In this work, we propose solving the Information Bottleneck (IB) and Privacy Funnel (PF) problems with Douglas-Rachford Splitting methods (DRS). We study a general Markovian information-theoretic Lagrangian that includes IB and PF into a unified framework. We prove the linear convergence of the proposed solvers using the Kurdyka- ojasiewicz inequality. Moreover, our analysis is beyond IB and PF and applies to any convex-weakly convex pair objectives. Based on the results, we develop two types of linearly convergent IB solvers, with one improves the performance of convergence over existing solvers while the other can be independent to the relevance-compression trade-off. Moreover, our results apply to PF, yielding a new class of linearly convergent PF solvers. Empirically, the proposed IB solvers IB obtain solutions that are comparable to the Blahut-Arimoto-based benchmark and is convergent for a wider range of the penalty coefficients than existing solvers. For PF, our non-greedy solvers can characterize the privacy-utility trade-off better than the clustering-based greedy solvers.

Application of Deep learning (DL) to modulation classification has shown significant performance improvements. The focus has been model centric, where newer architectures are attempted on benchmark dataset RADIOML.2016.10A (RML16). RML16 is a high impact effort that laid the foundation for generating a synthetic dataset for applying DL models to wireless problems. This encouraged development of newer architectures to RML16. We use a data centric DL approach where focus moves from model architectures to data quality. RML16 has shortcomings such as errors and ad-hoc choices of parameters. We build upon RML16 and provide realistic and correct methodology of generating dataset. A new benchmark dataset RML22 is generated. Going forward, we envision researchers to improve model quality on RML22. We attempt to improve data quality by studying the impact of information sources. Further, the choices of artifacts and signal model parameterization are analyzed carefully. The Python source code used to generate RML22 is shared to enable researchers to further improve dataset quality.

In this work, we generalize the information bottleneck (IB) approach to the multi-view learning context. The exponentially growing complexity of the optimal representation motivates the development of two novel formulations with more favorable performance-complexity tradeoffs. The first approach is based on forming a stochastic consensus and is suited for scenarios with significant representation overlap between the different views. The second method, relying on incremental updates, is tailored for the other extreme scenario with minimal representation overlap. In both cases, we extend our earlier work on the alternating directional methods of multiplier (ADMM) solver and establish its convergence and scalability. Empirically, we find that the proposed methods outperform state-of-the-art approaches in multi-view classification problems under a broad range of modelling parameters.

The Information bottleneck (IB) method enables optimizing over the trade-off between compression of data and prediction accuracy of learned representations, and has successfully and robustly been applied to both supervised and unsupervised representation learning problems. However, IB has several limitations. First, the IB problem is hard to optimize. The IB Lagrangian$\mathcal{L}_{IB}: =I(X;Z)-\beta I(Y;Z)$is non-convex and existing solutions guarantee only local convergence. As a result, the obtained solutions depend on initialization. Second, the evaluation of a solution is also a challenging task. Conventionally, it resorts to characterizing the information plane, that is, plotting$I(Y;Z)$versus$I(X;Z)$for all solutions obtained from different initial points. Furthermore, the IB Lagrangian has phase transitions while varying the multiplier$\beta$. At phase transitions, both$I(X;Z)$and$I(Y;Z)$increase abruptly and the rate of convergence becomes significantly slow for existing solutions. Recent works with IB adopt variational surrogate bounds to the IB Lagrangian. Although allowing efficient optimization, how close are these surrogates to the IB Lagrangian is not clear. In this work, we solve the IB Lagrangian using augmented Lagrangian methods. With augmented variables, we show that the IB objective can be solved with the alternating direction method of multipliers (ADMM). Different from prior works, we prove that the proposed algorithm is consistently convergent, regardless of the value of$\beta$. Empirically, our gradient-descent-based method results in information plane points that are comparable to those obtained through the conventional Blahut-Arimoto-based solvers, and is convergent for a wider range of the penalty coefficient than previous ADMM-based solvers.

