Two-loop Improved Truncation of the Ghost-Gluon Dyson-Schwinger Equations: Multiplicatively Renormalizable Propagators and Nonperturbative Running Coupling

The coupled Dyson-Schwinger equations for the gluon and ghost propagators are investigated in the Landau gauge using a two-loop improved truncation that preserves the multiplicative renormalizability of the propagators. In this truncation all diagrams contribute to the leading order infrared analysis. The infrared contributions of the nonperturbative two-loop diagrams to the gluon vacuum polarization are computed analytically, and this reveals that infrared power behaved propagator solutions only exist when the squint diagram contribution is taken into account. For small momenta the gluon and ghost dressing functions behave respectively like (p^2)^{2\kappa} and (p^2)^{-\kappa}, and the running coupling exhibits a fixed point. The values of the infrared exponent and fixed point depend on the precise details of the truncation. The coupled ghost-gluon system is solved numerically for all momenta, and the solutions have infrared behaviors consistent with the predictions of the infrared analysis. For truncation parameters chosen such that \kappa=0.5, the two-loop improved truncation is able to produce solutions for the propagators and running coupling which are in very good agreement with recent lattice simulations.Comment: 41 pages, LateX; minor corrections; accepted for publication in Few-Body System

Strong Coordination over a Line Network

We study the problem of strong coordination in a three-terminal line network, in which agents use common randomness and communicate over a line network to ensure that their actions follow a prescribed behavior, modeled by a target joint distribution of actions. We provide inner and outer bounds to the coordination capacity region, and show that these bounds are partially optimal. We leverage this characterization to develop insight into the interplay between communication and coordination. Specifically, we show that common randomness helps to achieve optimal communication rates between agents, and that matching the network topology to the behavior structure may reduce inter-agent communication rates.Comment: To be presented at ISIT 2013, Istanbul, Turke

Secret key generation from Gaussian sources using lattice hashing

We propose a simple yet complete lattice-based scheme for secret key generation from Gaussian sources in the presence of an eavesdropper, and show that it achieves strong secret key rates up to 1/2 nat from the optimal in the case of "degraded" source models. The novel ingredient of our scheme is a lattice-hashing technique, based on the notions of flatness factor and channel intrinsic randomness. The proposed scheme does not require dithering.Comment: 5 pages, Conference (ISIT 2013

Covert Capacity of Non-Coherent Rayleigh-Fading Channels

The covert capacity is characterized for a non-coherent fast Rayleigh-fading wireless channel, in which a legitimate user wishes to communicate reliably with a legitimate receiver while escaping detection from a warden. It is shown that the covert capacity is achieved with an amplitude-constrained input distribution that consists of a finite number of mass points including one at zero and numerically tractable bounds are provided. It is also conjectured that distributions with two mass points in fixed locations are optimal

Comment on "Nucleon form factors and a nonpointlike diquark"

Authors of Phys. Rev. C 60, 062201 (1999) presented a calculation of the electromagnetic form factors of the nucleon using a diquark ansatz in the relativistic three-quark Faddeev equations. In this Comment it is pointed out that the calculations of these form factors stem from a three-quark bound state current that contains overcounted contributions. The corrected expression for the three-quark bound state current is derived.Comment: 6 pages, 1 figure, revtex, eps

Polar Coding for Secret-Key Generation

Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m broadcast model and (iv) the Markov tree model with uniform marginals. For models (i) and (ii) our coding schemes remain valid for non-degraded sources, although they may not achieve the secret-key capacity. For models (i), (ii) and (iii), our schemes rely on pre-shared secret seed of negligible rate; however, we provide special cases of these models for which no seed is required. Finally, we show an application of our results to secrecy and privacy for biometric systems. We thus provide the first examples of low-complexity secret-key capacity-achieving schemes that are able to handle vector quantization for model (ii), or multiterminal communication for models (iii) and (iv).Comment: 26 pages, 9 figures, accepted to IEEE Transactions on Information Theory; parts of the results were presented at the 2013 IEEE Information Theory Worksho