Strong converse theorems using Rényi entropies
نویسندگان
چکیده
منابع مشابه
A Preferred Definition of Conditional Rényi Entropy
The Rényi entropy is a generalization of Shannon entropy to a one-parameter family of entropies. Tsallis entropy too is a generalization of Shannon entropy. The measure for Tsallis entropy is non-logarithmic. After the introduction of Shannon entropy , the conditional Shannon entropy was derived and its properties became known. Also, for Tsallis entropy, the conditional entropy was introduced a...
متن کاملAnalysis of Remaining Uncertainties and Exponents under Various Conditional Rényi Entropies
In this paper, we analyze the asymptotics of the normalized remaining uncertainty of a source when a compressed or hashed version of it and correlated side-information is observed. For this system, commonly known as Slepian-Wolf source coding, we establish the optimal (minimum) rate of compression of the source to ensure that the remaining uncertainties vanish. We also study the exponential rat...
متن کاملMultiplicativity of completely bounded $p$-norms implies a strong converse for entanglement-assisted capacity
The fully quantum reverse Shannon theorem establishes the optimal rate of noiseless classical communication required for simulating the action of many instances of a noisy quantum channel on an arbitrary input state, while also allowing for an arbitrary amount of shared entanglement of an arbitrary form. Turning this theorem around establishes a strong converse for the entanglement-assisted cla...
متن کاملRelative entropies and their use in quantum information theory
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations of the optimal rates for quantum source coding, state redistribution, and measurement compression with quantum side information via second order asymptotic ...
متن کاملAdder MAC and estimates for Rényi entropy
This paper discusses a possible program for improving the outer (converse) bounds on the finite-blocklength performance of multiple-access codes. The program is based on a certain conjecture involving Rényi entropy of a sum of two independent binary vectors. Some partial results towards showing the conjecture are presented. The problem of bounding the joint Rényi entropy in terms of the margina...
متن کامل