We study information theoretic models of interference networks that consist of K Base Station (BS) - Mobile Terminal (MT) pairs. BS i is connected to the MTs with indices in the se t{i,i+1,.. .,i+L}. We fix the value of Land study the per user Degrees of Freedom (puDoF) in large networks. We assume that each MT can be associated with Nc BSs, and these associations are determined by a cloud-based controller that has a global view of the network. An MT has to be associated with a BS, for the BS to transmit its message in the downlink, or have its decoded message in the uplink. We propose puDoF inner bounds for arbitrary values of L for the uplink, and prove their optimality when only zero-forcing schemes are allowed. We then introduce new achievable average uplink-downlink puDoF values, and show their optimality for the range when Nc≤ L1/2 and when we restrict our attention to zero-forcing schemes. Additionally, for the remaining range, we characterize the optimal downlink scheme when the uplink-optimal associations are used. Finally, we show that the proposed scheme is information theoretically optimal for Wyner's linear interference network.

The problem of interference management is considered in the context of a linear interference network that is subject to long term channel fluctuations due to shadow fading. The slow fading model used is one where communication takes place over blocks of time slots and each link in the network is subject independently to block erasure with probability p. It is assumed that each receiver in the network is interested in one unique message, which is made available at M transmitters. For the case where M = 1, the cell association problem is considered, and for M > 1, the problem of setting up the backhaul links for Coordinated Multi-Point (CoMP) transmission is investigated. In both cases, optimal schemes from a Degrees of Freedom (DoF) viewpoint are analyzed for the setting of no erasures, and new schemes are proposed with better average DoF performance at higher probabilities of erasure. Assuming separate coding over different deep fading erasure blocks, the average per user DoF for M = 1 is characterized for every value of p, and optimal message assignments are identified. For M > 1, it is first established that there is no strategy for assigning messages to transmitters in networks that is optimal for all values of p. The optimal cooperative zero-forcing scheme for M = 2 is then identified, and shown to be information-theoretically optimal when the size of the largest subnetwork that contains no erased links is at most five.

Coded caching techniques have received significant attention lately due to their provable gains in reducing the cost of data delivery in wireless networks. These gains, however, have only been demonstrated under the assumption of a free placement phase. This unrealistic assumption poses a significant limitation, especially in cases where aggressive placement strategies can lead to a significant transmission cost that may even be higher than the corresponding cost of the delivery phase. In this paper, we relax this assumption and propose a general caching framework that captures the transmission cost of the two phases, and hence, results in minimizing the overall rate of the caching network. We model the dynamic nature of the network through a cost structure that allows for varying the network architecture and cost per transmission, across the placement and delivery phases. We start with the scenario where the individual users have no limit on the available caching memory and characterize the jointly optimal solution as a function of the different parameters in our cost structure. Then, we characterize the effect of memory constraints on the optimal solution in certain special cases. Interestingly, our results identify regions where the uncoded caching scheme outperforms its coded counterpart. Further, coded caching is shown to offer performance gains only when the network architecture during the placement phase is different from that during the delivery phase.

In this work, we study a large linear interference network with an equal number of transmitters and receivers, where each transmitter is connected to two subsequent receivers. Each transmitter has individual access to a backhaul link (fetching the equivalent of MTfiles), while each receiver can cache a fraction γ of the library. We explore the tradeoff between the communication rate, backhaul load, and caching storage by designing algorithms that can harness the benefits of cooperative transmission in partially connected networks, while exploiting the advantages of multicast transmissions attributed to user caching. We show that receiver caching and fetching content from the backhaul are two resources that can simultaneously increase the delivery performance in synergistic ways. Specifically, an interesting outcome of this work is that user caching of a fraction γ of the library can increase the per-user Degrees of Freedom (puDoF) by γ. Further, the results reveal significant savings in the backhaul load, even in the small cache size region. For example, the puDoF achieved using the pair (MT= 8,γ = 0) can also be achieved with the pairs (MT= 4,γ = 0.035) and (MT= 2,γ = 0.1), showing that small caches can provide significant savings in the backhaul load.

