Lov\'asz's Theta Function, R\'enyi's Divergence and the Sphere-Packing Bound

Lov\'asz's bound to the capacity of a graph and the the sphere-packing bound to the probability of error in channel coding are given a unified presentation as information radii of the Csisz\'ar type using the R{\'e}nyi divergence in the classical-quantum setting. This brings together two results in coding theory that are usually considered as being of a very different nature, one being a "combinatorial" result and the other being "probabilistic". In the context of quantum information theory, this difference disappears.Comment: An excerpt from arXiv:1201.5411v3 (with a different notation) accepted at ISIT 201

Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels

The sphere packing bound, in the form given by Shannon, Gallager and Berlekamp, was recently extended to classical-quantum channels, and it was shown that this creates a natural setting for combining probabilistic approaches with some combinatorial ones such as the Lov\'asz theta function. In this paper, we extend the study to the case of constant composition codes. We first extend the sphere packing bound for classical-quantum channels to this case, and we then show that the obtained result is related to a variation of the Lov\'asz theta function studied by Marton. We then propose a further extension to the case of varying channels and codewords with a constant conditional composition given a particular sequence. This extension is then applied to auxiliary channels to deduce a bound which can be interpreted as an extension of the Elias bound.Comment: ISIT 2014. Two issues that were left open in Section IV of the first version are now solve

Contributions to national geodetic satellite program: Global correlations

Various forms of geophysical information as indicators of the physical properties of the planet are studied. It is useful to study the interrelationships of these various geophysical parameters in an attempt to determine whether they are generated by the same mechanism and if not, to assess the association of the various generating mechanisms. The formulas for studying such correlations are summarized

Aspects of average response computation by aperiodic stimulation

A mathematical analysis of the variance of the average evoked-response computation as a function of the numberN of stimuli presented is made for the case when the response is disturbed by additive stationary noise. A comparison is made between the variance for purely periodic stimuli and that for stimuli of which the interstimulus durations are Gaussian distributed. In the latter situation, the interval durations may be correlated with each other, e.g. according to a Gaussian Markov process. It is deduced that, in general, the introduction of aperiodic stimulation tends to make the functional relationship between the variance andN behave as though it holds for noise with a very broad frequency spectrum; the variance is proportional to 1/N

Technique for measuring time-base errors of magnetic instrumentation recorders/reproducers

Time-base error analysis of magnetically recorded and played back digital data using tape flutter spectral density and amplitude probability distribution measurements and rms time plot

State and parameter estimation using Monte Carlo evaluation of path integrals

Transferring information from observations of a dynamical system to estimate the fixed parameters and unobserved states of a system model can be formulated as the evaluation of a discrete time path integral in model state space. The observations serve as a guiding potential working with the dynamical rules of the model to direct system orbits in state space. The path integral representation permits direct numerical evaluation of the conditional mean path through the state space as well as conditional moments about this mean. Using a Monte Carlo method for selecting paths through state space we show how these moments can be evaluated and demonstrate in an interesting model system the explicit influence of the role of transfer of information from the observations. We address the question of how many observations are required to estimate the unobserved state variables, and we examine the assumptions of Gaussianity of the underlying conditional probability.Comment: Submitted to the Quarterly Journal of the Royal Meteorological Society, 19 pages, 5 figure