Certain deterministic interference channels have been shown to accurately model Gaussian interference channels in the asymptotic low-noise regime. Motivated by this correspondence, we investigate a K user-pair, cyclically symmetric, deterministic interference channel in which each receiver experiences interference only from its neighboring transmitters (Wyner model). We establish the sum capacity for a large set of channel parameters, thus generalizing previous results for the 2-pair case.
This work presents novel achievable schemes for the 2-user symmetric linear deterministic interference channel with limited-rate transmitter cooperation and perfect secrecy constraints at the receivers. The proposed achievable scheme consists of a combination of interference cancelation, relaying of the other user's data bits, time sharing, and transmission of random bits, depending on the rate of the cooperative link and the relative strengths of the signal and the interference. The results show, for example, that the proposed scheme achieves the same rate as the capacity without the secrecy …
We propose the idea of extended networks, which is constructed by replicating the users in the two-user deterministic interference channel (DIC) and designing the interference structure among them, such that any rate that can be achieved by each user in the original network can also be achieved simultaneously by all replicas of that user in the extended network. We demonstrate that by carefully designing extended networks and applying the generalized cut-set (GCS) bound to them, we can derive a tight converse for the two-user DIC. Furthermore, we generalize our techniques to the three-user DIC…
In this paper, the $η$-Nash equilibrium ($η$-NE) region of the two-user linear deterministic interference channel (IC) with noisy channel-output feedback is characterized for all $η> 0$. The $η$-NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an $η$-NE. More specifically, given an $η$-NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than $η$ bits per channel use. Existing results such as the $η$-NE region of the…
In this paper the study of 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. We derive the capacity for the semideterministic channel in which the output at the cognitive decoder is a deterministic function of the channel inputs. We also show capacity to within a constant gap and a constant factor for the Gaussian channel in which the outputs are linear combinations of the channel inputs plus an additive Gaussian noise term. Most of these results are shown using an i…
In this paper, we study the capacity of the two-user multiple-input multiple-output (MIMO) linear deterministic interference channel (IC), with possible correlations within/between the channel matrices. The capacity region is characterized in terms of the rank of the channel matrices. It is shown that \emph{linear precoding} with Han-Kobayashi type of rate-splitting, i.e., splitting the information-bearing symbols of each user into common and private parts, is sufficient to achieve all the rate pairs in the derived capacity region. The capacity result is applied to obtain an achievable rate re…
It has been shown recently by Geng et al. that in a $K$ user Gaussian interference network, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all signal strengths measured in dB scale), then power control and treating interference as noise (TIN) is sufficient to achieve the entire generalized degrees of freedom (GDoF) region. Motivated by the intuition that the deterministic model of Avestimehr et al. (ADT deterministic model) is particularly suited for exploring the op…
We characterize the capacity region of the symmetric injective K-user Deterministic Interference Channel (DIC) for all channel parameters. The achievable rate region is derived by first projecting the achievable rate region of Han-Kobayashi (HK) scheme, which is in terms of common and private rates for each user, along the direction of aggregate rates for each user (i.e., the sum of common and private rates). We then show that the projected region is characterized by only the projection of those facets in the HK region for which the coefficient of common rate and private rate are the same for …
In this technical report, the capacity region of the two-user linear deterministic (LD) interference channel with noisy output feedback (IC-NOF) is fully characterized. This result allows the identification of several asymmetric scenarios in which implementing channel-output feedback in only one of the transmitter-receiver pairs is as beneficial as implementing it in both links, in terms of achievable individual rate and sum-rate improvements w.r.t. the case without feedback. In other scenarios, the use of channel-output feedback in any of the transmitter-receiver pairs benefits only one of th…
Interference alignment is a key technique for communication scenarios with multiple interfering links. In several such scenarios, interference alignment was used to characterize the degrees-of-freedom of the channel. However, these degrees-of-freedom capacity approximations are often too weak to make accurate predictions about the behavior of channel capacity at finite signal-to-noise ratios (SNRs). The aim of this paper is to significantly strengthen these results by showing that interference alignment can be used to characterize capacity to within a constant gap. We focus on real, time-invar…
In this paper, the capacity region of the two-user linear deterministic (LD) interference channel with noisy output feedback (IC-NOF) is fully characterized. This result allows the identification of several asymmetric scenarios in which imple- menting channel-output feedback in only one of the transmitter- receiver pairs is as beneficial as implementing it in both links, in terms of achievable individual rate and sum-rate improvements w.r.t. the case without feedback. In other scenarios, the use of channel-output feedback in any of the transmitter-receiver pairs benefits only one of the two pa…
