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This paper obtains the first degrees of freedom (DoFs) bound that is provably sensitive tonetworkcoherence time, i.e., coherence time in an interference network, where all channels experience the same coherence patterns. This is accomplished by a novel adaptation of the aligned image sets bound and settles various open problems noted previously by Naderi and Avestimehr and by Gouet al.For example, a necessary and sufficient condition is obtained for the optimality of 1/2 DoF per user in a partially connected interference network, where the channel state information at the receivers (CSIRs) is perfect, the channel state information at the transmitters (CSITs) is instantaneous but limited to finite precision, and the network coherence time is $T_{c}=1$. The surprising insight that emerges is that even with perfect CSIR and instantaneous finite precision CSIT, the network coherence time matters, i.e., it has a DoF impact. [ABSTRACT FROM AUTHOR]

For the $K=2$ user MISO BC, i.e., the wireless broadcast channel where a transmitter equipped with $K=2$ antennas sends independent messages to $K=2$ receivers each of which is equipped with a single antenna, the generalized degrees of freedom (GDoFs) region are characterized for arbitrary channel strength and channel uncertainty levels for each of the channel coefficients. The result is extended to K>2 users under additional restrictions which include the assumption of symmetry. [ABSTRACT FROM AUTHOR]

The main result of this paper is that an orthogonal access scheme, such as time division multiple access achieves the all-unicast degrees of freedom (DoF) region of the topological interference management problem if and only if the network topology graph is chordal bipartite, i.e., every cycle that can contain a chord, does contain a chord. The all-unicast DoF region includes the DoF region for any arbitrary choice of a unicast message set, so e.g., the results of Maleki and Jafar on the optimality of orthogonal access for the sum-DoF of one-dimensional convex networks are recovered as a special case. The result is also established for the corresponding topological representation of the index coding problem. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a novel “genie chains” approach to obtain information theoretic degrees of freedom (DoF) outer bounds for MIMO wireless interference networks. This new approach creates a chain of mappings from genie signals provided to a receiver to the exposed signal spaces at that receiver, and then the exposed signal spaces serve as the genie signals for the next receiver in the chain subject to certain linear independence requirements. Our approach essentially converts an information theoretic DoF outer bound problem into a linear algebra problem. Several applications of the genie chains approach are presented. [ABSTRACT FROM AUTHOR]

We consider the problem of network coding across three unicast sessions over a directed acyclic graph, where the sender and receiver of each unicast session are both connected to the network via a single edge of unit capacity. We consider a network model in which the middle of the network can only perform random linear network coding, and restrict our approaches to precoding-based linear schemes, where the senders use precoding matrices to encode source symbols. We adapt a precoding-based interference alignment technique, originally developed for the wireless interference channel, to construct a precoding-based linear scheme, which we refer to as precoding-based network alignment scheme (PBNA). A primary difference between this setting and the wireless interference channel is that the network topology can introduce dependencies among the elements of the transfer matrix, which we refer to as coupling relations, and can potentially affect the achievable rate of PBNA. We identify all these coupling relations and interpret them in terms of network topology. We then present polynomial-time algorithms to check the presence of these coupling relations in a particular network. Finally, we show that, depending on the coupling relations present in the network, the optimal symmetric rate achieved by precoding-based linear scheme can take only three possible values, all of which can be achieved by PBNA. [ABSTRACT FROM PUBLISHER]

Starting from the elemental $2\times 2\times 2$ interference channel, there has been much progress in the understanding of multihop multiflow wireless networks through degrees of freedom (DoF) studies that have produced important ideas such as (aligned) interference neutralization. However, much of this progress has been limited to layered connectivity models that are essentially motivated by the assumption that wireless networks can only operate in half-duplex mode. Motivated by recent breakthroughs in full-duplex radio technology, in this work, we expand the $2\times 2\times 2$ interference channel model beyond layered connectivity in order to study the impact of full-duplex operation. In particular, we study the impact of intra-layer connectivity between relays that are in the same layer, the impact of direct inter-layer connectivity between sources and destinations, and the impact of intermediate inter-layer connectivity that connects sources or destinations, not directly to each other, but to relay nodes in non-adjacent layers in a $2\times 2\times 2\times 2$ interference channel. We show that intra-layer links and intermediate inter-layer interference links do not cause a collapse of DoF, whereas direct interference links do cause a collapse of DoF. [ABSTRACT FROM PUBLISHER]

