scholarly journals On Approximation by Algebraic Version of the Trigonometric Jackson Integrals Gs,n in Weighted Integral Metric

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Teodora Zapryanova
Keyword(s):  
Converse Theorem ◽  
Algebraic Version ◽  
Weighted Integral ◽  
Strong Converse Theorem ◽  
Strong Converse

We characterize the errors of the algebraic version of trigonometric Jackson integrals Gs,n in weighted integral metric. We prove direct and strong converse theorem in terms of the weighted K-functional.

scholarly journals Exponential Strong Converse for One Helper Source Coding Problem

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 567 ◽  
Author(s):  
Yasutada Oohama
Keyword(s):  
Error Probability ◽  
Source Coding ◽  
Small Error ◽  
Converse Theorem ◽  
Correlated Sources ◽  
Strong Converse Theorem ◽  
Explicit Lower Bound ◽  
Source Block ◽  
Strong Converse ◽  
The One

We consider the one helper source coding problem posed and investigated by Ahlswede, Körner and Wyner. Two correlated sources are separately encoded and are sent to a destination where the decoder wishes to decode one of the two sources with an arbitrary small error probability of decoding. In this system, the error probability of decoding goes to one as the source block length n goes to infinity. This implies that we have a strong converse theorem for the one helper source coding problem. In this paper, we provide the much stronger version of this strong converse theorem for the one helper source coding problem. We prove that the error probability of decoding tends to one exponentially and derive an explicit lower bound of this exponent function.

scholarly journals Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 410
Author(s):  
Lin Zhou ◽  
Alfred Hero
Keyword(s):  
Current Problem ◽  
Source Coding ◽  
Side Information ◽  
Rate Distortion ◽  
Converse Theorem ◽  
Successive Refinement ◽  
Strong Converse Theorem ◽  
Variational Form ◽  
Strong Converse ◽  
Special Case

We consider the k-user successive refinement problem with causal decoder side information and derive an exponential strong converse theorem. The rate-distortion region for the problem can be derived as a straightforward extension of the two-user case by Maor and Merhav (2008). We show that for any rate-distortion tuple outside the rate-distortion region of the k-user successive refinement problem with causal decoder side information, the joint excess-distortion probability approaches one exponentially fast. Our proof follows by judiciously adapting the recently proposed strong converse technique by Oohama using the information spectrum method, the variational form of the rate-distortion region and Hölder’s inequality. The lossy source coding problem with causal decoder side information considered by El Gamal and Weissman is a special case ( k = 1 ) of the current problem. Therefore, the exponential strong converse theorem for the El Gamal and Weissman problem follows as a corollary of our result.

scholarly journals A Strong Converse Theorem for Hypothesis Testing Against Independence over a Two-Hop Network

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1171 ◽  
Author(s):  
Daming Cao ◽  
Lin Zhou ◽  
Vincent Y. F. Tan
Keyword(s):  
Hypothesis Testing ◽  
Soft Information ◽  
Information Costs ◽  
Change Of Measure ◽  
Converse Theorem ◽  
Converse Theorems ◽  
Converse Result ◽  
Strong Converse Theorem ◽  
Strong Converse ◽  
Measure Technique

By proving a strong converse theorem, we strengthen the weak converse result by Salehkalaibar, Wigger and Wang (2017) concerning hypothesis testing against independence over a two-hop network with communication constraints. Our proof follows by combining two recently-proposed techniques for proving strong converse theorems, namely the strong converse technique via reverse hypercontractivity by Liu, van Handel, and Verdú (2017) and the strong converse technique by Tyagi and Watanabe (2018), in which the authors used a change-of-measure technique and replaced hard Markov constraints with soft information costs. The techniques used in our paper can also be applied to prove strong converse theorems for other multiterminal hypothesis testing against independence problems.

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