This paper explores the two-user Gaussian interference channel through the lens of a natural deterministic channel model. The main result is that the deterministic channel uniformly approximates the Gaussian channel, the capacity regions differing by a universal constant. The problem of finding the capacity of the Gaussian channel to within a constant error is therefore reduced to that of finding the capacity of the far simpler deterministic channel. Thus, the paper provides an alternative derivation of the recent constant gap capacity characterization of Etkin, Tse, and Wang. Additionally, the deterministic model gives significant insight towards the Gaussian channel.
An interference alignment example is constructed for the deterministic channel model of the $K$ user interference channel. The deterministic channel example is then translated into the Gaussian setting, creating the first known example of a fully connected Gaussian $K$ user interference network with single antenna nodes, real, non-zero and contant channel coefficients, and no propagation delays where the degrees of freedom outerbound is achieved. An analogy is drawn between the propagation delay based interference alignment examples and the deterministic channel model which also allows similar…
This paper extends the literature on interference alignment to more general classes of deterministic channels which incorporate non-linear input-output relationships. It is found that the concept of alignment extends naturally to these deterministic interference channels, and in many cases, the achieved degrees of freedom (DoF) can be shown to be optimal.
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.
An inner bound to the capacity region of a class of deterministic interference channels with three user pairs is presented. The key idea is to simultaneously decode the combined interference signal and the intended message at each receiver. It is shown that this interference-decoding inner bound is tight under certain strong interference conditions. The inner bound is also shown to strictly contain the inner bound obtained by treating interference as noise, which includes interference alignment for deterministic channels. The gain comes from judicious analysis of the number of combined interfe…
In this paper, we study the uplink of a cellular system using the linear deterministic approximation model, where there are two users transmitting to a receiver, mutually interfering with a third transmitter communicating with a second receiver. We give an achievable coding scheme and prove its optimality, i.e. characterize the capacity region. This scheme is a form of interference alignment which exploits the channel gain difference of the two-user cell.
In this paper we study the effect of rate-limited feedback on the sum-rate capacity of the deterministic interference channel. We characterize the sum-rate capacity of this channel in the symmetric case and show that having feedback links can increase the sum-rate capacity by at most the rate of the available feedback. Our proof includes a novel upper-bound on the sum-rate capacity and a set of new achievability strategies.
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 …
In this paper, we first present an outer bound for a general interference channel with a cognitive relay, i.e., a relay that has non-causal knowledge of both independent messages transmitted in the interference channel. This outer bound reduces to the capacity region of the deterministic broadcast channel and of the deterministic cognitive interference channel through nulling of certain channel inputs. It does not, however, reduce to that of certain deterministic interference channels for which capacity is known. As such, we subsequently tighten the bound for channels whose outputs satisfy an …
The cognitive interference channel (C-IFC) consists of a classical two-user interference channel in which the message of one user (the "primary" user) is non-causally available at the transmitter of the other user (the "cognitive" user). We obtain the capacity of the semi-deterministic C-IFC: a discrete memoryless C-IFC in which the cognitive receiver output is a noise-less deterministic function of the channel inputs. We then use the insights obtained from the capacity-achieving scheme for the semi-deterministic model to derive new, unified and tighter constant gap results for the complex-val…
In this paper, we study the effect of channel output feedback on the sum capacity in a two-user symmetric deterministic interference channel. We find that having a single feedback link from one of the receivers to its own transmitter results in the same sum capacity as having a total of 4 feedback links from both the receivers to both the transmitters. Hence, from the sum capacity point of view, the three additional feedback links are not helpful. We also consider a half-duplex feedback model where the forward and the feedback resources are symmetric and timeshared. Surprisingly, we find that …
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…
The capacity region of the interference channel in which one transmitter non-causally knows the message of the other, termed the cognitive interference channel, has remained open since its inception in 2005. A number of subtly differing achievable rate regions and outer bounds have been derived, some of which are tight under specific conditions. In this work we present a new unified inner bound for the discrete memoryless cognitive interference channel. We show explicitly how it encompasses all known discrete memoryless achievable rate regions as special cases. The presented achievable region …
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 paper, we investigate optimal coding strategies for a class of linear deterministic relay networks. The network under study is a relay network, with one source, one destination, and two relay nodes. Additionally, there is a disturbing source of signals that causes interference with the information signals received by the relay nodes. Our model captures the effect of the interference of message signals and disturbing signals on a single relay network, or the interference of signals from multiple relay networks with each other in the linear deterministic framework. For several ranges of …
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 characterize the capacity region to within 2 bits/s/Hz and the symmetric capacity to within 1 bit/s/Hz for the two-user Gaussian interference channel (IC) with feedback. We develop achievable schemes and derive a new outer bound to arrive at this conclusion. One consequence of the result is that feedback provides multiplicative gain, i.e., the gain becomes arbitrarily large for certain channel parameters. It is a surprising result because feedback has been so far known to provide no gain in memoryless point-to-point channels and only bounded additive gain in multiple access channels. The ga…
