arXiv subjects

Daniela Tuninetti

Publications and source records attributed to Daniela Tuninetti.

At least 73 records · Page 4Linked to original sources

arXiv2016

On Communication through a Gaussian Channel with an MMSE Disturbance Constraint

This paper considers a Gaussian channel with one transmitter and two receivers. The goal is to maximize the communication rate at the intended/primary receiver subject to a disturbance constraint at the unintended/secondary receiver. The disturbance is measured in terms of minimum mean square error (MMSE) of the interference that the transmission to the primary receiver inflicts on the secondary receiver. The paper presents a new upper bound for the problem of maximizing the mutual information subject to an MMSE constraint. The new bound holds for vector inputs of any length and recovers a previously known limiting (when the length of vector input tends to infinity) expression from the work of Bustin $\textit{et al.}$ The key technical novelty is a new upper bound on the MMSE. This bound allows one to bound the MMSE for all signal-to-noise ratio (SNR) values $\textit{below}$ a certain SNR at which the MMSE is known (which corresponds to the disturbance constraint). This bound complements the `single-crossing point property' of the MMSE that upper bounds the MMSE for all SNR values $\textit{above}$ a certain value at which the MMSE value is known. The MMSE upper bound provides a refined characterization of the phase-transition phenomenon which manifests, in the limit as the length of the vector input goes to infinity, as a discontinuity of the MMSE for the problem at hand. For vector inputs of size $n=1$, a matching lower bound, to within an additive gap of order $O \left( \log \log \frac{1}{\sf MMSE} \right)$ (where ${\sf MMSE}$ is the disturbance constraint), is shown by means of the mixed inputs technique recently introduced by Dytso $\textit{et al.}$

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arXiv2016

On Caching with More Users than Files

Caching appears to be an efficient way to reduce peak hour network traffic congestion by storing some content at the user's cache without knowledge of later demands. Recently, Maddah-Ali and Niesen proposed a two-phase, placement and delivery phase, coded caching strategy for centralized systems (where coordination among users is possible in the placement phase), and for decentralized systems. This paper investigates the same setup under the further assumption that the number of users is larger than the number of files. By using the same uncoded placement strategy of Maddah-Ali and Niesen, a novel coded delivery strategy is proposed to profit from the multicasting opportunities that arise because a file may be demanded by multiple users. The proposed delivery method is proved to be optimal under the constraint of uncoded placement for centralized systems with two files, moreover it is shown to outperform known caching strategies for both centralized and decentralized systems.

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arXiv2015

On the Optimality of Uncoded Cache Placement

Caching is an efficient way to reduce peak-hour network traffic congestion by storing some contents at user's local cache without knowledge of later demands. Maddah-Ali and Niesen initiated a fundamental study of caching systems; they proposed a scheme (with uncoded cache placement and linear network coding delivery) that is provably optimal to within a factor 12. In this paper, by noticing that when the cache contents and the demands are fixed, the caching problem can be seen as an index coding problem, we show the optimality of Maddah-Ali and Niesen's scheme assuming that cache placement is restricted to be uncoded and the number of users is not less than the number of files. Furthermore, this result states that further improvement to the Maddah-Ali and Niesen's scheme in this regimes can be obtained only by coded cache placement.

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arXiv2015

Multi-user Cognitive Interference Channels: A Survey and New Capacity Results

This paper provides a survey of the state-of-the-art information theoretic analysis for overlay multi-user (more than two pairs) cognitive networks and reports new capacity results. In an overlay scenario, cognitive / secondary users share the same frequency band with licensed / primary users to efficiently exploit the spectrum. They do so without degrading the performance of the incumbent users, and may possibly even aid in transmitting their messages as cognitive users are assumed to possess the message(s) of primary user(s) and possibly other cognitive user(s). The survey begins with a short overview of the two-user overlay cognitive interference channel. The evolution from two-user to three-user overlay cognitive interference channels is described next, followed by generalizations to multi-user (arbitrary number of users) cognitive networks. The rest of the paper considers K-user cognitive interference channels with different message knowledge structures at the transmitters. Novel capacity inner and outer bounds are proposed. Channel conditions under which the bounds meet, thus characterizing the information theoretic capacity of the channel, for both Linear Deterministic and Gaussian channel models, are derived. The results show that for certain channel conditions distributed cognition, or having a cumulative message knowledge structure at the nodes, may not be worth the overhead as (approximately) the same capacity can be achieved by having only one global cognitive user whose role is to manage all the interference in the network. The paper concludes with future research directions.

