Related papers: Sharp Second-Order Pointwise Asymptotics for Lossl…
The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We begin by establishing…
Traditionally, data compression deals with the problem of concisely representing a data source, e.g. a sequence of letters, for the purpose of eventual reproduction (either exact or approximate). In this work we are interested in the case…
The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously…
We consider the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, we use a slightly different model that incorporates the notion of side information in…
In problems of lossy source/noisy channel coding with side information, the theoretical bounds are achieved using "good" source/channel codes that can be partitioned into "good" channel/source codes. A scheme that achieves optimality in…
We present a new inner bound for the rate region of the $t$-stage successive-refinement problem with side-information. We also present a new upper bound for the rate-distortion function for lossy-source coding with multiple decoders and…
We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
The problem of secure lossy source-channel wiretapping with arbitrarily correlated side informations at both receivers is investigated. This scenario consists of an encoder (referred to as Alice) that wishes to compress a source and send it…
In the last few years, there has been a great interest in extending the information-theoretic scenario for the non-asymptotic or one-shot case, i.e., where the channel is used only once. We provide the one-shot rate region for the…
We collect several observations that concern variable-length coding of two-sided infinite sequences in a probabilistic setting. Attention is paid to images and preimages of asymptotically mean stationary measures defined on subsets of these…
In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on…
We investigate how to measure and define the entropy of a simple chaotic system, three hard spheres on a ring. A novel approach is presented, which does not assume the ergodic hypothesis. It consists of transforming the particles collision…
In the context of goal-oriented communications, this paper addresses the achievable rate versus generalization error region of a learning task applied on compressed data. The study focuses on the distributed setup where a source is…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…
We investigate the second order asymptotics (source dispersion) of the successive refinement problem. Similarly to the classical definition of a successively refinable source, we say that a source is strongly successively refinable if…
This study considers the unconditional smooth R\'{e}nyi entropy, the smooth conditional R\'{e}nyi entropy proposed by Kuzuoka [\emph{IEEE Trans.\ Inf.\ Theory}, vol.~66, no.~3, pp.~1674--1690, 2020], and a new quantity which we term the…
Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the…
We derive the optimum second-order coding rates, known as second-order capacities, for erasure and list decoding. For erasure decoding for discrete memoryless channels, we show that second-order capacity is $\sqrt{V}\Phi^{-1}(\epsilon_t)$…
Inspired by the context of compressing encrypted sources, this paper considers the general tradeoff between rate, end-to-end delay, and probability of error for lossless source coding with side-information. The notion of end-to-end delay is…