In this work, the role of unidirectional limited rate transmitter cooperation is studied in the case of the 2-user Z interference channel (Z-IC) with secrecy constraints at the receivers, on achieving two conflicting goals simultaneously: mitigating interference and ensuring secrecy. First, the problem is studied under the linear deterministic model. The achievable schemes for the deterministic model use a fusion of cooperative precoding and transmission of a jamming signal. The optimality of the proposed scheme is established for the deterministic model for all possible parameter settings usi…
We establish an achievable rate region for discrete memoryless interference relay channels that consist of two source-destination pairs and one or more relays. We develop an achievable scheme combining Han-Kobayashi and noisy network coding schemes. We apply our achievability to two cases. First, we characterize the capacity region of a class of discrete memoryless interference relay channels. This class naturally generalizes the injective deterministic discrete memoryless interference channel by El Gamal and Costa and the deterministic discrete memoryless relay channel with orthogonal receive…
The best known inner bound for the 2-user discrete memoryless interference channel is the Han-Kobayashi rate region. The coding schemes that achieve this region are based on rate-splitting and superposition coding. In this paper, we develop a multicoding scheme to achieve the same rate region. A key advantage of the multicoding nature of the proposed coding scheme is that it can be naturally extended to more general settings, such as when encoders have state information or can overhear each other. In particular, we extend our coding scheme to characterize the capacity region of the state-depen…
In this paper, we study the impact of different channel output feedback architectures on the capacity of the two-user interference channel. For a two-user interference channel, a feedback link can exist between receivers and transmitters in 9 canonical architectures (see Fig. 2), ranging from only one feedback link to four feedback links. We derive the exact capacity region for the symmetric deterministic interference channel and the constant-gap capacity region for the symmetric Gaussian interference channel for all of the 9 architectures. We show that for a linear deterministic symmetric int…
This paper derives outer bounds on the secrecy capacity region of the 2-user Z interference channel (Z-IC) with rate-limited unidirectional cooperation between the transmitters. First, the model is studied under the linear deterministic setting. The derivation of the outer bounds on the secrecy capacity region involves careful selection of the side information to be provided to the receivers and using the secrecy constraints at the receivers in a judicious manner. To this end, a novel partitioning of the encoded messages and outputs is proposed for the deterministic model based on the strength…
The K-user cyclic Z-interference channel models a situation in which the kth transmitter causes interference only to the (k-1)th receiver in a cyclic manner, e.g., the first transmitter causes interference only to the Kth receiver. The impact of noiseless feedback on the capacity of this channel is studied by focusing on the Gaussian cyclic Z-interference channel. To this end, the symmetric feedback capacity of the linear shift deterministic cyclic Z-interference channel (LD-CZIC) is completely characterized for all interference regimes. Using insights from the linear deterministic channel mod…
In this paper, we first study a two-user interference channel with generalized feedback. We establish an inner bound on its capacity region. The coding scheme that we employ for the inner bound is based on an appropriate combination of Han-Kobayash rate splitting and compress-and-forward at the senders. Each sender compresses the channel output that is observes using a compression scheme that is à-la Lim et al. noisy network coding and Avestimeher et al. quantize-map-and-forward. Next, we study an injective deterministic model in which the senders obtain output feedback only intermittently. Sp…
We consider the two-user interference channel with rate-limited feedback. Related prior works focus on the case where feedback links have infinite capacity, while no research has been done for the rate-limited feedback problem. Several new challenges arise due to the capacity limitations of the feedback links, both in deriving inner-bounds and outer-bounds. We study this problem under three different interference models: the El Gamal-Costa deterministic model, the linear deterministic model, and the Gaussian model. For the first two models, we develop an achievable scheme that employs three te…
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 c…
The paper establishes the optimal generalized degrees of freedom (GDOF) of 3-user $M \times N$ multiple-input multiple-output (MIMO) Gaussian interference channel (GIC) in which each transmitter has $M$ antennas and each receiver has $N$ antennas. A constraint of $2M \leq N$ is imposed so that random coding with message-splitting achieves the optimal GDOF. Unlike symmetric case, two cross channels to unintended receivers from each transmitter can have different strengths, and hence, well known Han-Kobayashi common-private message splitting would not achieve the optimal GDOF. Instead, splitting…
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 it cognitive relay. For this Interference Channel with a Cognitive Relay (ICCR) 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, wh…
We consider secure communication over a two-user Gaussian interference channel, where each transmitter sends a confidential message to its legitimate receiver. For this setting, we identify a regime where the simple scheme of using Gaussian wiretap codebook at each transmitter (without cooperative jamming) and treating interference as noise at each intended receiver (in short, GWC-TIN scheme) achieves the optimal secure sum capacity to within a constant gap. The results are proved by first considering the deterministic interference channel model and identifying a regime in which a simple schem…
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 memoryless (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 {\em et al}. For the semi-deterministic MAC-IC-MAC, it is shown that single-user cod…
