arXiv subjects

Daniela Tuninetti

Publications and source records attributed to Daniela Tuninetti.

At least 55 records · Page 3Linked to original sources

arXiv2018

On Erasure Broadcast Channels with Hard Deadlines

This paper considers packet scheduling over a broadcast channel with packet erasures to multiple receivers with different messages (multiple uni-cast) each with possibly different hard deadline constraints. A novel metric is proposed and evaluated: the global deadline outage probability, which gives the probability that the hard communication deadline is not met for at least one of the receivers. The cut-set upper bound is derived and a scheduling policy is proposed to determine which receiver's packets should be sent in each time slot. This policy is shown to be optimal among all scheduling policies, i.e., it achieves all boundary points of cut-set upper bounds when the transmitter knows the erasure patterns for all the receivers ahead of making the scheduling decision. An expression for the global deadline outage probability is obtained for two receivers and is plotted and interpreted for various system parameters. These plots are not Monte-Carlo simulations, and hence the obtained expression may be used in the design of future downlink broadcast networks. Future extensions to per-user deadline outage probabilities as well as to scenarios with causal knowledge of the channel states are briefly discussed.

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arXiv2018

On the Capacity of the Slotted Strongly Asynchronous Channel with a Bursty User

In this paper, the trade-off between the number of transmissions (or burstiness) $K_n=e^{nν}$ of a user, the asynchronism level $A_n=e^{nα}$ in a slotted strongly asynchronous channel, and the ability to distinguish $M_n=e^{nR}$ messages per transmission with vanishingly error probability is investigated in the asymptotic regime as blocklength $n$ goes to infinity. The receiver must locate and decode, with vanishing error probability in $n$, all of the transmitted messages. Achievability and converse bounds on the trade-off among $(R,α,ν)$ is derived. For cases where $ν=0$ and $ R=0$, achievability and converse bounds coincide. A second model for a bursty user with random access in which the user may access and transmit a message in each block with probability $e^{-nβ}$ in then considered. Achievability and converse bounds on the trade-off between $(R, α, β)$ is also characterized. For cases where $β=α$ and $R=0$, the achievability and converse bounds match.

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arXiv2018

The Strongly Asynchronous Massive Access Channel

This paper considers a Strongly Asynchronous and Slotted Massive Access Channel (SAS-MAC) where $K_n:=e^{nν}$ different users transmit a randomly selected message among $M_n:=e^{nR}$ ones within a strong asynchronous window of length $A_n:=e^{nα}$ blocks, where each block lasts $n$ channel uses. A global probability of error is enforced, ensuring that all the users' identities and messages are correctly identified and decoded. Achievability bounds are derived for the case that different users have similar channels, the case that users' channels can be chosen from a set which has polynomially many elements in the blocklength $n$, and the case with no restriction on the users' channels. A general converse bound on the capacity region and a converse bound on the maximum growth rate of the number of users are derived.

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arXiv2018

An Information Theoretic Converse for the "Consecutive Complete--$S$" PICOD Problem

Pliable Index CODing (PICOD) is a variant of the Index Coding (IC) problem in which a user is satisfied whenever it can successfully decode any one message that is not in its side information set, as opposed to a fixed pre-determined message. The complete--$S$ PICOD with $m$ messages, for $S\subseteq[0:m-1]$, has $n = \sum_{s\in S} \binom{m}{s}$ users with distinct side information sets. Past work on PICOD provided tight converse results when either the sender is constrained to use linear codes, or for some special classes of complete--$S$ PICOD. This paper provides a tight information theoretic converse result (i.e., no restriction to linear codes) for the so-called "consecutive complete--$S$" PICOD, where the set $S$ satisfies $S=[s_{min} : s_{max}]$ for some $0\leq s_{min} \leq s_{max} \leq m-1$. This result extends existing converse results and shows that linear codes have the smallest possible code length given by $\min(m-s_{\min},1+s_{\max})$. The central contribution is a novel proof technique rooted in combinatorics. The main idea is to consider all the messages a user can eventually successfully decode, in addition to its own desired message. This allows us to circumvent the necessity of essentially considering all possible assignments of desired messages for the users. The keystone of the proof is to show that, for the case of $S=\{s\}$ and $m = 2s+1$, there exists at least one user who can decode $s+1$ messages. From this, the extension to the "consecutive complete--$S$" PICOD follows.

