Related papers: Relations between Information and Estimation in Di…
In the era of big data, it is necessary to split extremely large data sets across multiple computing nodes and construct estimators using the distributed data. When designing distributed estimators, it is desirable to minimize the amount of…
By employing various empirical estimators for the Mutual Information (MI) measure, we calculate and compare the estimates and their confidence intervals for both normal and non-normal bivariate data samples. We find that certain nonlinear…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
Estimating the probability of rare channel conditions is a central challenge in ultra-reliable wireless communication, where random events, such as deep fades, can cause sudden variations in the channel quality. This paper proposes a…
As shown by M\'edard, the capacity of fading channels with imperfect channel-state information (CSI) can be lower-bounded by assuming a Gaussian channel input $X$ with power $P$ and by upper-bounding the conditional entropy $h(X|Y,\hat{H})$…
Speech is a fundamental means of communication that can be seen to provide two channels for transmitting information: the lexical channel of which words are said, and the non-lexical channel of how they are spoken. Both channels shape…
We provide a simple and realistic model to study memory effects in a lossy bosonic quantum channel over arbitrary number of uses. The noise correlation among different uses is introduced by contiguous modes interactions which results in an…
Given a quantum channel -- that is, a completely positive trace-preserving linear map -- as the only communication resource available between two parties, we consider the problem of characterizing the set of classical noisy channels that…
The mutual information is bounded from above by a decreasing affine function of the square of the distance between the input distribution and the set of all capacity-achieving input distributions $\Pi_{\mathcal{A}}$, on small enough…
We construct intrinsic on-and off-diagonal upper and lower estimates for the transition probability density of a L\'evy process in small time. By intrinsic we mean that such estimates reflect the structure of the characteristic exponent of…
We consider a new formulation of a class of synchronization error channels and derive analytical bounds and numerical estimates for the capacity of these channels. For the binary channel with only deletions, we obtain an expression for the…
New capacity upper bounds are presented for the discrete-time Poisson channel with no dark current and an average-power constraint. These bounds are a simple consequence of techniques developed for the seemingly unrelated problem of upper…
Estimation methods for the L\'{e}vy density of a L\'{e}vy process are developed under mild qualitative assumptions. A classical model selection approach made up of two steps is studied. The first step consists in the selection of a good…
We develop the information geometry of L\'evy processes. Deriving $\alpha$-divergences directly in terms of the L\'evy triplets of the L\'evy processes, we identify Fisher information matrix and $\alpha$-connection on the statistical…
Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. We study this problem of secret communication and secret key generation when two…
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good…
We investigate the transmission of a secret message from Alice to Bob in the presence of an eavesdropper (Eve) and many of decode-and-forward relay nodes. Each link comprises a set of parallel channels, modeling for example an orthogonal…
This paper considers a sequential sensor scheduling and remote estimation problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process and makes a…
The paper derives the optimal second-order coding rate for the continuous-time Poisson channel. We also obtain bounds on the third-order coding rate. This is the first instance of a second-order result for a continuous-time channel. The…
The conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential…