1,527 research outputs found
R\'enyi Bounds on Information Combining
Bounds on information combining are entropic inequalities that determine how
the information, or entropy, of a set of random variables can change when they
are combined in certain prescribed ways. Such bounds play an important role in
information theory, particularly in coding and Shannon theory. The arguably
most elementary kind of information combining is the addition of two binary
random variables, i.e. a CNOT gate, and the resulting quantities are
fundamental when investigating belief propagation and polar coding. In this
work we will generalize the concept to R\'enyi entropies. We give optimal
bounds on the conditional R\'enyi entropy after combination, based on a certain
convexity or concavity property and discuss when this property indeed holds.
Since there is no generally agreed upon definition of the conditional R\'enyi
entropy, we consider four different versions from the literature. Finally, we
discuss the application of these bounds to the polarization of R\'enyi
entropies under polar codes.Comment: 14 pages, accepted for presentation at ISIT 202
An improved rate region for the classical-quantum broadcast channel
We present a new achievable rate region for the two-user binary-input
classical-quantum broadcast channel. The result is a generalization of the
classical Marton-Gelfand-Pinsker region and is provably larger than the best
previously known rate region for classical-quantum broadcast channels. The
proof of achievability is based on the recently introduced polar coding scheme
and its generalization to quantum network information theory.Comment: 5 pages, double column, 1 figure, based on a result presented in the
Master's thesis arXiv:1501.0373
Event-Triggered Estimation of Linear Systems: An Iterative Algorithm and Optimality Properties
This report investigates the optimal design of event-triggered estimation for
first-order linear stochastic systems. The problem is posed as a two-player
team problem with a partially nested information pattern. The two players are
given by an estimator and an event-trigger. The event-trigger has full state
information and decides, whether the estimator shall obtain the current state
information by transmitting it through a resource constrained channel. The
objective is to find an optimal trade-off between the mean squared estimation
error and the expected transmission rate. The proposed iterative algorithm
alternates between optimizing one player while fixing the other player. It is
shown that the solution of the algorithm converges to a linear predictor and a
symmetric threshold policy, if the densities of the initial state and the noise
variables are even and radially decreasing functions. The effectiveness of the
approach is illustrated on a numerical example. In case of a multimodal
distribution of the noise variables a significant performance improvement can
be achieved compared to a separate design that assumes a linear prediction and
a symmetric threshold policy
Convexity and Operational Interpretation of the Quantum Information Bottleneck Function
In classical information theory, the information bottleneck method (IBM) can
be regarded as a method of lossy data compression which focusses on preserving
meaningful (or relevant) information. As such it has recently gained a lot of
attention, primarily for its applications in machine learning and neural
networks. A quantum analogue of the IBM has recently been defined, and an
attempt at providing an operational interpretation of the so-called quantum IB
function as an optimal rate of an information-theoretic task, has recently been
made by Salek et al. However, the interpretation given in that paper has a
couple of drawbacks; firstly its proof is based on a conjecture that the
quantum IB function is convex, and secondly, the expression for the rate
function involves certain entropic quantities which occur explicitly in the
very definition of the underlying information-theoretic task, thus making the
latter somewhat contrived. We overcome both of these drawbacks by first proving
the convexity of the quantum IB function, and then giving an alternative
operational interpretation of it as the optimal rate of a bona fide
information-theoretic task, namely that of quantum source coding with quantum
side information at the decoder, and relate the quantum IB function to the rate
region of this task. We similarly show that the related privacy funnel function
is convex (both in the classical and quantum case). However, we comment that it
is unlikely that the quantum privacy funnel function can characterize the
optimal asymptotic rate of an information theoretic task, since even its
classical version lacks a certain additivity property which turns out to be
essential.Comment: 17 pages, 7 figures; v2: improved presentation and explanations, one
new figure; v3: Restructured manuscript. Theorem 2 has been found previously
in work by Hsieh and Watanabe; it is now correctly attribute
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