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arXiv2018

Caching in Combination Networks: Novel Multicast Message Generation and Delivery by Leveraging the Network Topology

Maddah-Ali and Niesen's original coded caching scheme for shared-link broadcast networks is now known to be optimal to within a factor two, and has been applied to other types of networks. For practical reasons, this paper considers that a server communicates to cache-aided users through $H$ intermediate relays. In particular, it focuses on combination networks where each of the $K = \binom{H}{r}$ users is connected to a distinct $r$-subsets of relays. By leveraging the symmetric topology of the network, this paper proposes a novel method to general multicast messages and to deliver them to the users. By numerical evaluations, the proposed scheme is shown to reduce the download time compared to the schemes available in the literature. The idea is then extended to decentralized combination networks, more general relay networks, and combination networks with cache-aided relays and users. Also in these cases the proposed scheme outperforms known ones.

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arXiv2018

On Combination Networks with Cache-aided Relays and Users

Caching is an efficient way to reduce peak hour network traffic congestion by storing some contents at the user's cache without knowledge of later demands. Coded caching strategy was originally proposed by Maddah-Ali and Niesen to give an additional coded caching gain compared the conventional uncoded scheme. Under practical consideration, the caching model was recently considered in relay network, in particular the combination network, where the central server communicates with $K=\binom{H}{r}$ users (each is with a cache of $M$ files) through $H$ immediate relays, and each user is connected to a different $r-$subsets of relays. Several inner bounds and outer bounds were proposed for combination networks with end-user-caches. This paper extends the recent work by the authors on centralized combination networks with end-user caches to a more general setting, where both relays and users have caches. In contrast to the existing schemes in which the packets transmitted from the server are independent of the cached contents of relays, we propose a novel caching scheme by creating an additional coded caching gain to the transmitted load from the server with the help of the cached contents in relays. We also show that the proposed scheme outperforms the state-of-the-art approaches.

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arXiv2018

On the Benefits of Asymmetric Coded Cache Placement in Combination Networks with End-User Caches

This paper investigates the fundamental tradeoff between cache size and download time in the (H;r;M;N) combination network, where a server with N files is connected to H relays (without caches) and each of the K:=\binom{H}{r} users (with caches of size M files) is connected to a different subset of r relays. Existing schemes fall within two categories: either use the uncoded symmetric cache placement originally proposed for the shared-link model and design delivery phase dependent on the network topology, or effectively divide the combination network into H independent shared-link networks each serving \binom{H-1}{r-1} users; in either case, the placement phase is independent of network topology. In this paper, a novel strategy is proposed where the coded cache placement is dependent on network topology. The proposed scheme is shown to be information theoretically optimal for large cache size. In addition, when not exactly optimal, the proposed scheme can also outperform existing schemes.

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arXiv2018

Caching in Combination Networks: A Novel Delivery by Leveraging the Network Topology

Maddah-Ali and Niesen (MAN) in 2014 surprisingly showed that it is possible to serve an arbitrarily large number of cache-equipped users with a constant number of transmissions by using coded caching in shared-link broadcast networks. This paper studies the tradeoff between the user's cache size and the file download time for combination networks, where users with caches communicate with the servers through intermediate relays. Motivated by the so-called separation approach, it is assumed that placement and multicast message generation are done according to the MAN original scheme and regardless of the network topology. The main contribution of this paper is the design of a novel two-phase delivery scheme that, accounting to the network topology, outperforms schemes available in the literature. The key idea is to create additional (compared to MAN) multicasting opportunities: in the first phase coded messages are sent with the goal of increasing the amount of `side information' at the users, which is then leveraged during the second phase. The download time with the novel scheme is shown to be proportional to 1=H (with H being the number or relays) and to be order optimal under the constraint of uncoded placement for some parameter regimes.

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arXiv2018

A Novel Asymmetric Coded Placement in Combination Networks with end-user Caches

The tradeoff between the user's memory size and the worst-case download time in the $(H,r,M,N)$ combination network is studied, where a central server communicates with $K$ users through $H$ immediate relays, and each user has local cache of size $M$ files and is connected to a different subset of $r$ relays. The main contribution of this paper is the design of a coded caching scheme with asymmetric coded placement by leveraging coordination among the relays, which was not exploited in past work. Mathematical analysis and numerical results show that the proposed schemes outperform existing schemes.