The index coding problem is studied from an interference alignment perspective providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between the capacity of multiple unicast index coding (where each message is desired by exactly one receiver), and groupcast index coding (where a message can be desired by multiple receivers), which settles the heretofore open question of insufficiency of linear codes for the multiple unicast index coding problem by equivalence with groupcast settings, where this question has previously been answered. Necessary and sufficient conditions for the achievability of rate half per message in the index coding problem are shown to be a natural consequence of interference alignment constraints, and generalizations to feasibility of rate \({1}/(L+1)\) per message when each destination desires at least \(L\) messages, are similarly obtained. Finally, capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks. The solutions are based on vector linear coding. [ABSTRACT FROM AUTHOR]

This paper explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over \(\mathbb {F}_{\!p^n}\) are analogous to \(n\times n\) vector (MIMO) channels in the wireless setting, but with an important distinction—there is additional structure due to finite field arithmetic, which enforces commutativity of matrix multiplication and limits the channel diversity to \(n\) , making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity or linear capacity optimal solutions for their finite field counterparts. This is shown through the study of capacity of the 2-user X channel and linear capacity of the 3-user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over \(\mathbb {F}_{\!p^n}\) also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between \(p\) and SNR, and \(n\) and diversity. [ABSTRACT FROM AUTHOR]

We explore the degrees of freedom (DoF) of three classes of finite state compound wireless networks in this paper. First, we study the multiple-input single-output (MISO) finite state compound broadcast channel (BC) with arbitrary number of users and antennas at the transmitter. In prior work, Weingarten have found inner and outer bounds on the DoF with 2 users. The bounds have a different character. While the inner bound collapses to unity as the number of states increases, the outer bound does not diminish with the increasing number of states beyond a threshold value. It has been conjectured that the outer bound is loose and the inner bound represents the actual DoF. In the complex setting (all signals, noise, and channel coefficients are complex variables), we solve a few cases to find that the outer bound—and not the inner bound—of Weingarten is tight. For the real setting (all signals, noise, and channel coefficients are real variables), we completely characterize the DoF, once again proving that the outer bound of Weingarten is tight. We also extend the results to arbitrary number of users. Second, we characterize the DoF of finite state scalar (single antenna nodes) compound X networks with arbitrary number of users in the real setting. Third, we characterize the DoF of finite state scalar compound interference networks with arbitrary number of users in both the real and complex setting. The key finding is that scalar interference networks and (real) X networks do not lose any DoF due to channel uncertainty at the transmitter in the finite state compound setting. The finite state compound MISO BC does lose DoF relative to the perfect CSIT scenario. However, what is lost is only the DoF benefit of joint processing at transmit antennas, without which the MISO BC reduces to an X network. [ABSTRACT FROM AUTHOR]

Recent results establish the optimality of interference alignment to approach the Shannon capacity of interference networks at high SNR. However, the extent to which interference can be aligned over a finite number of signalling dimensions remains unknown. Another important concern for interference alignment schemes is the requirement of global channel knowledge. In this work, we provide examples of iterative algorithms that utilize the reciprocity of wireless networks to achieve interference alignment with only local channel knowledge at each node. These algorithms also provide numerical insights into the feasibility of interference alignment that are not yet available in theory. [ABSTRACT FROM AUTHOR]

We study a layered K-user M-hop Gaussian relay network consisting of Km nodes in the m^th layer, where M\geq 2 and K=K1=KM+1. We observe that the time-varying nature of wireless channels or fading can be exploited to mitigate the interuser interference. The proposed amplify-and-forward relaying scheme exploits such channel variations and works for a wide class of channel distributions including Rayleigh fading. We show a general achievable degrees of freedom (DoF) region for this class of Gaussian relay networks. Specifically, the set of all (d1,\ldots , dK) such that di\leq 1 for all i and \sum i=1^{K} di\leq K\Sigma is achievable, where di is the DoF of the i^th source-destination pair and K\Sigma is the maximum integer such that K\Sigma \leq \mathop min\limits m\{Km\} and M/K\Sigma is an integer. We show that surprisingly the achievable DoF region coincides with the cut-set outer bound if M/ \mathop min\limits m\{Km\} is an integer; thus, interference-free communication is possible in terms of DoF. We further characterize an achievable DoF region assuming multi-antenna nodes and general message set, which again coincides with the cut-set outer bound for a certain class of networks. [ABSTRACT FROM PUBLISHER]