Graph-based methods have been quite successful in solving unsupervised and semi-supervised learning problems, as they provide a means to capture the underlying geometry of the dataset. It is often desirable for the constructed graph to satisfy two properties: first, data points that are similar in the feature space should be strongly connected on the graph, and second, the class label information should vary smoothly with respect to the graph, where smoothness is measured using the spectral properties of the graph Laplacian matrix. Recent works have justified some of these smoothness conditions by showing that they are strongly linked to the semi-supervised smoothness assumption and its variants. In this work, we reinforce this connection by viewing the problem from a graph sampling theoretic perspective, where class indicator functions are treated as bandlimited graph signals (in the eigenvector basis of the graph Laplacian) and label prediction as a bandlimited reconstruction problem. Our approach involves analyzing the bandwidth of class indicator signals generated from statistical data models with separable and nonseparable classes. These models are quite general and mimic the nature of most real-world datasets. Our results show that in the asymptotic limit, the bandwidth of any class indicator is also closely related to the geometry of the dataset. This allows one to theoretically justify the assumption of bandlimitedness of class indicator signals, thereby providing a sampling theoretic interpretation of graph-based semi-supervised classification.

Degrees of freedom (DoFs) gains are studied in wireless networks with cooperative transmission under a backhaul load constraint that limits the average number of messages that can be delivered from a centralized controller to base station transmitters. The backhaul load is defined as the sum of all the messages available at all the transmitters per channel use, normalized by the number of users. For Wyner's linear interference network, where each transmitter is connected to the receiver having the same index as well as one succeeding receiver, the per user DoF is characterized and the optimal scheme is presented. Furthermore, it is shown that the optimal assignment of messages to transmitters is asymmetric and satisfies a local cooperation constraint and the optimal coding scheme relies only on one-shot cooperative zero-forcing transmit beamforming. Using insights from the analysis of Wyner's linear interference network, the results are extended to the more practical hexagonal sectored cellular network, and coding schemes based on cooperative zero-forcing are shown to deliver significant DoF gains. It is established that by allowing for cooperative transmission and a flexible message assignment that is constrained only by an average backhaul load, one can deliver the rate gains promised by information-theoretic upper bounds with practical one-shot schemes that incur little or no additional load on the backhaul. Finally, useful upper bounds on the per user DoF for schemes based on cooperative zero-forcing are presented for lower values of the average backhaul load constraint, and an optimization framework is formulated for the general converse problem.

We study the problem of finding the optimal cell association as well as the per user degrees of freedom (puDoF) in large interference networks with local connectivity, where each base station is connected to the mobile terminal with the same index as well as L following mobile terminals. In order for a base station transmitter to transmit the message desired by a mobile receiver in the downlink, or for a base station receiver to decode the message transmitted by a mobile transmitter in the uplink, we have the necessary condition that the base station has to be associated with the mobile terminal. We assume that each mobile terminal can only be associated with Nc base stations. The association constraint reflects a rate-limited backhaul network as well as potential handshaking overhead. We restrict our attention to cooperative zero- forcing schemes in the downlink and message passing decoding in the uplink. In previous work, this problem was settled when considering only the downlink, as well as when considering only the uplink for the case when Nc ≥ [L/2]. Here, we settle the problem when only the uplink is considered by providing a converse proof for the case when . We then show how this result combined with existing results in the literature settles the uplink-downlink average puDoF problem when Nc ≤ [L/2]. We finally make progress towards solving the average puDoF problem when , by fixing the uplink scheme to the uplink-only optimal scheme and then finding the optimal downlink scheme, and consequently the average puDoF under this constraint.

In this work, we study the value of cooperative transmission in wireless networks if no channel state information is available at the transmitters (no CSIT). Our focus is on large locally connected networks, where each transmitter is connected to the receiver that has the same index as well as L succeeding receivers. The cases of L = 1 and L = 2 represent Wyner's asymmetric and symmetric network models, respectively. The considered performance metric is the per user Degrees of Freedom (puDoF) as the number of transmitter-receiver pairs goes to infinity. For the case when L = 1, it was shown in previous work that linear cooperation schemes do not increase the puDoF value, and that the optimal scheme relies on assigning each message to a single transmitter and using orthogonal access (TDMA). Here, we extend this conclusion to the case where L = 2, by proving optimality of TDMA in this case as well. We conclude by discussing whether increasing the value of L can create a value for linear cooperation schemes from a DoF perspective.

We consider the problem of non-coherent interference alignment, in which the goal is to align the signals of multiple interfering transmitters at a single receiver where the transmitters are not aware of the channel state information. We cast this problem as a problem of determining rank loss conditions for a column concatenation of full-rank matrices, such that each row of the composing matrices is scaled by a random coefficient. We determine necessary and sufficient conditions for the design of each matrix, such that the random ensemble will almost surely lose rank by a certain amount. The result is proved by converting the problem to determining rank loss conditions for the union of some specific matroids, and then using tools from matroid and graph theories to derive the necessary and sufficient conditions. As an application, we discuss how this result can be applied to the problem of topological interference management, and characterize the linear symmetric degrees of freedom for a class of network topologies.

We study the problem of associating mobile terminals to base stations in a linear interference network, with the goal of maximizing the average rate achieved over both the uplink and downlink sessions. The cell association decision is made at a centralized cloud level, with access to global network topology information. More specifically, given the constraint that each mobile terminal can be associated to a maximum of Ncbase stations at once, we characterize the maximum achievable pre-log factor (degrees of freedom) and the corresponding cell association pattern. Interestingly, the result indicates that for the case where Nc≥ 2, the optimal cell association guarantees the achievability of the maximum uplink rate even when optimizing for the uplink alone, and for the case where Nc= 1, the optimal cell association is that of the downlink. Hence, this work draws attention to the question of characterizing network topologies for which the problem can be simplified by optimizing only for the uplink or only for the downlink.

Graph-based methods play an important role in unsupervised and semi-supervised learning tasks by taking into account the underlying geometry of the data set. In this paper, we consider a statistical setting for semi-supervised learning and provide a formal justification of the recently introduced framework of bandlimited interpolation of graph signals. Our analysis leads to the interpretation that, given enough labeled data, this method is very closely related to a constrained low density separation problem as the number of data points tends to infinity. We demonstrate the practical utility of our results through simple experiments.

We study the problem of interference management in fast fading wireless networks, in which the transmitters are only aware of network topology. We consider a class of retransmission-based schemes, where transmitters in the network are only allowed to resend their symbols in order to assist with the neutralization of interference at the receivers. We introduce a necessary and sufficient condition on the network topology, under which half symmetric degrees-of-freedom (DoF) is achievable through the considered retransmission-based schemes. This corresponds to the “best” topologies since half symmetric DoF is the highest possible value for the symmetric DoF in the presence of interference. We show that when the condition is satisfied, there always exists a set of carefully chosen transmitters in the network, such that by retransmission of their symbols at an appropriate time slot, we can neutralize all the interfering signals at the receivers. Quite surprisingly, we also show that for any given network topology, if we cannot achieve half symmetric DoF by retransmission-based schemes, then there does not exist any linear scheme that can do so. We also consider a practical network scenario that models cell edge users in a heterogeneous network, and show that the characterized condition on the network topology occurs frequently. Furthermore, we numerically evaluate the achievable rates of the DoF-optimal retransmission-based scheme in such network scenario, and show that its throughput gain is not restricted to the asymptotic DoF analysis.

We propose a novel interference management framework for the cellular downlink through cooperative transmission. A sectored cellular network is studied where the interference is only due to sectors in neighboring cells and intra cell interference is ignored. We first explore the potential degrees of freedom (DoF) gain in a scenario where mobile receivers can be associated to any neighboring cell but no cooperative transmission is allowed. We show that the maximum achievable per user DoF for orthogonal schemes is between 1/3 and 3/7. On the other hand, if cooperative transmission is combined with flexible message assignment to the transmitters, we show that it is possible to achieve a per user DoF of 7/15. In addition, the proposed cooperative transmission scheme does not require extra backhaul capacity, as it uses a smart assignment of messages to transmitters to meet an average backhaul load constraint of one message per transmitter.

We consider the problem of determining rank loss conditions for a concatenation of full-rank matrices, such that each row of the composing matrices is scaled by a random coefficient. This problem has applications in wireless interference management and recommendation systems. We determine necessary and sufficient conditions for the design of each matrix, such that the random ensemble will almost surely lose rank by a certain amount. The result is proved by converting the problem to determining rank loss conditions for the union of some specific matroids, and then using tools from matroid and graph theories to derive the necessary and sufficient conditions. As an application, we discuss how this result can be applied to the problem of topological interference management, and characterize the linear symmetric degrees of freedom for a class of network topologies.