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arXiv2015

On the DoF region of the two-user Interference Channel with an Instantaneous Relay

This paper studies the Degrees of Freedom (DoF) of the two-user multi-antenna Gaussian interference channel with an {\em instantaneous relay}, or relay without delay, where the relay transmitted signal in channel use $t$ can depend on all received signals up to and including that at channel use $t$. It is assumed that the two transmitters and the two receivers have $M$ antennas, while the relay receives through $N$ antennas and transmits through $L$ antennas. An achievable DoF region is derived, for all possible values of $(M,N,L)$, based on a memoryless linear transmission strategy at the relay that aims to {\it neutralize} as much interference as possible at the receivers. The proposed scheme is shown to attain the largest sum DoF among all memoryless linear transmission strategies at the relay and to actually be optimal for certain values of $(M,N,L)$.

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arXiv2015

Interference as Noise: Friend or Foe?

This paper shows that for the two-user Gaussian Interference Channel (G-IC) Treating Interference as Noise without Time Sharing (TINnoTS) achieves the closure of the capacity region to within either a constant gap, or to within a gap of the order O(logln(min(S,I))) where S is the largest Signal to Noise Ratio (SNR) on the direct links and I is the largest Interference to Noise Ratio (INR) on the cross links. As a consequence, TINnoTS is optimal from a generalized Degrees of Freedom (gDoF) perspective for all channel gains except for a subset of zero measure. TINnoTS with Gaussian inputs is known to be optimal to within 1/2 bit for a subset of the weak interference regime. Surprisingly, this paper shows that TINnoTS is gDoG optimal in all parameter regimes, even in the strong and very strong interference regimes where joint decoding of Gaussian inputs is optimal. For approximate optimality of TINnoTS in all parameter regimes it is critical to use non-Gaussian inputs. This work thus proposes to use mixed inputs as channel inputs where a mixed input is the sum of a discrete and a Gaussian random variable. Interestingly, compared to the Han-Kobayashi inner bound, the discrete part of a mixed input is shown to effectively act as a common message in the sense that, although treated as noise, its effect on the achievable rate region is as if it were jointly decoded together with the desired messages at a non-intended receiver. The practical implication is that a discrete interfering input is a 'friend', while a Gaussian interfering input is in general a 'foe'. Since TINnoTS requires neither joint decoding nor time sharing, the results of this paper are applicable to a variety of oblivions or asynchronous channels, such as the block asynchronous G-IC (which is not an information stable) and the G-IC with partial codebook knowledge at one or more receivers.

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arXiv2015

The Two-user Causal Cognitive Interference Channel: Novel Outer Bounds and Constant Gap Result for the Symmetric Gaussian Noise Channel in Weak Interference

This paper studies the two-user Causal Cognitive Interference Channel (CCIC), where two transmitters aim to communicate independent messages to two different receivers via a common channel. One source, referred to as the cognitive, is capable of overhearing the other source, referred to as the primary, through a noisy in-band link and thus can assist in sending the primary's data. Two novel outer bounds of the type $2R_p+R_c$ and $R_p+2R_c$ are derived for the class of injective semi-deterministic CCICs where the noises at the different source-destination pairs are independent. An achievable rate region is derived based on Gelfand-Pinsker binning, superposition coding and simultaneous decoding at the receivers. The lower and outer bounds are then specialized to the practically relevant Gaussian noise case. The authors of this paper recently characterized to within a constant gap the capacity of the symmetric Gaussian CCIC in (a) the strong interference regime, and (b) for a subset of the weak interference regime when the cooperation link is larger than a given threshold. This work characterizes to within a constant gap the capacity for the symmetric Gaussian CCIC in the regime that was still open. In particular, it is shown that the novel outer bounds are necessary to characterize the capacity to within a constant gap when the cooperation link is weaker than the direct links, that is, in this regime unilateral cooperation leaves some system resources underutilized.

