Related papers: Information-Theoretic Extensions of the Shannon-Ny…
In this paper, we prove a mimicking theorem for stochastic processes with an additive Gaussian noise along with some entropy and transport type estimates. As an application of these results, we prove sharp quantitative propagation of chaos…
When a noisy communication channel is used multiple times, the errors occurring at different times generally exhibit correlations. Classically, these correlations do not affect the evolution of individual particles: a single classical…
Explicit constructions of polar codes and polar lattices for both lossless and lossy Gray-Wyner problems are studied. Polar codes are employed to extract Wyner's common information of doubly symmetric binary source; polar lattices are then…
We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features.…
Shannon-Hartley theorem can accurately calculate the channel capacity when the signal observation time is infinite. However, the calculation of finite-time mutual information, which remains unknown, is essential for guiding the design of…
The mathematical framework of quantum theory, though fundamentally distinct from classical physics, raises the question of whether quantum processes can be efficiently simulated using classical resources. For instance, a sender (Alice)…
Information theory is introduced in this lecture note with a particular emphasis on its relevance to algebraic coding theory. The document develops the mathematical foundations for quantifying uncertainty and information transmission by…
Many different quantum information communication protocols such as teleportation, dense coding and entanglement based quantum key distribution are based on the faithful transmission of entanglement between distant location in an optical…
In spite of their outstanding experimental relevance, Gaussian operations in continuous-variable quantum systems are subjected to fundamental limitations, as it is known that general resources cannot be distilled within the Gaussian…
The full solution of the optimization problem giving the Gaussian capacity of the single-mode fiducial Gaussian quantum channel is provided. Since it was shown that the Gaussian capacity of an arbitrary (phase-sensitive or insensitive)…
In this paper, we propose a new method of channel estimation for asynchronous additive white Gaussian noise channels in satellite communications. This method is based on signals correlation and multiuser interference cancellation which…
We study the problem of communication over an additive white Gaussian noise (AWGN) channel with an AWGN feedback channel. When the feedback channel is noiseless, the classic Schalkwijk-Kailath (S-K) scheme is known to achieve capacity in a…
Shannon's information theory deliberately excludes message semantics. This paper develops a rigorous framework for semantic communication that integrates formal proof systems with Shannon-theoretic tools. We introduce an axiomatic…
Gaussian channel simulation is an essential paradigm in understanding the evolution of bosonic quantum states. It allows us to investigate how such states are influenced by the environment and how they transmit quantum information. This…
The conditional Gaussian nonlinear system (CGNS) is a broad class of nonlinear stochastic dynamical systems. Given the trajectories for a subset of state variables, the remaining follow a Gaussian distribution. Despite the conditionally…
Finding a computable expression for the feedback capacity of channels with colored Gaussian, additive noise is a long standing open problem. In this paper, we solve this problem in the scenario where the channel has multiple inputs and…
We describe how to analyze the wide class of non stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability…
Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…
Understanding a complex system entails capturing the non-trivial collective phenomena that arise from interactions between its different parts. Information theory is a flexible and robust framework to study such behaviours, with several…
We study the problem of sampling a random signal with sparse support in frequency domain. Shannon famously considered a scheme that instantaneously samples the signal at equispaced times. He proved that the signal can be reconstructed as…