The considered problem is that of maximizing the degrees of freedom (DoF) in cellular downlink, under a backhaul load constraint that limits the number of messages that can be delivered from a centralized controller to the base station transmitters. A linear interference channel model is considered, where each transmitter is connected to the receiver having the same index as well as one succeeding receiver. The backhaul load is defined as the sum of all the messages available at all the transmitters normalized by the number of users. When the backhaul load is constrained to an integer level B, the asymptotic per user DoF is shown to equal equation, and it is shown that the optimal assignment of messages to transmitters is asymmetric and satisfies a local cooperation constraint and that the optimal coding scheme relies only on zero-forcing transmit beamforming. Finally, an extension of the presented coding scheme for the case where B = 1 is shown to apply for more general locally connected and two-dimensional networks.

Coordinated multipoint (CoMP) transmission is an infrastructural enhancement under consideration for next generation wireless networks. In this paper, the capacity gain achieved through CoMP transmission is studied in various models of wireless networks that have practical significance. The capacity gain is analyzed through the degrees of freedom (DoF) criterion. The DoF available for communication provides an analytically tractable way to characterize the capacity of interference channels. The considered channel model has K transmitter/receiver pairs, and each receiver is interested in one unique message from a set of K independent messages. Each message can be available at more than one transmitter. The maximum number of transmitters at which each message can be available, is defined as the cooperation order M. For fully connected interference channels, it is shown that the asymptotic per user DoF, as K goes to infinity, remains at 1/2 as M is increased from 1 to 2. Furthermore, the same negative result is shown to hold for all M ≥ 2 for any message assignment that satisfies a local cooperation constraint. On the other hand, when the assumption of full connectivity is relaxed to local connectivity, and each transmitter is connected only to its own receiver as well as L neighboring receivers, it is shown that local cooperation is optimal. The asymptotic per user DoF is shown to be at least max {1/2, 2M/(2M + L)} for locally connected channels, and is shown to be 2M/(2M + 1) for the special case of Wyner's asymmetric model where L = 1. An interesting feature of the proposed achievability scheme is that it relies on simple zero-forcing transmit beams and does not require symbol extensions. Also, to achieve the optimal per user DoF for Wyner's model, messages are assigned to transmitters in an asymmetric fashion unlike traditional assignments where message i has to be available at transmitter i. It is also worth noting that some receivers have to be inactive, and fractional reuse is needed to achieve equal DoF for all users.

The two-way wiretap channel is considered in this paper. Two legitimate users, Alice and Bob, wish to exchange messages securely in the presence of a passive eavesdropper Eve. In the full-duplex scenario, where each node can transmit and receive simultaneously, new achievable secrecy rate regions are obtained based on the idea of allowing the two users to jointly optimize their channel prefixing distributions and binning codebooks in addition to key sharing. The new regions are shown to be strictly larger than the known ones for a wide class of discrete memoryless and Gaussian channels. In the half-duplex case, where a user can only transmit or receive on any given degree of freedom, the idea of randomized scheduling is introduced and shown to offer a significant gain in terms of the achievable secrecy sum-rate. A practical setup is further developed based on a near field wireless communication scenario, and it is shown that one can exploit the two-way nature of the communication, via appropriately randomizing the transmit power levels and transmission schedule, to introduce significant ambiguity at a noiseless Eve.

The degrees of freedom (DoF) available for communication provides an analytically tractable way to characterize the information-theoretic capacity of interference channels. In this paper, the DoF of a K-user interference channel is studied under the assumption that the transmitters can cooperate via coordinated multi-point (CoMP) transmission. In [1], the authors considered the linear asymmetric model of Wyner, where each transmitter is connected to its own receiver and its successor, and is aware of its own message as well as M − 1 preceding messages. The per user DoF was shown to go to M/M+1 as the number of users increases to infinity. In this work, the same model of channel connectivity is considered, with a relaxed cooperation constraint that bounds the maximum number of transmitters at which each message can be available, by a cooperation order M. We show that the relaxation of the cooperation constraint, while maintaining the same load imposed on a backhaul link needed to distribute the messages, results in a gain in the DoF. In particular, the asymptotic limit of the per user DoF under the cooperation order constraint is 2M/2M+1. Moreover, the optimal transmit set selection satisfies a local cooperation constraint. i.e., each message needs only to be available at neighboring transmitters.