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arXiv2015

Coverage in mmWave Cellular Networks with Base station Cooperation

The presence of signal outage, due to shadowing and blockage, is expected to be the main bottleneck in millimeter wave (mmWave) networks. Moreover, with the anticipated vision that mmWave networks would have a dense deployment of base stations, interference from strong line-of-sight base stations increases too, thus further increasing the probability of outage. To address the issue of reducing outage, this paper explores the possibility of base station cooperation in the downlink of a mmWave heterogenous network. The main focus of this work is showing that, in a stochastic geometry framework, cooperation from randomly located base stations decreases outage probability. With the presumed vision that less severe fading will be experienced due to highly directional transmissions, one might expect that cooperation would increase the coverage probability; our numerical examples suggest that is in fact the case. Coverage probabilities are derived accounting for: different fading distributions, antenna directionality and blockage. Numerical results suggest that coverage with base station cooperation in dense mmWave systems and with no small scale fading considerably exceeds coverage with no cooperation. In contrast, an insignificant increase is reported when mmWave networks are less dense with a high probability of signal blockage and with Rayleigh fading.

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arXiv2014

On the Optimality of Simple Schedules for Networks with Multiple Half-Duplex Relays

This paper studies networks with N half-duplex relays assisting the communication between a source and a destination. In ISIT'12 Brahma, Özgür and Fragouli conjectured that in Gaussian half-duplex diamond networks (i.e., without a direct link between the source and the destination, and with N non-interfering relays) an approximately optimal relay scheduling policy (i.e., achieving the cut-set upper bound to within a constant gap) has at most N+1 active states (i.e., at most N+1 out of the $2^N$ possible relay listen-transmit states have a strictly positive probability). Such relay scheduling policies were referred to as simple. In ITW'13 we conjectured that simple approximately optimal relay scheduling policies exist for any Gaussian half-duplex multi-relay network irrespectively of the topology. This paper formally proves this more general version of the conjecture and shows it holds beyond Gaussian noise networks. In particular, for any memoryless half-duplex N-relay network with independent noises and for which independent inputs are approximately optimal in the cut-set upper bound, an approximately optimal simple relay scheduling policy exists. A convergent iterative polynomial-time algorithm, which alternates between minimizing a submodular function and maximizing a linear program, is proposed to find the approximately optimal simple relay schedule. As an example, for N-relay Gaussian networks with independent noises, where each node in equipped with multiple antennas and where each antenna can be configured to listen or transmit irrespectively of the others, the existence of an approximately optimal simple relay scheduling policy with at most N+1 active states is proved. Through a line-network example it is also shown that independently switching the antennas at each relay can provide a strictly larger multiplexing gain compared to using the antennas for the same purpose.

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arXiv2014

The Approximate Optimality of Simple Schedules for Half-Duplex Multi-Relay Networks

In ISIT'12 Brahma, Özgür and Fragouli conjectured that in a half-duplex diamond relay network (a Gaussian noise network without a direct source-destination link and with $N$ non-interfering relays) an approximately optimal relay scheduling (achieving the cut-set upper bound to within a constant gap uniformly over all channel gains) exists with at most $N+1$ active states (only $N+1$ out of the $2^N$ possible relay listen-transmit configurations have a strictly positive probability). Such relay scheduling policies are said to be simple. In ITW'13 we conjectured that simple relay policies are optimal for any half-duplex Gaussian multi-relay network, that is, simple schedules are not a consequence of the diamond network's sparse topology. In this paper we formally prove the conjecture beyond Gaussian networks. In particular, for any memoryless half-duplex $N$-relay network with independent noises and for which independent inputs are approximately optimal in the cut-set upper bound, an optimal schedule exists with at most $N+1$ active states. The key step of our proof is to write the minimum of a submodular function by means of its Lovász extension and use the greedy algorithm for submodular polyhedra to highlight structural properties of the optimal solution. This, together with the saddle-point property of min-max problems and the existence of optimal basic feasible solutions in linear programs, proves the claim.

