Multi-Message Private Information Retrieval: Capacity Results and Near-Optimal Schemes

Banawan, Karim; Ulukuş, Şennur

doi:10.1109/tit.2018.2828310

Cited by 152 publications

(148 citation statements)

References 35 publications

Supporting

Mentioning

148

Contrasting

Order By: Relevance

“…This proof is similar to the proof in [7] changed to match the current problem setting. To show the limits of capacity, this proof needs to be split in two parts, achievability and converse.…”

Section: A Proof Of Theoremmentioning

confidence: 61%

“…Now, as mentioned in [7], H(Â 1 |X (L) P 1 , X (L) P 2 ,Q) (in the modified problem) is quite similar to the H(Â 1 |Q) in an equivalent problem where the user wants to retrieve a subset of inner products indexed by P ⊆ T 2 and T 2 = T 1 \ (P 1 ∪ P 2 ) and thus |T 2 | = T 1 − 2P . The difference between the modified problem and its equivalent problem is that in the modified problem we have conditions on X (L) P 1 , X (L) P 2 , while in the equivalent problem the conditions don't exist.…”

Section: Conversementioning

confidence: 90%

“…February 19, 2019 DRAFT where (91) follows from (25) noting that X (L) \ X (L) P ⊆ X (L) P ; (93) is true because of (24); and (95) is the result of Lemma 6. Now, we proceed to the converse following the approach of [7] as,…”

Section: Conversementioning

confidence: 99%

“…While this converse is based on [7], a few changes are needed to be made to reach our goal. This is because of the difference in retrieving inner products instead of data files in [7].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Private Inner Product Retrieval for Distributed Machine Learning

Mousavi

Maddah-Ali

Mirmohseni

2019

2019 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

In this paper, we argue that in many basic algorithms for machine learning, including support vector machine (SVM) for classification, principal component analysis (PCA) for dimensionality reduction, and regression for dependency estimation, we need the inner products of the data samples, rather than the data samples themselves.Motivated by the above observation, we introduce the problem of private inner product retrieval for distributed machine learning, where we have a system including a database of some files, duplicated across some non-colluding servers. A user intends to retrieve a subset of specific size of the inner products of the data files with minimum communication load, without revealing any information about the identity of the requested subset. For achievability, we use the algorithms for multi-message private information retrieval. For converse, we establish that as the length of the files becomes large, the set of all inner products converges to independent random variables with uniform distribution, and derive the rate of convergence. To prove that, we construct special dependencies among sequences of the sets of all inner products with different length, which forms a time-homogeneous irreducible Markov chain, without affecting the marginal distribution. We show that this Markov chain has a uniform distribution as its unique stationary distribution, with rate of convergence dominated by the second largest eigenvalue of the transition probability matrix. This allows us to develop a converse, which converges to a tight bound in some cases, as the size of the files becomes large. While this converse is based on the one in multi-message private information retrieval due to the nature of retrieving inner products instead of data itself some changes are made to reach the desired result.

show abstract

Section: A Proof Of Theoremmentioning

confidence: 61%

Section: Conversementioning

confidence: 90%

Section: Conversementioning

confidence: 99%

“…While this converse is based on [7], a few changes are needed to be made to reach our goal. This is because of the difference in retrieving inner products instead of data files in [7].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Private Inner Product Retrieval for Distributed Machine Learning

Mousavi

Maddah-Ali

Mirmohseni

2019

2019 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

show abstract

“…However, this implies that X W ′ cannot be the demand, and this will violate the privacy. 6 Now, since E ⊥ is an LRC with block-length n = K, dimension k = K − T , and locality r = M from Theorem 1, we have from (7) that…”

Section: A Single-message Pir-si Schemes and Lrcsmentioning

confidence: 99%

On an Equivalence Between Single-Server PIR with Side Information and Locally Recoverable Codes

Kadhe

Heidarzadeh

Sprintson

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

View full text Add to dashboard Cite

Private Information Retrieval (PIR) problem has recently attracted a significant interest in the information-theory community. In this problem, a user wants to privately download one or more messages belonging to a database with copies stored on a single or multiple remote servers. In the single server scenario, the user must have prior side information, i.e., a subset of messages unknown to the server, to be able to privately retrieve the required messages in an efficient way.In the last decade, there has also been a significant interest in Locally Recoverable Codes (LRC), a class of storage codes in which each symbol can be recovered from a limited number of other symbols. More recently, there is an interest in cooperative locally recoverable codes, i.e., codes in which multiple symbols can be recovered from a small set of other code symbols.In this paper, we establish a relationship between coding schemes for the single-server PIR problem and LRCs. In particular, we show the following results: (i) PIR schemes designed for retrieving a single message are equivalent to classical LRCs; and (ii) PIR schemes for retrieving multiple messages are equivalent to cooperative LRCs. These equivalence results allow us to recover upper bounds on the download rate for PIR-SI schemes, and to obtain a novel rate upper bound on cooperative LRCs. We show results for both linear and non-linear codes.

show abstract

Cache-Aided Multi-message Private Information Retrieval

Liu

Kang

2021

Communications and Networking

View full text Add to dashboard Cite

Multi-Message Private Information Retrieval: Capacity Results and Near-Optimal Schemes

Cited by 152 publications

References 35 publications

Private Inner Product Retrieval for Distributed Machine Learning

Private Inner Product Retrieval for Distributed Machine Learning

On an Equivalence Between Single-Server PIR with Side Information and Locally Recoverable Codes

Cache-Aided Multi-message Private Information Retrieval

Contact Info

Product

Resources

About