We consider locally connected K-user MISO interference channels where each transmitter has N antennas and is connected to the receiver with the same index as well as [L/2] successively preceding receivers and [L/2] following receivers. We assume that each receiver is interested in one message, which can be available at a maximum of M transmitters. Under these assumptions, we study the available degrees of freedom as well as the optimal way to assign messages to transmitters. For the case where each message is assigned to the transmitter with the same index, we know from [1] that [KN/N+1] DoF is achievable for the considered locally connected channel using interference alignment as the number of symbol extensions goes to infinity. In this work, we show that a simple linear strategy employing zero forcing transmit beams achieves min {2MN/M(N+1)+L, 1} per user degrees of freedom. In particular, the N/N+1 per user DoF is achievable by coding over only one channel realization, for any value of M ≥ L/N+1. Moreover, we show that the proposed scheme is optimal among a class of linear strategies where each receiver is either inactive or enjoys interference-free communication. Finally, we generalize the upper bound proved for Wyner's asymmetric channel model (L = 1) in [2], and show that message assignments satisfying a local cooperation constraint are optimal for a general setting of the parameters.

We study the degrees of freedom (DoF) of the$K$-user interference channel with coordinated multipoint (CoMP) transmission and reception. Each message is jointly transmitted by$M_{t}$successive transmitters, and is jointly received by$M_{r}$successive receivers. We refer to this channel as the CoMP channel with a transmit cooperation order of$M_{t}$and receive cooperation order of$M_{r}$. Since the channel has a total of$K$transmit antennas and$K$receive antennas, the maximum possible DoF is equal to$K$. We show that the CoMP channel has$K$DoF if and only if$M_{t} + M_{r} \geq K+1$. The key idea is that the zero forcing of the interference corresponding to the$i{{\rm th}}$message at the decoder of the$j{{\rm th}}$message, where$j \ne i$, can be viewed as a shared responsibility between the$M_{t}$transmitters carrying the$i{{\rm th}}$message, and the$M_{r}$receivers decoding the$j{{\rm th}}$message. For the general case, we derive an outer bound that states that the DoF is bounded above by$\left \lceil (K+M_{t}+M_{r}-2)/2\right \rceil$. For the special case with only CoMP transmission, i.e,$M_{r} = 1$, we propose a scheme that can achieve$(K+M_{t}-1)/2$DoF for all$K < 10$, and conjecture that the result holds true for all$K$. In the proposed coding scheme, the$M_{t}$transmitters carrying each message are used to cancel the interference introduced by this message at the first$M_{t}-1$receivers, thereby allowing each of these receivers to enjoy 1 DoF, and asymptotic interference alignment is used to align the interfering signals at each other receiver to occupy half the signal space. The achievability proofs are based on the notion of algebraic independence from algebraic geometry.

We study the degrees of freedom (DoF) of a Gaussian interference network with K transmitters and K receivers, where the transmitters are allowed to cooperate (partially) to transmit information to the receivers.

We consider the K-user Gaussian interference channel in the context of the downlink of a cellular system where the base stations can exchange messages through a backhaul network, and the interfering users can be jointly served by multiple base stations. To limit the load on the backhaul network, the number of (base station) transmitters sharing a given message is bounded by a number M, which we call the cooperation order. We provide outer bounds on the sum degrees of freedom of this system, which are shown to be tight in special cases.

This paper develops a new physical layer framework for secure two-way wireless communication in the presence of a passive eavesdropper, i.e., Eve. Our approach achieves perfect information theoretic secrecy via a novel randomized scheduling and power allocation scheme. The key idea is to allow Alice and Bob to send symbols at random time instants. While Alice will be able to determine the symbols transmitted by Bob, Eve will suffer from ambiguity regarding the source of any particular symbol. This desirable ambiguity is enhanced, in our approach, by randomizing the transmit power level. Our theoretical analysis, in a 2-D geometry, reveals the ability of the proposed approach to achieve relatively high secure data rates under mild conditions on the spatial location of Eve. These theoretical claims are then validated by experimental results using IEEE 802.15.4-enabled sensor boards in different configurations, motivated by the spatial characteristics of Wireless Body Area Networks (WBAN).