arXiv subjects

Abbas El Gamal

Publications and source records attributed to Abbas El Gamal.

At least 37 records · Page 2Linked to original sources

arXiv2016

Maximal Correlation Secrecy

This paper shows that the Hirschfeld-Gebelein-Rényi maximal correlation between the message and the ciphertext provides good secrecy guarantees for cryptosystems that use short keys. We first establish a bound on the eavesdropper's advantage in guessing functions of the message in terms of maximal correlation and the Rényi entropy of the message. This result implies that maximal correlation is stronger than the notion of entropic security introduced by Russell and Wang. We then show that a small maximal correlation $ρ$ can be achieved via a randomly generated cipher with key length $\approx2\log(1/ρ)$, independent of the message length, and by a stream cipher with key length $2\log(1/ρ)+\log n+2$ for a message of length $n$. We establish a converse showing that these ciphers are close to optimal. This is in contrast to entropic security for which there is a gap between the lower and upper bounds. Finally, we show that a small maximal correlation implies secrecy with respect to several mutual information based criteria but is not necessarily implied by them. Hence, maximal correlation is a stronger and more practically relevant measure of secrecy than mutual information.

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arXiv2016

An Efficient Feedback Coding Scheme with Low Error Probability for Discrete Memoryless Channels

Existing fixed-length feedback communication schemes are either specialized to particular channels (Schalkwijk--Kailath, Horstein), or apply to general channels but either have high coding complexity (block feedback schemes) or are difficult to analyze (posterior matching). This paper introduces a new fixed-length feedback coding scheme which achieves the capacity for all discrete memoryless channels, has an error exponent that approaches the sphere packing bound as the rate approaches the capacity, and has $O(n\log n)$ coding complexity. These benefits are achieved by judiciously combining features from previous schemes with new randomization technique and encoding/decoding rule. These new features make the analysis of the error probability for the new scheme easier than for posterior matching.

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arXiv2016

A Universal Coding Scheme for Remote Generation of Continuous Random Variables

We consider a setup in which Alice selects a pdf $f$ from a set of prescribed pdfs $\mathscr{P}$ and sends a prefix-free codeword $W$ to Bob in order to allow him to generate a single instance of the random variable $X\sim f$. We describe a universal coding scheme for this setup and establish an upper bound on the expected codeword length when the pdf $f$ is bounded, orthogonally concave (which includes quasiconcave pdf), and has a finite first absolute moment. A dyadic decomposition scheme is used to express the pdf as a mixture of uniform pdfs over hypercubes. Alice randomly selects a hypercube according to its weight, encodes its position and size into $W$, and sends it to Bob who generates $X$ uniformly over the hypercube. Compared to previous results on channel simulation, our coding scheme applies to any continuous distribution and does not require two-way communication or shared randomness. We apply our coding scheme to classical simulation of quantum entanglement and obtain a better bound on the average codeword length than previously known.

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arXiv2015

Capacity Theorems for Broadcast Channels with Two Channel State Components Known at the Receivers

We establish the capacity region of several classes of broadcast channels with random state in which the channel to each user is selected from two possible channel state components and the state is known only at the receivers. When the channel components are deterministic, we show that the capacity region is achieved via Marton coding. This channel model does not belong to any class of broadcast channels for which the capacity region was previously known and is useful in studying wireless communication channels when the fading state is known only at the receivers. We then establish the capacity region when the channel components are ordered, e.g., degraded. In particular we show that the capacity region for the broadcast channel with degraded Gaussian vector channel components is attained via Gaussian input distribution. Finally, we extend the results on ordered channels to two broadcast channel examples with more than two channel components, but show that these extensions do not hold in general.

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arXiv2015

Superposition Coding is Almost Always Optimal for the Poisson Broadcast Channel

This paper shows that the capacity region of the continuous-time Poisson broadcast channel is achieved via superposition coding for most channel parameter values. Interestingly, the channel in some subset of these parameter values does not belong to any of the existing classes of broadcast channels for which superposition coding is optimal (e.g., degraded, less noisy, more capable). In particular, we introduce the notion of effectively less noisy broadcast channel and show that it implies less noisy but is not in general implied by more capable. For the rest of the channel parameter values, we show that there is a gap between Marton's inner bound and the UV outer bound.