It has been conjectured by Hø-Madsen and Nosratinia that complex Gaussian interference channels with constant channel coefficients have only one degree-of-freedom regardless of the number of users. While several examples are known of constant channels that achieve more than 1 degree-of-freedom, these special cases only span a subset of measure zero. In other words, for almost all channel coefficient values, it is not known if more than 1 degree-of-freedom is achievable. In this paper, we settle the Høst-Madsen–Nosratinia conjecture in the negative. We show that at least 1.2 degrees-of-freedom are achievable for all values of complex channel coefficients except for a subset of measure zero. For the class of linear beamforming and interference alignment schemes considered in this paper, it is also shown that 1.2 is the maximum number of degrees-of-freedom achievable on the complex Gaussian 3 user interference channel with constant channel coefficients, for almost all values of channel coefficients. To establish the achievability of 1.2 degrees-of-freedom we use the novel idea of asymmetric complex signaling – i.e., the inputs are chosen to be complex but not circularly symmetric. It is shown that unlike Gaussian point-to-point, multiple-access and broadcast channels where circularly symmetric complex Gaussian inputs are optimal, for interference channels optimal inputs are in general asymmetric. With asymmetric complex signaling, we also show that the 2 user complex Gaussian X channel with constant channel coefficients achieves the outer bound of 4/3 degrees-of-freedom, i.e., the assumption of time-variations/frequency-selectivity used in prior work to establish the same result, is not needed. [ABSTRACT FROM PUBLISHER]

We explore the feasibility of interference alignment in signal vector space—based only on beamforming—for K-user MIMO interference channels. Our main contribution is to relate the feasibility issue to the problem of determining the solvability of a multivariate polynomial system which is considered extensively in algebraic geometry. It is well known, e.g., from Bezout's theorem, that generic polynomial systems are solvable if and only if the number of equations does not exceed the number of variables. Following this intuition, we classify signal space interference alignment problems as either proper or improper based on the number of equations and variables. Rigorous connections between feasible and proper systems are made through Bernshtein's theorem for the case where each transmitter uses only one beamforming vector. The multibeam case introduces dependencies among the coefficients of a polynomial system so that the system is no longer generic in the sense required by both theorems. In this case, we show that the connection between feasible and proper systems can be further strengthened (since the equivalency between feasible and proper systems does not always hold) by including standard information theoretic outer bounds in the feasibility analysis. [ABSTRACT FROM PUBLISHER]

In this work, we consider a two-hop multiuser amplify-and-forward relay network with multi-antenna nodes. The results are three-fold. First, for any relay amplification matrix D in the multiple-access channel (MAC), we show that duality holds when ,cD† is employed in the broadcast channel (BC), and vice versa, where ic is obtained from switching the total source and relay power constraints. Second, under a total network power constraint, we show that MAC-BC duality holds when D and D† are the relaying matrices in the MAC and BC respectively. Third, for any D in the MAC and cD† in the BC where c is any positive real scalar, MAC-BC duality under total network power constraint holds only for the above two cases. [ABSTRACT FROM AUTHOR]

We explore the degrees of freedom of M x N user wireless X networks, i.e., networks of M transmitters and N receivers where every transmitter has an independent message for every receiver. We derive a general outer bound on the degrees of freedom region of these networks. When all nodes have a single antenna and all channel coefficients vary in time or frequency, we show that the total number of degrees of freedom of the X network is equal to MN/M+N-1 per orthogonal time and frequency dimension. Achievability is proved by constructing interference alignment schemes for X networks that can come arbitrarily close to the outer bound on degrees of freedom. For the case where either M = 2 or N = 2 we find that the degrees of freedom characterization also provides a capacity approximation that is accurate to within O(1). For these cases the degrees of freedom outer bound is exactly achievable. [ABSTRACT FROM AUTHOR]

