Information Theory

Thomas, J.; Marks, Robert J.; Verdú, S.; Poor, H. Vincent; Looney, C; Cover, Thomas M.

doi:10.1201/9781420049763.ch73

Cited by 51 publications

(78 citation statements)

References 19 publications

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“…the average density of states (DOS) of U and the average distribution of a set of complex numbers {b z } that determine the asymptotics of the eigenstates, when u(t) is drawn from a zero-mean, δ-correlated Gaussian distribution, describing the distribution of transmitted codewords. Gaussian input signals are often used in information theory, and in linear transmission problems they often reach the Shannon capacity [7]. In addition, when the characteristic signal amplitude u 0 is much smaller than its bandwidth τ −1 (but with D ≡ u 2 0 τ arbitrary), it is reasonable to approximate [8] the input distribution with a δ-correlated Gaussian for eigenvalues z small in the scale of τ −1 .…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Schrödinger equation with random Gaussian input: Distribution of inverse scattering data and eigenvalues

Kazakopoulos

Moustakas

2008

Phys. Rev. E

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We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive non-linear Schrödinger equation with a Gaussian random pulse as initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We also calculate the distribution of a set of scattering data of the Zakharov-Shabat operator that determine the asymptotics of the eigenfunctions. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of information transmission through non-linear optical fibers.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Schrödinger equation with random Gaussian input: Distribution of inverse scattering data and eigenvalues

Kazakopoulos

Moustakas

2008

Phys. Rev. E

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“…Finally, our analysis employs ideas from the classical communication theory [11,32,33]. But whereas source and channel coding attempt to represent the information in an efficient format for transmission, cryptographic engineers have the opposite goal to make their circuit's internal configurations unintelligible to the outside world.…”

Section: Introductionmentioning

confidence: 99%

A Unified Framework for the Analysis of Side-Channel Key Recovery Attacks

Standaert

Malkin

Yung

2009

Lecture Notes in Computer Science

687

557

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Abstract. The fair evaluation and comparison of side-channel attacks and countermeasures has been a long standing open question, limiting further developments in the field. Motivated by this challenge, this work makes a step in this direction and proposes a framework for the analysis of cryptographic implementations that includes a theoretical model and an application methodology. The model is based on commonly accepted hypotheses about side-channels that computations give rise to. It allows quantifying the effect of practically relevant leakage functions with a combination of information theoretic and security metrics, measuring the quality of an implementation and the strength of an adversary, respectively. From a theoretical point of view, we demonstrate formal connections between these metrics and discuss their intuitive meaning. From a practical point of view, the model implies a unified methodology for the analysis of side-channel key recovery attacks. The proposed solution allows getting rid of most of the subjective parameters that were limiting previous specialized and often ad hoc approaches in the evaluation of physically observable devices. It typically determines the extent to which basic (but practically essential) questions such as "How to compare two implementations? " or "How to compare two side-channel adversaries? " can be answered in a sound fashion.

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“…This proposition is well known (Varshamov-Gilbert lemma, see [7]). We give here a sketch of proof for the reader's convenience.…”

Section: Proof Of Propositionmentioning

confidence: 84%

Replicant compression coding in Besov spaces

Kerkyacharian¹,

Picard²

2003

ESAIM: PS

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Abstract. We present here a new proof of the theorem of Birman and Solomyak on the metric entropy of the unit ball of a Besov space B s π,q on a regular domain ofThis proof takes advantage of the representation of such spaces on wavelet type bases and extends the result to more general spaces. The lower bound is a consequence of very simple probabilistic exponential inequalities. To prove the upper bound, we provide a new universal coding based on a thresholding-quantizing procedure using replication.Mathematics Subject Classification. 41A25, 41A46, 65F99, 65N12, 65N55.

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Information Theory

Cited by 51 publications

References 19 publications

Nonlinear Schrödinger equation with random Gaussian input: Distribution of inverse scattering data and eigenvalues

Nonlinear Schrödinger equation with random Gaussian input: Distribution of inverse scattering data and eigenvalues

A Unified Framework for the Analysis of Side-Channel Key Recovery Attacks

Replicant compression coding in Besov spaces

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