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arXiv2015

Capacity Approximations for Gaussian Relay Networks

Consider a Gaussian relay network where a source node communicates to a destination node with the help of several layers of relays. Recent work has shown that compress-and-forward based strategies can achieve the capacity of this network within an additive gap. Here, the relays quantize their received signals at the noise level and map them to random Gaussian codebooks. The resultant gap to capacity is independent of the SNRs of the channels in the network and the topology but is linear in the total number of nodes. In this paper, we provide an improved lower bound on the rate achieved by compress-and-forward based strategies (noisy network coding in particular) in arbitrary Gaussian relay networks, whose gap to capacity depends on the network not only through the total number of nodes but also through the degrees of freedom of the min cut of the network. We illustrate that for many networks, this refined lower bound can lead to a better approximation of the capacity. In particular, we demonstrate that it leads to a logarithmic rather than linear capacity gap in the total number of nodes for certain classes of layered networks. The improvement comes from quantizing the received signals of the relays at a resolution decreasing with the total number of nodes in the network. This suggests that the rule-of-thumb in literature of quantizing the received signals at the noise level can be highly suboptimal.

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arXiv2014

A Note on Broadcast Channels with Stale State Information at the Transmitter

This paper shows that the Maddah-Ali--Tse (MAT) scheme which establishes the symmetric capacity of two example broadcast channels with strictly causal state information at the transmitter is a simple special case of the Shayevitz--Wigger scheme for the broadcast channel with generalized feedback, which involves block Markov coding, compression, superposition coding, Marton coding, and coded time sharing. Focusing on the class of symmetric broadcast channels with state, we derive an expression for the maximum achievable symmetric rate using the Shayevitz--Wigger scheme. We show that the MAT results can be recovered by evaluating this expression for the special case in which superposition coding and Marton coding are not used. We then introduce a new broadcast channel example that shares many features of the MAT examples. We show that another special case of our maximum symmetric rate expression in which superposition coding is also used attains a higher symmetric rate than the MAT scheme. The symmetric capacity of this example is not known, however.

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arXiv2014

Compensating Demand Response Participants Via Their Shapley Values

Designing fair compensation mechanisms for demand response (DR) is challenging. This paper models the problem in a game theoretic setting and designs a payment distribution mechanism based on the Shapley Value. As exact computation of the Shapley Value is in general intractable, we propose estimating it using a reinforcement learning algorithm that approximates optimal stratified sampling. We apply this algorithm to two DR programs that utilize the Shapley Value for payments and quantify the accuracy of the resulting estimates.

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arXiv2014

Exact Common Information

This paper introduces the notion of exact common information, which is the minimum description length of the common randomness needed for the exact distributed generation of two correlated random variables $(X,Y)$. We introduce the quantity $G(X;Y)=\min_{X\to W \to Y} H(W)$ as a natural bound on the exact common information and study its properties and computation. We then introduce the exact common information rate, which is the minimum description rate of the common randomness for the exact generation of a 2-DMS $(X,Y)$. We give a multiletter characterization for it as the limit $\bar{G}(X;Y)=\lim_{n\to \infty}(1/n)G(X^n;Y^n)$. While in general $\bar{G}(X;Y)$ is greater than or equal to the Wyner common information, we show that they are equal for the Symmetric Binary Erasure Source. We do not know, however, if the exact common information rate has a single letter characterization in general.

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arXiv2014

Capacity Region of the Broadcast Channel with Two Deterministic Channel State Components

This paper establishes the capacity region of a class of broadcast channels with random state in which each channel component is selected from two possible functions and each receiver knows its state sequence. This channel model does not fit into any class of broadcast channels for which the capacity region was previously known and is useful in studying wireless communication channels when the fading state is known only at the receivers. The capacity region is shown to coincide with the UV outer bound and is achieved via Marton coding.

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arXiv2012

Optimal Achievable Rates for Interference Networks with Random Codes

The optimal rate region for interference networks is characterized when encoding is restricted to random code ensembles with superposition coding and time sharing. A simple simultaneous nonunique decoding rule, under which each receiver decodes for the intended message as well as the interfering messages, is shown to achieve this optimal rate region regardless of the relative strengths of signal, interference, and noise. This result implies that the Han-Kobayashi bound, the best known inner bound on the capacity region of the two-user-pair interference channel, cannot be improved merely by using the optimal maximum likelihood decoder.