We find the degrees of freedom of a network with S source nodes, B relay nodes, and D destination nodes, with random time-varying/frequency-selective channel coefficients and global channel knowledge at all nodes. We allow full-duplex operation at all nodes, as well as causal noise-free feedback of all received signals to all source and relay nodes. An outer bound to the capacity region of this network is obtained. Combining the outer bound with previous interference alignment based achiev-ability results, we conclude that the techniques of relays, feedback, full-duplex operation and noisy cooperation do not increase the degrees of freedom of interference and X networks. As a second contribution, we show that for a network with K full-duplex nodes and K ( K - 1) independent messages with one message from every node to each of the other K - 1 nodes, the total degrees of freedom are bounded above and below by K(K - 1)/(2K - 2) and K(K - 1)/(2K - 3) respectively. [ABSTRACT FROM AUTHOR]

Cognitive radios hold tremendous promise for increasing spectral efficiency in wireless systems. This paper surveys the fundamental capacity limits and associated transmission techniques for different wireless network design paradigms based on this promising technology. These paradigms are unified by the definition of a cognitive radio as an intelligent wireless communication device that exploits side information about its environment to improve spectrum utilization. This side information typically comprises knowledge about the activity, channels, codebooks, and/or messages of other nodes with which the cognitive node shares the spectrum. Based on the nature of the available side information as well as a priori rules about spectrum usage, cognitive radio systems seek to underlay, overlay, or interweave the cognitive radios' signals with the transmissions of noncognitive nodes. We provide a comprehensive summary of the known capacity characterizations in terms of upper and lower bounds for each of these three approaches. The increase in system degrees of freedom obtained through cognitive radios is also illuminated. This information-theoretic survey provides guidelines for the spectral efficiency gains possible through cognitive radios, as well as practical design ideas to mitigate the coexistence challenges in today's crowded spectrum. [ABSTRACT FROM AUTHOR]

The subject of this article is the long standing open problem of developing a general capacity theory for wireless networks, particularly a theory capable of describing the fundamental performance limits of mobile ad hoc networks. A MANET is a peer-to-peer network with no preexisting infrastructure. MANETs are the most general wireless networks, with single-hop, relay, interference, mesh, and star networks comprising special cases. The lack of a MANET capacity theory has stunted the development and com- mercialization of many types of wireless net- works, including emergency, military, sensor, and community mesh networks. Information theory, which has been vital for links and centralized networks, has not been successfully applied to decentralized wireless networks. Even if this was accomplished, for such a theory to truly characterize the limits of deployed MANETs it must overcome three key roadblocks. First, most current capacity results rely on the allowance of unbounded delay and reliability. Second, spatial and timescale decompositions have not yet been developed for optimally modeling the spatial and temporal dynamics of wireless networks. Third, a useful network capacity theory must integrate rather than ignore the important role of over-head messaging and feedback. This article describes some of the shifts in thinking that may be needed to overcome these roadblocks and develop a more general theory. [ABSTRACT FROM AUTHOR]

For the fully connected K user wireless interference channel where the channel coefficients are time-varying and are drawn from a continuous distribution, the sum capacity is characterized as C(SNR) =K/2 log(SNR) + o(log(SNR)). Thus, the K user time-varying interference channel almost surely has K/2 degrees of freedom. Achievability is based on the idea of interference alignment. Examples are also provided of fully connected K user interference channels with constant (not time-varying) coefficients where the capacity is exactly achieved by interference alignment at all SNR values. [ABSTRACT FROM AUTHOR]

We provide achievability as well as converse results for the degrees of freedom region of a multiple-input multiple-output (MIMO) X channel, i.e., a system with two transmitters, two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels from each transmitter to each receiver. The inner and outer bounds on the degrees of freedom region are Light whenever integer degrees of freedom are optimal for each message. With M = 1 antennas at each node, we find that the total (sum rate) degrees of freedom are bounded above and below as 1 ≤ η*X ≤ 4/3. If M > 1 and channel matrices are nondegenerate then the precise degrees of freedom η*X = 4/3 M. Thus, the MIMO X channel has noninteger degrees of freedom when M is nota multiple of 3. Simple zero forcing without dirty paper encoding or successive decoding, suffices to achieve the 4/3 M degrees of freedom. If the channels vary with time/frequency then the X channel with single antennas (M = 1) at all nodes has exactly 4/3 degrees of freedom. The key idea for the achievability of the degrees of freedom is interference alignment-i.e., signal spaces are aligned at receivers where they constitute interference white they are separable at receivers where they are desired. We also explore the increase in degrees of freedom when some of the messages are made available to a transmitter or receiver in the manner of cognitive radio. [ABSTRACT FROM AUTHOR]

