Achieving Maximum Distance Separable Private Information Retrieval Capacity With Linear Codes

Lin, Hsuan-Yin; Rosnes, Eirik; Amat, Alexandre Graell i

doi:10.48550/arxiv.1712.03898

Cited by 8 publications

(48 citation statements)

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“…where m s = N n=1 m n , as before, is the sum storage space and Dn is defined in (37). The solution of the relaxed problem is potentially lower than (11), since the optimal solution of ( 11) is feasible in (47). Note that the relaxed problem (47) depends only on the sum storage space m s and the number of databases N. Therefore, the corresponding relaxed problem is the same for all distributions of the storage space among databases under the same m s , including the uniform distribution which results in the homogeneous problem.…”

Section: Equivalence To the Homogeneous Problemmentioning

confidence: 99%

“…Finally, to show the equivalence of the original linear program in (11) and the relaxed linear problem in (47), we need to show that a feasible (non-negative) solution of (11) exists for every optimal solution of (47). That is, the optimal βs found in solving (47) can be mapped to a set of feasible αs in (11). We note that, we have shown this by finding an explicit solution for the case of N = 3 in Section 4.3.…”

Section: Equivalence To the Homogeneous Problemmentioning

confidence: 99%

“…Lemma 5 There exists a feasible (non-negative) solution of (11) corresponding to the optimal solution of the relaxed problem in (47).…”

Section: Equivalence To the Homogeneous Problemmentioning

confidence: 99%

See 2 more Smart Citations

The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases

Banawan¹,

Arasli²,

Wei³

et al. 2019

Preprint

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We consider private information retrieval (PIR) of a single file out of K files fromThe aim of this work is to jointly design the content placement phase and the information retrieval phase in order to minimize the download cost in the PIR phase. We characterize the optimal PIR download cost as a linear program. By analyzing the structure of the optimal solution of this linear program, we show that, surprisingly, the optimal download cost in our heterogeneous case matches its homogeneous counterpart where all databases have the same average storage constraint µ = 1 N N n=1 m n . Thus, we show that there is no loss in the PIR capacity due to heterogeneity of storage spaces of the databases. We provide the optimum content placement explicitly for N = 3.

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Section: Equivalence To the Homogeneous Problemmentioning

confidence: 99%

Section: Equivalence To the Homogeneous Problemmentioning

confidence: 99%

See 1 more Smart Citation

The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases

Banawan¹,

Arasli²,

Wei³

et al. 2019

Preprint

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show abstract

“…Since then, extensions of this model for several more setups have been rigorously studied; see e.g. [1], [2], [15], [20], [33], [34], [36], [38] and references therein.…”

Section: A Private Information Retrieval Private Computation and Prox...mentioning

confidence: 99%

“…L 1 = L 2 = 28. Since c (28,20,6) 25 [16] it follows that N(L, s, 11) 50 for this case. Note that other covering designs can be used in this case.…”

Section: Analysis Of the Lower And Upper Boundsmentioning

confidence: 99%

Private Proximity Retrieval Codes

Zhang

Yaakobi

Etzion

2019

Preprint

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A private proximity retrieval (PPR) scheme is a protocol which allows a user to retrieve the identities of all records in a database that are within some distance r from the user's record x. The user's privacy at each server is given by the fraction of the record x that is kept private. In this paper, this research is initiated and protocols that offer trade-offs between privacy and computational complexity and storage are studied. In particular, we assume that each server stores a copy of the database and study the required minimum number of servers by our protocol which provides a given privacy level. Each server gets a query in the protocol and the set of queries forms a code. We study the family of codes generated by the set of queries and in particular the minimum number of codewords in such a code which is the minimum number of servers required for the protocol. These codes are closely related to a family of codes known as covering designs. We introduce several lower bounds on the sizes of such codes as well as several constructions. This work focuses on the case when the records are binary vectors together with the Hamming distance. Other metrics such as the Johnson metric are also investigated.

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Capacity of Private Linear Computation for Coded Databases

Obead

Lin

Rosnes

et al. 2018

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

Self Cite

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We consider the problem of private linear computation (PLC) in a distributed storage system. In PLC, a user wishes to compute a linear combination of f messages stored in noncolluding databases while revealing no information about the coefficients of the desired linear combination to the databases. In extension of our previous work we employ linear codes to encode the information on the databases. We show that the PLC capacity, which is the ratio of the desired linear function size and the total amount of downloaded information, matches the maximum distance separable (MDS) coded capacity of private information retrieval for a large class of linear codes that includes MDS codes. In particular, the proposed converse is valid for any number of messages and linear combinations, and the capacity expression depends on the rank of the coefficient matrix obtained from all linear combinations.

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Achieving Maximum Distance Separable Private Information Retrieval Capacity With Linear Codes

Cited by 8 publications

References 0 publications

The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases

The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases

Private Proximity Retrieval Codes

Capacity of Private Linear Computation for Coded Databases

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