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arXiv2018

On Identifying a Massive Number of Distributions

Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of observed sequences, are let to grow with the observation blocklength $n$. Asymptotically matching upper and lower bounds on the probability of error are derived.

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arXiv2017

Half-Duplex Routing is NP-hard

Routing is a widespread approach to transfer information from a source node to a destination node in many deployed wireless ad-hoc networks. Today's implemented routing algorithms seek to efficiently find the path/route with the largest Full-Duplex (FD) capacity, which is given by the minimum among the point-to-point link capacities in the path. Such an approach may be suboptimal if then the nodes in the selected path are operated in Half-Duplex (HD) mode. Recently, the capacity (up to a constant gap that only depends on the number of nodes in the path) of an HD line network i.e., a path) has been shown to be equal to half of the minimum of the harmonic means of the capacities of two consecutive links in the path. This paper asks the questions of whether it is possible to design a polynomial-time algorithm that efficiently finds the path with the largest HD capacity in a relay network. This problem of finding that path is shown to be NP-hard in general. However, if the number of cycles in the network is polynomial in the number of nodes, then a polynomial-time algorithm can indeed be designed.

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arXiv2017

Network Simplification in Half-Duplex: Building on Submodularity

This paper explores the {\it network simplification} problem in the context of Gaussian Half-Duplex (HD) diamond networks. Specifically, given an $N$-relay diamond network, this problem seeks to derive fundamental guarantees on the capacity of the best $k$-relay subnetwork, as a function of the full network capacity. The main focus of this work is on the case when $k=N-1$ relays are selected out of the $N$ possible ones. First, a simple algorithm, which removes the relay with the minimum capacity (i.e., the worst relay), is analyzed and it is shown that the remaining $(N-1)$-relay subnetwork has an approximate (i.e., optimal up to a constant gap) HD capacity that is at least half of the approximate HD capacity of the full network. This fraction guarantee is shown to be tight if only the single relay capacities are known, i.e., there exists a class of Gaussian HD diamond networks with $N$ relays where, by removing the worst relay, the subnetwork of the remaining $k=N-1$ relays has an approximate capacity equal to half of the approximate capacity of the full network. Next, this work proves a fundamental guarantee, which improves over the previous fraction: there always exists a subnetwork of $k=N-1$ relays that achieves at least a fraction $\frac{N-1}{N}$ of the approximate capacity of the full network. This fraction is proved to be tight and it is shown that any optimal schedule of the full network can be used by at least one of the $N$ subnetworks of $N-1$ relays to achieve a worst-case performance guarantee of $\frac{N-1}{N}$. Additionally, these results are extended to derive lower bounds on the fraction guarantee for general $k \in [1:N]$. The key steps in the proofs lie in the derivation of properties of submodular functions, which provide a combinatorial handle on the network simplification problem in Gaussian HD diamond networks.

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arXiv2017

Efficiently Finding Simple Schedules in Gaussian Half-Duplex Relay Line Networks

The problem of operating a Gaussian Half-Duplex (HD) relay network optimally is challenging due to the exponential number of listen/transmit network states that need to be considered. Recent results have shown that, for the class of Gaussian HD networks with N relays, there always exists a simple schedule, i.e., with at most N +1 active states, that is sufficient for approximate (i.e., up to a constant gap) capacity characterization. This paper investigates how to efficiently find such a simple schedule over line networks. Towards this end, a polynomial-time algorithm is designed and proved to output a simple schedule that achieves the approximate capacity. The key ingredient of the algorithm is to leverage similarities between network states in HD and edge coloring in a graph. It is also shown that the algorithm allows to derive a closed-form expression for the approximate capacity of the Gaussian line network that can be evaluated distributively and in linear time. Additionally, it is shown using this closed-form that the problem of Half-Duplex routing is NP-Hard.

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arXiv2017

Novel Delivery Schemes for Decentralized Coded Caching in the Finite File Size Regime

This paper analyzes the achievable tradeoff between cache~size and download~rate in decentralized caching systems with the uncoded cache placement originally proposed by Maddah-Ali and Niesen. It proposes two novel delivery schemes that take advantage of the multicasting opportunities that arise when a file is demanded by multiple users. These delivery schemes are extensions of known ones to the regime where the file size is finite. Numerical evaluations for the case of file uniform popularity show that the proposed schemes outperform previous ones for all value of the cache size.