In this paper, we consider multihop multiple access (MAC) and broadcast channels (BC) where communication takes place with the assistance of relays that amplify and forward (AF) their received signals. For a two-hop parallel AF relay MAC, assuming a sum power constraint across all relays we characterize optimal relay amplification factors and the resulting optimal rate regions. We find the maximum sum rate and the maximum rate for each user in closed form and express the optimal rate pair ( R1, R2) that maximizes μ R1 + μ2 R2 as the solution of a pair of simultaneous equations. We find that the parallel AF relay MAC with total transmit power of the two users P1 + P2 = P and total relay power PR is the dual of the parallel AF relay BC where the MAC source nodes become the BC destination nodes, the MAC destination node becomes the BC source node, the dual BC source transmit power is PR and the total transmit power of the AF relays is P. The duality means that the rate region of the AF relay MAC with a sum power constraint P on the transmitters is the same as that of the dual BC. The duality relationship is found to be useful in characterizing the rate region of the AF relay BC as the union of MAC rate regions. The duality is established for distributed multiple antenna AF relay nodes and multiple (more than 2) hops as well. [ABSTRACT FROM AUTHOR]

In this correspondence, we show that the exact number of spatial degrees of freedom (DOF) for a two user nondegenerate (full rank channel matrices) multiple-input-multiple-output (MIMO) Gaussian interference channel with M1, M2 antennas at transmitters 1, 2 and N1, N2 antennas at the corresponding receivers, and perfect channel knowledge at all transmitters and receivers, is min {M1 + M2, N1 + N2, max( M1, N2 )max ( M2, N1 ) }. A constructive achievability proof shows that zero forcing is sufficient to achieve all the available DOF on the two user MIMO interference channel. We also show through an example of a share-and-transmit scheme how the gains of transmitter cooperation may be entirely offset by the cost of enabling that cooperation so that the available DOF are not increased. [ABSTRACT FROM AUTHOR]

Cognitive radios are promising solutions to the problem of overcrowded spectrum. In this article we explore the throughput potential of cognitive communication. Different interpretations of cognitive radio that underlay, overlay, and interweave the transmissions of the cognitive user with those of licensed users are described. Considering opportunistic communication as a baseline, we investigate the through- put improvements offered by the overlay methods. Channel selection techniques for opportunistic access such as frequency hopping, frequency tracking, and frequency coding are presented. The trade-off between regulation and autonomy inherent in the design and performance of cognitive networks is examined through a simple example, which shows that the optimal amount of licensing is equal to the duty cycle of the traffic arrivals. [ABSTRACT FROM AUTHOR]

ln this correspondence, we identify the common underlying form of the capacity expression that is applicable to both cases where causal or noncausal side information is made available to the transmitter. A genie-aided outerbound is developed that states that when a genie provides n bits of side information to a receiver the resulting capacity improvement cannot be more than n bits. Using the genie-bound we are able to bound the relative capacity advantage of noncausal side information over causal side information for both the single user point-to-point channel as well as the multiple-access channel (MAC) with independent side information at the transmitters. Applications of these capacity bounds are demonstrated through examples of random access channels. Interestingly, the capacity results indicate that the excessive MAC layer overheads common in present wireless systems may be avoided through coding across multiple-access blocks. It is also shown that even one bit of side information at the transmitter can result in unbounded capacity improvement. [ABSTRACT FROM AUTHOR]

Provides an overview of the extensive results on the Shannon capacity of single-user and multiuser multiple-input multiple-output (MIMO) wireless communication channels. Summary of ergodic and capacity versus outage results for single-user MIMO channels; Reasons behind the capacity gain obtained from multiple antennas; Open problems and design questions associated with MIMO systems.

An abstract of the monograph "Interference Alignment — A New Look at Signal Dimensions in a Communication Network," by Syed A. Jafar is presented.