-input multiple-output interference channel with a cognitive relay with delayed feedback as well as without feedback. For the single-input single-output scenario, optimal schemes are proposed based on retrospective interference alignment. It is shown that while a cognitive relay without feedback cannot improve the sum-DoF in the two-user single-input single-output interference channel, delayed feedback in the same scenario can increase the sum-DoF to $4/3$ . For the multiple-input multiple-output case, achievable schemes are obtained via extensions of retrospective interference alignment, leading to the DoF regions that meet the respective upper bounds.

On the High-SNR Capacity of the Gaussian Interference Channel and New Capacity Bounds

The best outer bound on the capacity region of the two-user Gaussian interference channel (GIC) is known to be the intersection of regions of various bounds, including genie-aided outer bounds, in which a genie provides noisy input signals to the intended receiver. The Han and Kobayashi (HK) scheme provides the best known inner bound. The rate difference between the best known lower and upper bounds on the sum capacity remains as large as 1 b/channel use, especially around $g^{2}=P^{-1/3}$ , where $P$ is the symmetric power constraint and $g$ is the symmetric real cross-channel coefficient. In this paper, we pay attention to the moderate interference regime where $g^{2}\in ~(\max (0.086, P^{-1/3}),1)$ . We propose a new upper-bounding technique that utilizes noisy observation of interfering signals as genie signals and applies time sharing to the genie signals at the receivers. A conditional version of the worst additive noise lemma is also introduced to derive new capacity bounds. The resulting upper (outer) bounds on the sum capacity (capacity region) are shown to be tighter than the existing bounds in a certain range of the moderate interference regime. Using the new upper bounds and the HK lower bound, we show that $R_{\text {sym}}^{*}=\frac {1}{2}\log \big (|g|P+|g|^{-1}(P+1)\big )$ characterizes the capacity of the symmetric real GIC to within 0.104 b/channel use in the moderate interference regime at any signal-to-noise ratio (SNR). We further establish a high-SNR characterization of the symmetric real GIC, where the proposed upper bound is at most 0.1 b far from a certain HK achievable scheme with Gaussian signalling and time sharing for $g^{2}\in ~(0,1]$ . In particular, $R_{\text {sym}}^{*}$ is achievable at high SNR by the proposed HK scheme and turns out to be the high-SNR capacity at least at $g^{2}=0.25, 0.5$ . We finally point out that there are two subregimes at high SNR in the weak interference regime, where $g^{2}\in (0,1]$ .