arXiv subjects

Michelle Effros

Publications and source records attributed to Michelle Effros.

At least 37 records · Page 2Linked to original sources

arXiv2019

Negligible Cooperation: Contrasting the Maximal- and Average-Error Cases

In communication networks, cooperative strategies are coding schemes where network nodes work together to improve network performance metrics such as the total rate delivered across the network. This work studies encoder cooperation in the setting of a discrete multiple access channel (MAC) with two encoders and a single decoder. A network node, here called the cooperation facilitator (CF), that is connected to both encoders via rate-limited links, enables the cooperation strategy. Previous work by the authors presents two classes of MACs: (i) one class where the average-error sum-capacity has an infinite derivative in the limit where CF output link capacities approach zero, and (ii) a second class of MACs where the maximal-error sum-capacity is not continuous at the point where the output link capacities of the CF equal zero. This work contrasts the power of the CF in the maximal- and average-error cases, showing that a constant number of bits communicated over the CF output link can yield a positive gain in the maximal-error sum-capacity, while a far greater number of bits, even numbers that grow sublinearly in the blocklength, can never yield a non-negligible gain in the average-error sum-capacity.

cs.IT↗

arXiv2019

Secure Network Coding in the Setting in Which a Non-Source Node May Generate Random Keys

It is common in the study of secure multicast network coding in the presence of an eavesdropper that has access to $z$ network links, to assume that the source node is the only node that generates random keys. In this setting, the secure multicast rate is well understood. Computing the secure multicast rate, or even the secure unicast rate, in the more general setting in which all network nodes may generate (independent) random keys is known to be as difficult as computing the (non-secure) capacity of multiple-unicast network coding instances --- a well known open problem. This work treats an intermediate model of secure unicast in which only one node can generate random keys, however that node need not be the source node. The secure communication rate for this setting is characterized again with an eavesdropper that has access to $z$ network links.

cs.IT↗

arXiv2019

A Local Perspective on the Edge Removal Problem

The edge removal problem studies the loss in network coding rates that results when a network communication edge is removed from a given network. It is known, for example, that in networks restricted to linear coding schemes and networks restricted to Abelian group codes, removing an edge e* with capacity Re* reduces the achievable rate on each source by no more than Re*. In this work, we seek to uncover larger families of encoding functions for which the edge removal statement holds. We take a local perspective: instead of requiring that all network encoding functions satisfy certain restrictions (e.g., linearity), we limit only the function carried on the removed edge e*. Our central results give sufficient conditions on the function carried by edge e* in the code used to achieve a particular rate vector under which we can demonstrate the achievability of a related rate vector once e* is removed.

cs.IT↗

arXiv2019

Universal Mutual Information Privacy Guarantees for Smart Meters

Smart meters enable improvements in electricity distribution system efficiency at some cost in customer privacy. Users with home batteries can mitigate this privacy loss by applying charging policies that mask their underlying energy use. A battery charging policy is proposed and shown to provide universal privacy guarantees subject to a constraint on energy cost. The guarantee bounds our strategy's maximal information leakage from the user to the utility provider under general stochastic models of user energy consumption. The policy construction adapts coding strategies for non-probabilistic permuting channels to this privacy problem.

cs.IT↗

arXiv2018

The Birthday Problem and Zero-Error List Codes

As an attempt to bridge the gap between the probabilistic world of classical information theory and the combinatorial world of zero-error information theory, this paper studies the performance of randomly generated codebooks over discrete memoryless channels under a zero-error list-decoding constraint. This study allows the application of tools from one area to the other. Furthermore, it leads to an information-theoretic formulation of the birthday problem, which is concerned with the probability that in a given population, a fixed number of people have the same birthday. Due to the lack of a closed-form expression for this probability when the distribution of birthdays is not uniform, the resulting expression is not simple to analyze; in the information-theoretic formulation, however, the asymptotic behavior of this probability can be characterized exactly for all distributions.

cs.IT↗

arXiv2018

Can Negligible Cooperation Increase Network Capacity? The Average-Error Case

In communication networks, cooperative strategies are coding schemes where network nodes work together to improve network performance metrics such as sum-rate. This work studies encoder cooperation in the setting of a discrete multiple access channel with two encoders and a single decoder. A node in the network that is connected to both encoders via rate-limited links, referred to as the cooperation facilitator (CF), enables the cooperation strategy. Previously, the authors presented a class of multiple access channels where the average-error sum-capacity has an infinite derivative in the limit where CF output link capacities approach zero. The authors also demonstrated that for some channels, the maximal-error sum-capacity is not continuous at the point where the output link capacities of the CF equal zero. This work shows that the the average-error sum-capacity is continuous when CF output link capacities converge to zero; that is, the infinite derivative of the average-error sum-capacity is not a result of its discontinuity as in the maximal-error case.

cs.IT↗

arXiv2017

The Benefit of Encoder Cooperation in the Presence of State Information

In many communication networks, the availability of channel state information at various nodes provides an opportunity for network nodes to work together, or "cooperate." This work studies the benefit of cooperation in the multiple access channel with a cooperation facilitator, distributed state information at the encoders, and full state information available at the decoder. Under various causality constraints, sufficient conditions are obtained such that encoder cooperation through the facilitator results in a gain in sum-capacity that has infinite slope in the information rate shared with the encoders. This result extends the prior work of the authors on cooperation in networks where none of the nodes have access to state information.

cs.IT↗

arXiv2016

The Unbounded Benefit of Encoder Cooperation for the $k$-user MAC

Cooperation strategies allow communication devices to work together to improve network capacity. Consider a network consisting of a $k$-user multiple access channel (MAC) and a node that is connected to all $k$ encoders via rate-limited bidirectional links, referred to as the "cooperation facilitator" (CF). Define the cooperation benefit as the sum-capacity gain resulting from the communication between the encoders and the CF and the cooperation rate as the total rate the CF shares with the encoders. This work demonstrates the existence of a class of $k$-user MACs where the ratio of the cooperation benefit to cooperation rate tends to infinity as the cooperation rate tends to zero. Examples of channels in this class include the binary erasure MAC for $k=2$ and the $k$-user Gaussian MAC for any $k\geq 2$.

cs.IT↗

arXiv2016

Can Negligible Cooperation Increase Network Reliability?

In network cooperation strategies, nodes work together with the aim of increasing transmission rates or reliability. This paper demonstrates that enabling cooperation between the transmitters of a two-user multiple access channel, via a cooperation facilitator that has access to both messages, always results in a network whose maximal- and average-error sum-capacities are the same---even when those capacities differ in the absence of cooperation and the information shared with the encoders is negligible. From this result, it follows that if a multiple access channel with no transmitter cooperation has different maximal- and average-error sum-capacities, then the maximal-error sum-capacity of the network consisting of this channel and a cooperation facilitator is not continuous with respect to the output edge capacities of the facilitator. This shows that there exist networks where sharing even a negligible number of bits per channel use with the encoders yields a non-negligible benefit.

cs.IT↗

arXiv2016

On the Capacity Advantage of a Single Bit

In this work we study the capacity advantage achieved by adding a single bit of communication -- not a link of capacity 1 but a single bit over all time -- to a memoryless network. Specifically, we present a memoryless network in which adding a single bit of communication strictly increases the capacity region.

cs.IT↗

arXiv2016

On the Impact of a Single Edge on the Network Coding Capacity

In this paper, we study the effect of a single link on the capacity of a network of error-free bit pipes. More precisely, we study the change in network capacity that results when we remove a single link of capacity $δ$. In a recent result, we proved that if all the sources are directly available to a single super-source node, then removing a link of capacity $δ$ cannot change the capacity region of the network by more than $δ$ in each dimension. In this paper, we extend this result to the case of multi-source, multi-sink networks for some special network topologies.