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arXiv2017

A Novel Index Coding Scheme and its Application to Coded Caching

This paper proposes a novel achievable scheme for the index problem and applies it to the caching problem. Index coding and caching are noiseless broadcast channel problems where receivers have message side information.In the index coding problem the side information sets are fixed, while in the caching problem the side information sets correspond the cache contents, which are under the control of the system designer. The proposed index coding scheme, based on distributed source coding and non-unique decoding,is shown to strictly enlarge the rate region achievable by composite coding.The novel index coding scheme applied to the caching problem is then shown to match an outer bound (previously proposed by the authors and also based on known results for the index coding problem) under the assumption of uncoded cache placement/prefetching.

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arXiv2017

On the Capacity of the AWGN Channel with Additive Radar Interference

This paper investigates the capacity of a communications channel that, in addition to additive white Gaussian noise, also suffers from interference caused by a co-existing radar transmission. The radar interference (of short duty-cycle and of much wider bandwidth than the intended communication signal) is modeled as an additive term whose amplitude is known and constant, but whose phase is independent and identically uniformly distributed at each channel use. The capacity achieving input distribution, under the standard average power constraint, is shown to have independent modulo and phase. The phase is uniformly distributed in $[0,2π]$. The modulo is discrete with countably infinitly many mass points, but only finitely many in any bounded interval. From numerical evaluations, a proper-complex Gaussian input is seen to perform quite well for weak radar interference. We also show that for very large radar interference, capacity is equal to $1/2\log (1 + S)$ and a proper-complex Gaussian input achieves it. It is concluded that the presence of the radar interference results in a loss of half of the degrees of freedom compared to an AWGN channel without radar interference.

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arXiv2016

On the Minimum Mean $p$-th Error in Gaussian Noise Channels and its Applications

The problem of estimating an arbitrary random vector from its observation corrupted by additive white Gaussian noise, where the cost function is taken to be the Minimum Mean $p$-th Error (MMPE), is considered. The classical Minimum Mean Square Error (MMSE) is a special case of the MMPE. Several bounds, properties and applications of the MMPE are derived and discussed. The optimal MMPE estimator is found for Gaussian and binary input distributions. Properties of the MMPE as a function of the input distribution, SNR and order $p$ are derived. In particular, it is shown that the MMPE is a continuous function of $p$ and SNR. These results are possible in view of interpolation and change of measure bounds on the MMPE. The `Single-Crossing-Point Property' (SCPP) that bounds the MMSE for all SNR values {\it above} a certain value, at which the MMSE is known, together with the I-MMSE relationship is a powerful tool in deriving converse proofs in information theory. By studying the notion of conditional MMPE, a unifying proof (i.e., for any $p$) of the SCPP is shown. A complementary bound to the SCPP is then shown, which bounds the MMPE for all SNR values {\it below} a certain value, at which the MMPE is known. As a first application of the MMPE, a bound on the conditional differential entropy in terms of the MMPE is provided, which then yields a generalization of the Ozarow-Wyner lower bound on the mutual information achieved by a discrete input on a Gaussian noise channel. As a second application, the MMPE is shown to improve on previous characterizations of the phase transition phenomenon that manifests, in the limit as the length of the capacity achieving code goes to infinity, as a discontinuity of the MMSE as a function of SNR. As a final application, the MMPE is used to show bounds on the second derivative of mutual information, that tighten previously known bounds.

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arXiv2016

On Network Simplification for Gaussian Half-Duplex Diamond Networks

This paper investigates the simplification problem in Gaussian Half-Duplex (HD) diamond networks. The goal is to answer the following question: what is the minimum (worst-case) fraction of the total HD capacity that one can always achieve by smartly selecting a subset of $k$ relays, out of the $N$ possible ones? We make progress on this problem for $k=1$ and $k=2$ and show that for $N=k+1, \ k \in \{1,2\}$ at least $\frac{k}{k+1}$ of the total HD capacity is always {approximately (i.e., up to a constant gap)} achieved. Interestingly, and differently from the Full-Duplex (FD) case, the ratio in HD depends on $N$, and decreases as $N$ increases. For all values of $N$ and $k$ for which we derive worst case fractions, we also show these to be {approximately} tight. This is accomplished by presenting $N$-relay Gaussian HD diamond networks for which the best $k$-relay subnetwork has {an approximate} HD capacity equal to the worst-case fraction of the total {approximate} HD capacity. Moreover, we provide additional comparisons between the performance of this simplification problem for HD and FD networks, which highlight their different natures.

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