Related papers: Shannon Bounds for Quadratic Rate-Distortion Probl…
Coherent network error correction is the error-control problem in network coding with the knowledge of the network codes at the source and sink nodes. With respect to a given set of local encoding kernels defining a linear network code, we…
We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a…
We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…
An information theoretic formulation of the distributed averaging problem previously studied in computer science and control is presented. We assume a network with m nodes each observing a WGN source. The nodes communicate and perform local…
The modelling of linear quadratic Gaussian optimal control problems on large complex networks is intractable computationally. Graphon theory provides an approach to overcome these issues by defining limit objects for infinite sequences of…
The rate-distortion saddle-point problem considered by Lapidoth (1997) consists in finding the minimum rate to compress an arbitrary ergodic source when one is constrained to use a random Gaussian codebook and minimum (Euclidean) distance…
We consider the Shannon cipher system in a setting where the secret key is delivered to the legitimate receiver via a channel with limited capacity. For this setting, we characterize the achievable region in the space of three figures of…
It is a common phenomenon that for high-dimensional and nonparametric statistical models, rate-optimal estimators balance squared bias and variance. Although this balancing is widely observed, little is known whether methods exist that…
We study the following semi-deterministic setting of the joint source-channel coding problem: a deterministic source sequence (a.k.a. individual sequence) is transmitted via a memoryless channel, using delay-limited encoder and decoder,…
A bilateral (i.e., upper and lower) bound on the mean-square error under a general model mismatch is developed. The bound, which is derived from the variational representation of the chi-square divergence, is applicable in the Bayesian and…
The indirect source-coding problem in which a Bernoulli process is compressed in a lossy manner from its noisy observations is considered. These noisy observations are obtained by passing the source sequence through a The indirect…
For the discrete-time AWGN channel with a power constraint, we give an alternative derivation of Shannon's sphere-packing upper bound on the optimal block error exponent and prove for the first time an analogous lower bound on the optimal…
A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a well-known connection to the deterministic estimation setting. Using the prior distribution, the bias…
Nonconvex optimization plays a key role in multi-user information theory and related fields, but it is usually difficult to solve. The rate region of the Gray--Wyner source coding system (or almost equivalently, the mutual information…
There is a large and important collection of Ramsey-type combinatorial problems, closely related to central problems in complexity theory, that can be formulated in terms of the asymptotic growth of the size of the maximum independent sets…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input…
The problem of estimating high-dimensional network models arises naturally in the analysis of many physical, biological and socio-economic systems. Examples include stock price fluctuations in financial markets and gene regulatory networks…
Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical…
This paper studies the Shannon regime for the random displacement of stationary point processes. Let each point of some initial stationary point process in $\R^n$ give rise to one daughter point, the location of which is obtained by adding…
I introduce rate-distortion theory for quantum coding, and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to encode a quantum source with a given maximum level of distortion per source…