cs.IT↗

arXiv2016

The Multivariate Covering Lemma and its Converse

The multivariate covering lemma states that given a collection of $k$ codebooks, each of sufficiently large cardinality and independently generated according to one of the marginals of a joint distribution, one can always choose one codeword from each codebook such that the resulting $k$-tuple of codewords is jointly typical with respect to the joint distribution. We give a proof of this lemma for weakly typical sets. This allows achievability proofs that rely on the covering lemma to go through for continuous channels (e.g., Gaussian) without the need for quantization. The covering lemma and its converse are widely used in information theory, including in rate-distortion theory and in achievability results for multi-user channels.

cs.IT↗

arXiv2015

A Perspective on Future Research Directions in Information Theory

Information theory is rapidly approaching its 70th birthday. What are promising future directions for research in information theory? Where will information theory be having the most impact in 10-20 years? What new and emerging areas are ripe for the most impact, of the sort that information theory has had on the telecommunications industry over the last 60 years? How should the IEEE Information Theory Society promote high-risk new research directions and broaden the reach of information theory, while continuing to be true to its ideals and insisting on the intellectual rigor that makes its breakthroughs so powerful? These are some of the questions that an ad hoc committee (composed of the present authors) explored over the past two years. We have discussed and debated these questions, and solicited detailed inputs from experts in fields including genomics, biology, economics, and neuroscience. This report is the result of these discussions.

cs.IT↗

arXiv2015

On the Cost and Benefit of Cooperation (Extended Version)

In a cooperative coding scheme, network nodes work together to achieve higher transmission rates. To obtain a better understanding of cooperation, we consider a model in which two transmitters send rate-limited descriptions of their messages to a "cooperation facilitator", a node that sends back rate-limited descriptions of the pair to each transmitter. This model includes the conferencing encoders model and a prior model from the current authors as special cases. We show that except for a special class of multiple access channels, the gain in sum-capacity resulting from cooperation under this model is quite large. Adding a cooperation facilitator to any such channel results in a network that does not satisfy the edge removal property. An important special case is the Gaussian multiple access channel, for which we explicitly characterize the sum-rate cooperation gain.

cs.IT↗

arXiv2014

On the Power of Cooperation: Can a Little Help a Lot? (Extended Version)

In this paper, we propose a new cooperation model for discrete memoryless multiple access channels. Unlike in prior cooperation models (e.g., conferencing encoders), where the transmitters cooperate directly, in this model the transmitters cooperate through a larger network. We show that under this indirect cooperation model, there exist channels for which the increase in sum-capacity resulting from cooperation is significantly larger than the rate shared by the transmitters to establish the cooperation. This result contrasts both with results on the benefit of cooperation under prior models and results in the network coding literature, where attempts to find examples in which similar small network modifications yield large capacity benefits have to date been unsuccessful.

cs.IT↗

arXiv2013

Zero vs. epsilon Error in Interference Channels

Traditional studies of multi-source, multi-terminal interference channels typically allow a vanishing probability of error in communication. Motivated by the study of network coding, this work addresses the task of quantifying the loss in rate when insisting on zero error communication in the context of interference channels.

cs.IT↗

arXiv2013

Multi-Resolution Video Streaming in Peer-to-peer Networks

We consider multi-resolution streaming in fully-connected peer-to-peer networks, where transmission rates are constrained by arbitrarily specified upload capacities of the source and peers. We fully characterize the capacity region of rate vectors achievable with arbitrary coding, where an achievable rate vector describes a vector of throughputs of the different resolutions that can be supported by the network. We then prove that all rate vectors in the capacity region can be achieved using pure routing strategies. This shows that coding has no capacity advantage over routing in this scenario.

cs.IT↗

arXiv2012

Separation of source-network coding and channel coding in wireline networks

In this paper we prove the separation of source-network coding and channel coding in wireline networks. For the purposes of this work, a wireline network is any network of independent, memoryless, point-to-point, finite-alphabet channels used to transmit dependent sources either losslessly or subject to a distortion constraint. In deriving this result, we also prove that in a general memoryless network with dependent sources, lossless and zero-distortion reconstruction are equivalent provided that the conditional entropy of each source given the other sources is non-zero. Furthermore, we extend the separation result to the case of continuous-alphabet, point-to-point channels such as additive white Gaussian noise (AWGN) channels.

cs.IT↗