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…
In this paper, we use the linear deterministic approximation model to study a two user multiple access channel mutually interfering with a point to point link, which represents a basic setup of a cellular system. We derive outer bounds on the achievable sum rate and construct coding schemes achieving the outer bounds. For a large parameter range, the sum capacity is identical to the sum capacity of the interference channel obtained by silencing the weaker user in the multiple access channel. For other interference configurations, the sum rate can be increased using interference alignment, whic…
The N+1 user, 1 x 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 symmetric 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 interferen…
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…
Recently, Etkin, Tse, and Wang found the capacity region of the two-user Gaussian interference channel to within one bit/s/Hz. A natural goal is to apply this approach to the Gaussian interference channel with an arbitrary number of users. We make progress towards this goal by finding the capacity region of the many-to-one and one-to-many Gaussian interference channels to within a constant number of bits. The result makes use of a deterministic model to provide insight into the Gaussian channel. The deterministic model makes explicit the dimension of signal scale. A central theme emerges: the …
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…
We study the capacity regions of two-user interference channels where transmitters base their transmission schemes on local views of the channel state. Under the local view model, each transmitter knows only a subset of the four channel gains, which may be mismatched from the other transmitter. We consider a set of seven local views, and find that for five out of the seven local views, TDM is sufficient to achieve the qualified notion of capacity region for the linear deterministic interference channel which approximates the Gaussian interference channel. For these five local views, the qualif…
In this paper, we investigate the sum-capacity of the two-user Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we find the constrained sum-capacity and its achievable schemes with the minimum number of messages, first in symmetric channels, and then in general asymmetric channels. We show that the constrained sum-capacity oscillates a…
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…
Recently there has been a lot of success in using the deterministic approach to provide approximate characterization of Gaussian network capacity. In this paper, we take a deterministic view and revisit the problem of wiretap channel with side information. A precise characterization of the secrecy capacity is obtained for a linear deterministic model, which naturally suggests a coding scheme which we show to achieve the secrecy capacity of the degraded Gaussian model (dubbed as "secret writing on dirty paper") to within half a bit.
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 code 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 informati…
This paper studies a symmetric K user Gaussian interference channel with K transmitters and K receivers. A "very strong" interference regime is derived for this channel setup. A "very strong" interference regime is one where the capacity region of the interference channel is the same as the capacity region of the channel with no interference. In this regime, the interference can be perfectly canceled by all the receivers without incurring any rate penalties. A "very strong" interference condition for an example symmetric K user deterministic interference channel is also presented.
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…
This paper studies a layered erasure interference channel model, which is a simplification of the Gaussian interference channel with fading using the deterministic model approach. In particular, the capacity region of the layered erasure one-sided interference channel is completely determined, assuming that the channel state information (CSI) is known to the receivers, but there is no CSI at transmitters (CSIT). The result holds for arbitrary fading statistics. Previous results of Aggarwal, Sankar, Calderbank and Poor on the capacity region or sum capacity under several interference configurat…
This paper presents an unusual view of interference wireless networks based on complex system thinking. To proceed with this analysis, a literature review of the different applications of complex systems is firstly presented to illustrate how such an approach can be used in a wide range of research topics, from economics to linguistics. Then the problem of quantifying the fundamental limits of wireless systems where the co-channel interference is the main limiting factor is described and hence contextualized in the perspective of complex systems. Specifically some possible internal and externa…
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 consider the discrete memoryless interference channel with common information, in which two senders need deliver not only private messages but also certain common messages to their corresponding receivers. We derive an achievable rate region for such a channel by exploiting a random coding strategy, namely cascaded superposition coding. We reveal that the derived achievable rate region generalizes some important existing results for the interference channels with or without common information. Furthermore, we specialize to a class of deterministic interference channels with c…
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…
The cognitive interference channel is an interference channel in which one transmitter is non-causally provided with the message of the other transmitter. This channel model has been extensively studied in the past years and capacity results for certain classes of channels have been proved. In this paper we present new inner and outer bounds for the capacity region of the cognitive interference channel as well as new capacity results. Previously proposed outer bounds are expressed in terms of auxiliary random variables for which no cardinality constraint is known. Consequently it is not possib…
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…
One of the fundamental challenges in the design of distributed wireless networks is the large dynamic range of network state. Since continuous tracking of global network state at all nodes is practically impossible, nodes can only acquire limited local views of the whole network to design their transmission strategies. In this paper, we study multi-layer wireless networks and assume that each node has only a limited knowledge, namely 1-local view, where each S-D pair has enough information to perform optimally when other pairs do not interfere, along with connectivity information for rest of t…
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…