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arXiv2014

The DoF of the Asymmetric MIMO Interference Channel with Square Direct Link Channel Matrices

This paper studies the sum Degrees of Freedom (DoF) of $K$-user {\em asymmetric} MIMO Interference Channel (IC) with square direct link channel matrices, that is, the $u$-th transmitter and its intended receiver have $M_u\in\mathbb{N}$ antennas each, where $M_u$ need not be the same for all $u\in[1:K]$. Starting from a $3$-user example, it is shown that existing cooperation-based outer bounds are insufficient to characterize the DoF. Moreover, it is shown that two distinct operating regimes exist. With a {\it dominant} user, i.e., a user that has more antennas than the other two users combined, %(say $M_1\geq M_2+M_3$), it is DoF optimal to let that user transmit alone on the IC. Otherwise, it is DoF optimal to {\em decompose} and operate the 3-user MIMO IC as an $(M_1+ M_2+M_3)$-user SISO IC. This indicates that MIMO operations are useless from a DoF perspective in systems without a dominant user. The main contribution of the paper is the derivation of a novel outer bound for the general $K$-user case that is tight in the regime where a dominant user is not present; this is done by generalizing the insights from the 3-user example to an arbitrary number of users.

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arXiv2014

On the Two-user Interference Channel with Lack of Knowledge of the Interference Codebook at one Receiver

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 outer bound is derived and shown to be achievable to within a gap for the class of injective semi-deterministic IC-ORs; the gap is shown to be zero for injective fully deterministic IC-ORs. For the linear deterministic IC-OR that models the Gaussian noise channel at high SNR, non i.i.d. Bernoulli(1/2) input bits are shown to achieve points not achievable by i.i.d. Bernoulli(1/2) input bits used in the same achievability scheme. For the real-valued Gaussian IC-OR the gap is shown to be at most 1/2 bit per channel use, even though the set of optimal input distributions for the derived outer bound could not be determined. Towards understanding the Gaussian IC-OR, an achievability strategy is evaluated in which the input alphabets at the non-oblivious transmitter are a mixture of discrete and Gaussian random variables, where the cardinality of the discrete part is appropriately chosen as a function of the channel parameters. Surprisingly, as the oblivious receiver intuitively should not be able to 'jointly decode' the intended and interfering messages (whose codebook is unavailable), it is shown that with this choice of input, the capacity region of the symmetric Gaussian IC-OR is to within 3.34 bits (per channel use per user) of an outer bound for the classical Gaussian IC with full codebook knowledge.

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arXiv2014

On the Capacity Region of the Two-user Interference Channel with a Cognitive Relay

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, which disregards the noise and focuses on the interaction among the users' signals. The capacity region of the symmetric LDA is completely characterized except for the regime of moderately weak interference and weak links from the CR to the destinations. The insights gained from the analysis of the LDA are then translated back to the symmetric Gaussian noise channel (GICCR). For the symmetric GICCR, an approximate characterization (to within a constant gap) of the capacity region is provided for a parameter regime where capacity was previously unknown. The approximately optimal scheme suggests that message cognition at a relay is beneficial for interference management as it enables simultaneous over the air neutralization of the interference at both destinations.

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arXiv2014

New Outer Bounds for the Interference Channel with Unilateral Source Cooperation

This paper studies the two-user interference channel with unilateral source cooperation, which consists of two source-destination pairs that share the same channel and where one full-duplex source can overhear the other source through a noisy in-band link. Novel outer bounds of the type 2Rp+Rc/Rp+2Rc are developed for the class of injective semi-deterministic channels with independent noises at the different source-destination pairs. The bounds are then specialized to the Gaussian noise case. Interesting insights are provided about when these types of bounds are active, or in other words, when unilateral cooperation is too weak and leaves "holes" in the system resources.

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arXiv2014

On the Gaussian Interference Channel with Half-Duplex Causal Cognition

This paper studies the two-user Gaussian interference channel with half-duplex causal cognition. This channel model consists of two source-destination pairs sharing a common wireless channel. One of the sources, referred to as the cognitive, overhears the other source, referred to as the primary, through a noisy link and can therefore assist in sending the primary's data. Due to practical constraints, the cognitive source is assumed to work in half-duplex mode, that is, it cannot simultaneously transmit and receive. This model is more relevant for practical cognitive radio systems than the classical information theoretic cognitive channel model, where the cognitive source is assumed to have a non-causal knowledge of the primary's message. Different network topologies are considered, corresponding to different interference scenarios: (i) the interference-symmetric scenario, where both destinations are in the coverage area of the two sources and hence experience interference, and (ii) the interference-asymmetric scenario, where one destination does not suffer from interference. For each topology the sum-rate performance is studied by first deriving the generalized Degrees of Freedom (gDoF), or "sum-capacity pre-log" in the high-SNR regime, and then showing relatively simple coding schemes that achieve a sum-rate upper bound to within a constant number of bits for any SNR. Finally, the gDoF of the channel is compared to that of the non-cooperative interference channel and to that of the non-causal cognitive channel to identify the parameter regimes where half-duplex causal cognition is useless in practice or attains its ideal ultimate limit, respectively.

