Fundamental Limits of Cache-Aided Private Information Retrieval with Unknown and Uncoded Prefetching

Wei, Yi-Peng; Banawan, Karim; Ulukuş, Şennur

doi:10.48550/arxiv.1709.01056

Cited by 15 publications

(52 citation statements)

References 25 publications

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“…A caching scheme based on Maximum Distance Separable (MDS) code was proposed. In [27]- [29], for the single-user PIR problem with end-user-cache, instead of caching the whole files, the user can choose any bits to store as in the coded caching model. Novel converse and achievable bounds were proposed in [27]- [29] for the cases where the user's cache is known, partially known, and unknown to the servers, respectively.…”

Section: Relation To Private Information Retrievalmentioning

confidence: 99%

“…In [27]- [29], for the single-user PIR problem with end-user-cache, instead of caching the whole files, the user can choose any bits to store as in the coded caching model. Novel converse and achievable bounds were proposed in [27]- [29] for the cases where the user's cache is known, partially known, and unknown to the servers, respectively. The authors in [30] considered the single-user PIR problem with end-database-caches, where each server can choose any bits to store instead of being able to access to the whole library.…”

Section: Relation To Private Information Retrievalmentioning

confidence: 99%

See 1 more Smart Citation

On Coded Caching with Private Demands

Wan¹,

Caire²

2019

Preprint

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Caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the user's local cache memory without knowledge of later demands. For the sharedlink caching model, Maddah-Ali and Niesen (MAN) proposed a two-phase (placement and delivery phases) coded caching strategy, which is order optimal within a constant factor. However, in the MAN scheme, each user can obtain the information about the demands of other users, i.e., the MAN scheme is inherently prone to tampering and spying the activity/demands of other users. In this paper, we formulate a shared-link caching model with private demands. Our goal is to design a two-phase private caching scheme with minimum load while preserving the privacy of the demands of each user with respect to other users. Two private caching schemes are proposed with some (order) optimality results for high memory regime. We also propose a private scheme to further reduce the transmitted load for the case where each user has a distinct request, e.g., in practical asynchronous streaming users always have distinct demands. Finally, this scheme is extended to the general demand case, which is order optimal for any memory size, but with an extremely high sub-packetization level. While the ensemble of our results essentially close the problem of (order) optimal coded caching subject to the privacy of users' demands, the problem of how to achieve this optimality in the small memory regime without an exponentially large expansion of the sub-packetization order remains as an interesting open problem for future investigation. I. INTRODUCTION A. Brief Review of Coded CachingRecent years have witnessed a steep increase of wireless devices connected to the Internet, leading to a heavy network traffic because of multimedia streaming, web-browsing and social networking. Furthermore, the high temporal variability of network traffic results in congestions K. Wan and G. Caire are with the Electrical Engineering and

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Section: Relation To Private Information Retrievalmentioning

confidence: 99%

Section: Relation To Private Information Retrievalmentioning

confidence: 99%

On Coded Caching with Private Demands

Wan¹,

Caire²

2019

Preprint

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“…side information [8], [14], [26], [29], [30]. It is expected that more variant models of PIR will arise according to different practical scenarios.…”

mentioning

confidence: 99%

A general private information retrieval scheme for MDS coded databases with colluding servers

Zhang

2019

Des. Codes Cryptogr.

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Private information retrieval (PIR) gets renewed attentions due to its information-theoretic reformulation and its application in distributed storage system (DSS). The general PIR model considers a coded database containing N servers storing M files. Each file is stored independently via the same arbitrary (N, K)-MDS code. A user wants to retrieve a specific file from the database privately against an arbitrary set of T colluding servers. A key problem is to analyze the PIR capacity, defined as the maximal number of bits privately retrieved per one downloaded bit. Several extensions for the general model appear by bringing in various additional constraints. In this paper, we propose a general PIR scheme for several variant PIR models including: PIR with robust servers, PIR with Byzantine servers, the multi-file PIR model and PIR with arbitrary collusion patterns.

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“…The result is somewhat pessimistic since the user cannot further reduce the download cost by using the cache content. This has motivated subsequent works which have considered the case where the databases are completely unaware or partially unaware of the cache content [30][31][32][33]36,39]. Within this sub-branch of literature, references [30,32,33] have considered PIR with PSI.…”

Section: Related Workmentioning

confidence: 99%

“…. , M. The caching scheme is subject to a memory size constraint, i.e., M i=1 r i = S. Note that in [31,36,39], for each message, the user randomly chooses Lr symbols out of the total L symbols to cache. In [31,36,39], to reliably reconstruct the desired message, the user should record the indices of the cached symbols within each message.…”

Section: Related Workmentioning

confidence: 99%

The Capacity of Private Information Retrieval With Private Side Information Under Storage Constraints

Wei

Ulukuş

2020

IEEE Trans. Inform. Theory

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We consider the problem of private information retrieval (PIR) of a single message out of K messages from N replicated and non-colluding databases where a cacheenabled user (retriever) of cache-size S possesses side information in the form of uncoded portions of the messages that are unknown to the databases. The identities of these side information messages need to be kept private from the databases, i.e., we consider PIR with private side information (PSI). We characterize the optimal normalized download cost for this PIR-PSI problem under the storage constraint S aswhere r i is the portion of the ith side information message that is cached with M i=1 r i = S. Based on this capacity result, we prove two facts: First, for a fixed memory size S and a fixed number of accessible messages M , uniform caching achieves the lowest normalized download cost, i.e., r i = S M , for i = 1, . . . , M , is optimum. Second, for a fixed memory size S, among all possible K − ⌈S⌉ + 1 uniform caching schemes, the uniform caching scheme which caches M = K messages achieves the lowest normalized download cost.

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Fundamental Limits of Cache-Aided Private Information Retrieval with Unknown and Uncoded Prefetching

Cited by 15 publications

References 25 publications

On Coded Caching with Private Demands

On Coded Caching with Private Demands

A general private information retrieval scheme for MDS coded databases with colluding servers

The Capacity of Private Information Retrieval With Private Side Information Under Storage Constraints

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