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arXiv2012

Limits on the Benefits of Energy Storage for Renewable Integration

The high variability of renewable energy resources presents significant challenges to the operation of the electric power grid. Conventional generators can be used to mitigate this variability but are costly to operate and produce carbon emissions. Energy storage provides a more environmentally friendly alternative, but is costly to deploy in large amounts. This paper studies the limits on the benefits of energy storage to renewable energy: How effective is storage at mitigating the adverse effects of renewable energy variability? How much storage is needed? What are the optimal control policies for operating storage? To provide answers to these questions, we first formulate the power flow in a single-bus power system with storage as an infinite horizon stochastic program. We find the optimal policies for arbitrary net renewable generation process when the cost function is the average conventional generation (environmental cost) and when it is the average loss of load probability (reliability cost). We obtain more refined results by considering the multi-timescale operation of the power system. We view the power flow in each timescale as the superposition of a predicted (deterministic) component and an prediction error (residual) component and formulate the residual power flow problem as an infinite horizon dynamic program. Assuming that the net generation prediction error is an IID process, we quantify the asymptotic benefits of storage. With the additional assumption of Laplace distributed prediction error, we obtain closed form expressions for the stationary distribution of storage and conventional generation. Finally, we propose a two-threshold policy that trades off conventional generation saving with loss of load probability. We illustrate our results and corroborate the IID and Laplace assumptions numerically using datasets from CAISO and NREL.

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arXiv2011

Lecture Notes on Network Information Theory

These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/.

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arXiv2011

Communication with Disturbance Constraints

Motivated by the broadcast view of the interference channel, the new problem of communication with disturbance constraints is formulated. The rate-disturbance region is established for the single constraint case and the optimal encoding scheme turns out to be the same as the Han-Kobayashi scheme for the two user-pair interference channel. This result is extended to the Gaussian vector (MIMO) case. For the case of communication with two disturbance constraints, inner and outer bounds on the rate-disturbance region for a deterministic model are established. The inner bound is achieved by an encoding scheme that involves rate splitting, Marton coding, and superposition coding, and is shown to be optimal in several nontrivial cases. This encoding scheme can be readily applied to discrete memoryless interference channels and motivates a natural extension of the Han-Kobayashi scheme to more than two user pairs.

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arXiv2011

3-Receiver Broadcast Channels with Common and Confidential Messages

This paper establishes inner bounds on the secrecy capacity regions for the general 3-receiver broadcast channel with one common and one confidential message sets. We consider two setups. The first is when the confidential message is to be sent to two receivers and kept secret from the third receiver. Achievability is established using indirect decoding, Wyner wiretap channel coding, and the new idea of generating secrecy from a publicly available superposition codebook. The inner bound is shown to be tight for a class of reversely degraded broadcast channels and when both legitimate receivers are less noisy than the third receiver. The second setup investigated in this paper is when the confidential message is to be sent to one receiver and kept secret from the other two receivers. Achievability in this case follows from Wyner wiretap channel coding and indirect decoding. This inner bound is also shown to be tight for several special cases.

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arXiv2011

On Marton's Inner Bound for the General Broadcast Channel

We establish several new results on Marton's coding scheme and its corresponding inner bound on the capacity region of the general broadcast channel. We show that unlike the Gaussian case, Marton's coding scheme without superposition coding is not optimal in general even for a degraded broadcast channel with no common message. We then establish properties of Marton's inner bound that help restrict the search space for computing the sum-rate. Next, we show that the inner bound is optimal along certain directions. Finally, we propose a coding scheme that may lead to a larger inner bound.

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arXiv2011

Interference Networks with Point-to-Point Codes

The paper establishes the capacity region of the Gaussian interference channel with many transmitter-receiver pairs constrained to use point-to-point codes. The capacity region is shown to be strictly larger in general than the achievable rate regions when treating interference as noise, using successive interference cancellation decoding, and using joint decoding. The gains in coverage and achievable rate using the optimal decoder are analyzed in terms of ensemble averages using stochastic geometry. In a spatial network where the nodes are distributed according to a Poisson point process and the channel path loss exponent is $β> 2$, it is shown that the density of users that can be supported by treating interference as noise can scale no faster than $B^{2/β}$ as the bandwidth $B$ grows, while the density of users can scale linearly with $B$ under optimal decoding.

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arXiv2011

Interference Decoding for Deterministic Channels

An inner bound to the capacity region of a class of deterministic interference channels with three user pairs is presented. The key idea is to simultaneously decode the combined interference signal and the intended message at each receiver. It is shown that this interference-decoding inner bound is tight under certain strong interference conditions. The inner bound is also shown to strictly contain the inner bound obtained by treating interference as noise, which includes interference alignment for deterministic channels. The gain comes from judicious analysis of the number of combined interference sequences in different regimes of input distributions and message rates. Finally, the inner bound is generalized to the case where each channel output is observed through a noisy channel.

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