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arXiv2014

On Discrete Alphabets for the Two-user Gaussian Interference Channel with One Receiver Lacking Knowledge of the Interfering Codebook

In multi-user information theory it is often assumed that every node in the network possesses all codebooks used in the network. This assumption is however impractical in distributed ad-hoc and cognitive networks. This work considers the two- user Gaussian Interference Channel with one Oblivious Receiver (G-IC-OR), i.e., one receiver lacks knowledge of the interfering cookbook while the other receiver knows both codebooks. We ask whether, and if so how much, the channel capacity of the G-IC- OR is reduced compared to that of the classical G-IC where both receivers know all codebooks. Intuitively, the oblivious receiver should not be able to jointly decode its intended message along with the unintended interfering message whose codebook is unavailable. We demonstrate that in strong and very strong interference, where joint decoding is capacity achieving for the classical G-IC, lack of codebook knowledge does not reduce performance in terms of generalized degrees of freedom (gDoF). Moreover, we show that the sum-capacity of the symmetric G-IC- OR is to within O(log(log(SNR))) of that of the classical G-IC. The key novelty of the proposed achievable scheme is the use of a discrete input alphabet for the non-oblivious transmitter, whose cardinality is appropriately chosen as a function of SNR.

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arXiv2013

On the Capacity of the Two-user Gaussian Causal Cognitive Interference Channel

This paper considers the two-user Gaussian Causal Cognitive Interference Channel (GCCIC), which consists of two source-destination pairs that share the same channel and where one full-duplex cognitive source can causally learn the message of the primary source through a noisy link. The GCCIC is an interference channel with unilateral source cooperation that better models practical cognitive radio networks than the commonly used model which assumes that one source has perfect non-causal knowledge of the other source's message. First the sum-capacity of the symmetric GCCIC is determined to within a constant gap. Then, the insights gained from the derivation of the symmetric sum-capacity are extended to characterize the whole capacity region to within a constant gap for more general cases. In particular, the capacity is determined (a) to within 2 bits for the fully connected GCCIC when, roughly speaking, the interference is not weak at both receivers, (b) to within 2 bits for the Z-channel, i.e., when there is no interference from the primary user, and (c) to within 2 bits for the S-channel, i.e., when there is no interference from the secondary user. The parameter regimes where the GCCIC is equivalent, in terms of generalized degrees-of-freedom, to the noncooperative interference channel (i.e., unilateral causal cooperation is not useful), to the non-causal cognitive interference channel (i.e., causal cooperation attains the ultimate limit of cognitive radio technology), and to bilateral source cooperation are identified. These comparisons shed lights into the parameter regimes and network topologies that in practice might provide an unbounded throughput gain compared to currently available (non cognitive) technologies.

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arXiv2013

Gaussian Half-Duplex Relay Networks: improved constant gap and connections with the assignment problem

This paper considers a general Gaussian relay network where a source transmits a message to a destination with the help of N half-duplex relays. It proves that the information theoretic cut-set upper bound to the capacity can be achieved to within 2:021(N +2) bits with noisy network coding, thereby reducing the previously known gap. Further improved gap results are presented for more structured networks like diamond networks. It is then shown that the generalized Degrees-of-Freedom of a general Gaussian half-duplex relay network is the solution of a linear program, where the coefficients of the linear inequality constraints are proved to be the solution of several linear programs, known in graph theory as the assignment problem, for which efficient numerical algorithms exist. The optimal schedule, that is, the optimal value of the 2^N possible transmit-receive configurations/states for the relays, is investigated and known results for diamond networks are extended to general relay networks. It is shown, for the case of 2 relays, that only 3 out of the 4 possible states have strictly positive probability. Extensive experimental results show that, for a general N-relay network with N<9, the optimal schedule has at most N +1 states with strictly positive probability. As an extension of a conjecture presented for diamond networks, it is conjectured that this result holds for any HD relay network and any number of relays. Finally, a 2-relay network is studied to determine the channel conditions under which selecting the best relay is not optimal, and to highlight the nature of the rate gain due to multiple relays.

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