On a new non-Shannon type information inequality

Zhang, Zhen

doi:10.4310/cis.2003.v3.n1.a4

Cited by 46 publications

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“…The first known non-Shannon information inequality was presented by Zhang and Yeung [37]. Subsequently, many other rank and information inequalities have been found in [14,15,16,27,28,36] and other works.…”

Section: Polymatroids Rank Inequalities and Information Inequalitiesmentioning

confidence: 99%

“…By executing a brute-force algorithm using a computer program, they checked that Csirmaz's solution is compatible with every rank inequality in that finite set. In addition, they manually executed their algorithm on a symbolic representation of the infinite sequence of information inequalities given by Zhang [36]. This sequence contains inequalities on arbitrarily many variables and generalizes the infinite sequences from previous works.…”

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confidence: 99%

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Secret Sharing, Rank Inequalities, and Information Inequalities

Molleví

Padrö

2016

IEEE Trans. Inform. Theory

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Beimel and Orlov proved that all information inequalities on four or five variables, together with all information inequalities on more than five variables that are known to date, provide lower bounds on the size of the shares in secret sharing schemes that are at most linear on the number of participants. We present here another two negative results about the power of information inequalities in the search for lower bounds in secret sharing. First, we prove that all information inequalities on a bounded number of variables can only provide lower bounds that are polynomial on the number of participants. And second, we prove that the rank inequalities that are derived from the existence of two common informations can provide only lower bounds that are at most cubic in the number of participants.

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Section: Polymatroids Rank Inequalities and Information Inequalitiesmentioning

confidence: 99%

mentioning

confidence: 99%

Secret Sharing, Rank Inequalities, and Information Inequalities

Molleví

Padrö

2016

IEEE Trans. Inform. Theory

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“…The existence of such inequalities was unknown when Csirmaz [9] formalized that method. The first one was presented by Zhang and Yeung [30] and many others have been found subsequently [11,13,23,29]. When dealing with linear secret sharing schemes, one can improve the linear program by using rank inequalities, which apply to configurations of vector subspaces or, equivalently, to the joint entropies of collections of random variables defined from linear maps.…”

Section: Conjecturementioning

confidence: 99%

Secret Sharing, Rank Inequalities and Information Inequalities

Martín

Padrö

2013

Advances in Cryptology – CRYPTO 2013

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Abstract. Beimel and Orlov proved that all information inequalities on four or five variables, together with all information inequalities on more than five variables that are known to date, provide lower bounds on the size of the shares in secret sharing schemes that are at most linear on the number of participants. We present here another negative result about the power of information inequalities in the search for lower bounds in secret sharing. Namely, we prove that all information inequalities on a bounded number of variables only can provide lower bounds that are polynomial on the number of participants.

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“…The work of Han, Fujishige, Zhang and Yeung, [2], [3], [4], [5], [1] [5], [6], [7], [8], [9]. Although these non-shannon type inequalities give outer bounds for F4, its complete characterization remains an open problem.…”

Section: Introductionmentioning

confidence: 99%

“…However, a rather obvious solution and one that does not depend on a, the normal vector of the hyperplane is the following: for any a C N: Px,, (x) = cc, or 0 (8) for some constant c,z, independent of the point xei e {1, ...., N}I'l. In other words, these are distributions that take on zero or a constant value for all possible marginals, px, ( ).…”

Section: Introductionmentioning

confidence: 99%

On a Construction of Entropic Vectors Using Lattice-Generated Distributions

Hassibi

Shadbakht

2007

2007 IEEE International Symposium on Information Theory

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Abstract-The problem of determining the region of entropic vectors is a central one in information theory. Recently, there has been a great deal of interest in the development of nonShannon information inequalities, which provide outer bounds to the aforementioned region; however, there has been less recent work on developing inner bounds. This paper develops an inner bound that applies to any number of random variables and which is tight for 2 and 3 random variables (the only cases where the entropy region is known). The construction is based on probability distributions generated by a lattice. The region is shown to be a polytope generated by a set of linear inequalities. Study of the region for 4 and more random variables is currently under investigation.

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On a new non-Shannon type information inequality

Cited by 46 publications

References 0 publications

Secret Sharing, Rank Inequalities, and Information Inequalities

Secret Sharing, Rank Inequalities, and Information Inequalities

Secret Sharing, Rank Inequalities and Information Inequalities

On a Construction of Entropic Vectors Using Lattice-Generated Distributions

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