In multi-user information theory it is often assumed that every node in the network possesses all codebooks used in the network. This assumption may be impractical in distributed ad-hoc, cognitive or heterogeneous networks. This work considers the two-user Interference Channel with one Oblivious Receiver (IC-OR), i.e., one receiver lacks knowledge of the interfering cookbook while the other receiver knows both codebooks. The paper asks whether, and if so how much, the channel capacity of the IC-OR is reduced compared to that of the classical IC where both receivers know all codebooks. A novel …
An achievable rate region for certain noisy three-user-pair interference channels is proposed. The channel class under consideration generalizes the three-pair deterministic interference channel (3-DIC) in the same way as the Telatar-Tse noisy two-pair interference channel generalizes the El Gamal-Costa injective channel. Specifically, arbitrary noise is introduced that acts on the combined interference signal before it affects the desired signal. This class of channels includes the Gaussian case. The rate region includes the best-known inner bound on the 3-DIC capacity region, dominates treat…
In this paper, we develop achievability schemes for symmetric $K$-user interference channels with a rate-limited feedback from each receiver to the corresponding transmitter. We study this problem under two different channel models: the linear deterministic model, and the Gaussian model. For the deterministic model, the proposed scheme achieves a symmetric rate that is the minimum of the symmetric capacity with infinite feedback, and the sum of the symmetric capacity without feedback and the symmetric amount of feedback. For the Gaussian interference channel, we use lattice codes to propose a …
In this work, we study the performance of random isometric precoders over quasi-static and correlated fading channels. We derive deterministic approximations of the mutual information and the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver and provide simple provably converging fixed-point algorithms for their computation. Although these approximations are only proven exact in the asymptotic regime with infinitely many antennas at the transmitters and receivers, simulations suggest that they closely match the performance of small-di…
We study opportunistic interference management when there is bursty interference in parallel 2-user linear deterministic interference channels. A degraded message set communication problem is formulated to exploit the burstiness of interference in M subcarriers allocated to each user. We focus on symmetric rate requirements based on the number of interfered subcarriers rather than the exact set of interfered subcarriers. Inner bounds are obtained using erasure coding, signal-scale alignment and Han-Kobayashi coding strategy. Tight outer bounds for a variety of regimes are obtained using the El…
We investigate how to exploit intermittent feedback for interference management. Focusing on the two-user linear deterministic interference channel, we completely characterize the capacity region. We find that the characterization only depends on the forward channel parameters and the marginal probability distribution of each feedback link. The scheme we propose makes use of block Markov encoding and quantize-map-and-forward at the transmitters, and backward decoding at the receivers. Matching outer bounds are derived based on novel genie-aided techniques. As a consequence, the perfect-feedbac…
This work studies the Gaussian interference channel (IC) with a relay, which transmits and receives in a band that is orthogonal to the IC. The channel associated with the relay is thus an out-of-band relay channel (OBRC). The focus is on a symmetric channel model, in order to assess the fundamental impact of the OBRC on the signal interaction of the IC, in the simplest possible setting. First, the linear deterministic model is investigated and the sum capacity of this channel is established for all possible channel parameters. In particular, it is observed that the impact of OBRC, as its link…
Recent investigations have shown sum capacity results within a constant bit-gap for several channel models, e.g. the two-user Gaussian interference channel (G-IC), k-user G-IC or the Gaussian X-channel. This has motivated investigations of interference-limited multi-user channels, for example, the Gaussian interfering multiple access channel (G-IMAC). Networks with interference usually require the use of interference alignment (IA) as a technique to achieve the upper bounds of a network. A promising approach in view of constant-gap capacity results is a special form of IA called signal-scale a…
This paper studies the value of limited rate cooperation between the transmitters for managing interference and simultaneously ensuring secrecy, in the 2-user Gaussian symmetric interference channel (GSIC). First, the problem is studied in the symmetric linear deterministic IC (SLDIC) setting, and achievable schemes are proposed, based on interference cancelation, relaying of the other user's data bits, and transmission of random bits. In the proposed achievable scheme, the limited rate cooperative link is used to share a combination of data bits and random bits depending on the model paramete…
This paper studies the two-user interference channel with unilateral source cooperation, which consists of two source-destination pairs that share the same channel and where one full-duplex source can overhear the other source through a noisy in-band link. Novel outer bounds of the type 2Rp+Rc/Rp+2Rc are developed for the class of injective semi-deterministic channels with independent noises at the different source-destination pairs. The bounds are then specialized to the Gaussian noise case. Interesting insights are provided about when these types of bounds are active, or in other words, when…
We study the discrete memoryless Z-interference channel (ZIC) where the transmitter of the pair that suffers from interference is cognitive. We first provide an upper bound on the capacity of this channel. We then show that, when the channel of the transmitter-receiver pair that does not experience interference is deterministic, our proposed upper bound matches the known lower bound provided by Cao and Chen in 2008. The obtained results imply that, unlike in the Gaussian cognitive ZIC, in the considered channel superposition encoding at the non-cognitive transmitter as well as Gel'fand-Pinsker…
