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The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. In this paper, we derive the exact exponent for the asymptotic decay of the small modification of the quantum state in smoothing the…

Quantum Physics · Physics 2023-06-02 Ke Li , Yongsheng Yao , Masahito Hayashi

This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…

Information Theory · Computer Science 2023-03-27 Amedeo Roberto Esposito , Adrien Vandenbroucque , Michael Gastpar

Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend…

Information Theory · Computer Science 2019-07-16 Mengfan Zheng , Ling Liu , Cong Ling

We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…

Statistical Mechanics · Physics 2007-05-23 James P. Crutchfield , David P. Feldman

We study the problem of exact sampling under an exponential communication cost, specifically Campbell's average codeword length $L(t)$ of order $t$, and R\'enyi's entropy. We provide a lower bound on the Campbell cost of exact sampling that…

Information Theory · Computer Science 2026-04-03 Spencer Hill , Fady Alajaji , Tamás Linder

This paper investigates the relation between the second-order coding rate, where the second-order turns out to be strictly larger than $\sqrt{n}$, and the mutual information as the leaked information for a fixed error probability by using…

Information Theory · Computer Science 2024-05-13 Kagan Akcay

New non-asymptotic random coding theorems (with error probability $\epsilon$ and finite block length $n$) based on Gallager parity check ensemble and Shannon random code ensemble with a fixed codeword type are established for discrete input…

Information Theory · Computer Science 2013-03-05 En-hui Yang , Jin Meng

This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…

Information Theory · Computer Science 2014-03-05 Jonathan Scarlett , Alfonso Martinez , Albert Guillén i Fàbregas

We express the joint R\'enyi entropy of progressively censored order statistics in terms of an incomplete integral of the hazard function, and provide a simple estimate of the joint R\'enyi entropy of progressively Type-II censored data.…

Methodology · Statistics 2013-03-25 Akram Kohansal , Saeid Rezakhah

The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…

Information Theory · Computer Science 2017-05-01 Maciej Skorski

We consider the problem of estimating the probability of error in multi-hypothesis testing when MAP criterion is used. This probability, which is also known as the Bayes risk is an important measure in many communication and information…

Information Theory · Computer Science 2007-07-16 Nandakishore Santhi , Alexander Vardy

This paper studies the second-order asymptotics of the Gaussian multiple-access channel with degraded message sets. For a fixed average error probability $\varepsilon \in (0,1)$ and an arbitrary point on the boundary of the capacity region,…

Information Theory · Computer Science 2015-10-07 Jonathan Scarlett , Vincent Y. F. Tan

We consider a Shannon cipher system for memoryless sources, in which distortion is allowed at the legitimate decoder. The source is compressed using a rate distortion code secured by a shared key, which satisfies a constraint on the…

Information Theory · Computer Science 2016-11-17 Nir Weinberger , Neri Merhav

In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy…

Information Theory · Computer Science 2013-01-24 Lavanya Sivakumar , Matthias Dehmer

This work provides data-processing and majorization inequalities for $f$-divergences, and it considers some of their applications to coding problems. This work also provides tight bounds on the R\'{e}nyi entropy of a function of a discrete…

Information Theory · Computer Science 2021-04-01 Igal Sason

This paper characterizes the second-order coding rates for lossy source coding with side information available at both the encoder and the decoder. We first provide non-asymptotic bounds for this problem and then specialize the…

Information Theory · Computer Science 2014-10-13 Sy-Quoc Le , Vincent Y. F. Tan , Mehul Motani

This paper provides upper and lower bounds on the optimal guessing moments of a random variable taking values on a finite set when side information may be available. These moments quantify the number of guesses required for correctly…

Information Theory · Computer Science 2018-06-22 Igal Sason , Sergio Verdú

We study the first- and second-order asymptotics of covert communication over binary-input DMC for three different covertness metrics and under maximum probability of error constraint. When covertness is measured in terms of the relative…

Information Theory · Computer Science 2019-01-09 Mehrdad Tahmasbi , Matthieu R. Bloch

In this correspondence, we correct an erroneous result on the achievability part of the R\'enyi common information with order $1+s\in(1,2]$ in [1]. The new achievability result (upper bound) of the R\'enyi common information no longer…

Information Theory · Computer Science 2020-02-18 Lei Yu , Vincent Y. F. Tan

Second order asymptotics of fixed-length source coding and intrinsic randomness is discussed with a constant error constraint. There was a difference between optimal rates of fixed-length source coding and intrinsic randomness, which never…

Information Theory · Computer Science 2010-01-23 Masahito Hayashi