Multiterminal Source Coding Under Logarithmic Loss

Courtade, Thomas A.; Weissman, Tsachy

doi:10.1109/tit.2013.2288257

Cited by 146 publications

(148 citation statements)

References 29 publications

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“…We first note that the cardinality bounds in the definition of RD i can be imposed without any loss of generality. This is a consequence of [7,Lemma 2.2] and is discussed in detail in the full manuscript [3]. Thus, it suffices to show that (R 1 , R 2 , D 1 , D 2 ) ∈ RD i , ignoring the cardinality constraints.…”

Section: Multiterminal Source Codingmentioning

confidence: 94%

“…2 , D (3) ) is also dominated by a point in RD i CEO . Since RD o CEO is the convex hull of all such extreme points (i.e., the convex hull of the union of extreme points over all appropriate joint distributions), the theorem is proved.…”

Section: B a Matching Outer Boundmentioning

confidence: 97%

“…The key observation is that Lemma 1 continues to hold. The reader is directed to the complete manuscript [3] for details.…”

Section: B a Matching Outer Boundmentioning

confidence: 99%

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Multiterminal source coding under logarithmic loss

Courtade

Weissman

2012

2012 IEEE International Symposium on Information Theory Proceedings

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176

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Abstract-We consider the two-encoder multiterminal source coding problem subject to distortion constraints computed under logarithmic loss. We provide a single-letter description of the achievable rate distortion region for arbitrarily correlated sources with finite alphabets. In doing so, we also give the rate distortion region for the CEO problem under logarithmic loss. Notably, the Berger-Tung inner bound is tight in both settings.

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Section: Multiterminal Source Codingmentioning

confidence: 94%

Section: B a Matching Outer Boundmentioning

confidence: 97%

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Multiterminal source coding under logarithmic loss

Courtade

Weissman

2012

2012 IEEE International Symposium on Information Theory Proceedings

Self Cite

176

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show abstract

“…can be interpreted as the optimal prediction risk or regret under logarithmic loss. Recently, Courtade and Weissman [3] showed that the longstanding open problem of multiterminal source coding could be completely solved under logarithmic loss, providing yet another concrete example of its special nature. The use of the logarithm in defining entropy arises due to its various axiomatic characterizations, the first of which dates back to Shannon [4].…”

Section: Definition 1 (Logarithmic Lossmentioning

confidence: 99%

Justification of Logarithmic Loss via the Benefit of Side Information

Jiao

Courtade

Venkat

et al. 2015

IEEE Trans. Inform. Theory

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Abstract-We consider a natural measure of relevance: the reduction in optimal prediction risk in the presence of side information. For any given loss function, this relevance measure captures the benefit of side information for performing inference on a random variable under this loss function. When such a measure satisfies a natural data processing property, and the random variable of interest has alphabet size greater than two, we show that it is uniquely characterized by the mutual information, and the corresponding loss function coincides with logarithmic loss. In doing so, our work provides a new characterization of mutual information, and justifies its use as a measure of relevance. When the alphabet is binary, we characterize the only admissible forms the measure of relevance can assume while obeying the specified data processing property. Our results naturally extend to measuring causal influence between stochastic processes, where we unify different causal-inference measures in the literature as instantiations of directed information.

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“…More recently, Courtade and Weissman [15] gave the rate-distortion region of the CEO problem under the logarithmic-loss distortion measure.…”

Section: Csit] 11 Feb 2015mentioning

confidence: 99%

The CEO problem with secrecy constraints

Naghibi

Salimi

Skoglund

2014

2014 IEEE International Symposium on Information Theory

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Abstract-We study a lossy source coding problem with secrecy constraints in which a remote information source should be transmitted to a single destination via multiple agents in the presence of a passive eavesdropper. The agents observe noisy versions of the source and independently encode and transmit their observations to the destination via noiseless rate-limited links. The destination should estimate the remote source based on the information received from the agents within a certain mean distortion threshold. The eavesdropper, with access to side information correlated to the source, is able to listen in on one of the links from the agents to the destination in order to obtain as much information as possible about the source. This problem can be viewed as the so-called CEO problem with additional secrecy constraints. We establish inner and outer bounds on the ratedistortion-equivocation region of this problem. We also obtain the region in special cases where the bounds are tight. Furthermore, we study the quadratic Gaussian case and provide the optimal rate-distortion-equivocation region when the eavesdropper has no side information and an achievable region for a more general setup with side information at the eavesdropper.

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Multiterminal Source Coding Under Logarithmic Loss

Cited by 146 publications

References 29 publications

Multiterminal source coding under logarithmic loss

Multiterminal source coding under logarithmic loss

Justification of Logarithmic Loss via the Benefit of Side Information

The CEO problem with secrecy constraints

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