48,816 research outputs found

    Private Information Retrieval with Side Information and Coding for Security

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    This dissertation studies privacy and security problems from an information-theoretic point of view. We study the privacy problem via the private information retrieval (PIR) problem with a focus on its interactions with available side information. We study the security problem via the wiretap channel with a focus on the design of practical coding schemes to achieve information-theoretically achievable random-coding based secrecy rates. First, we consider the problem of PIR from NN non-colluding and replicated databases when the user is equipped with a cache that holds an uncoded fraction rr from each of the KK stored messages in the databases. We consider the case where the databases are unaware of the cache content. We investigate Dβˆ—(r)D^*(r) the optimal download cost normalized with the message size as a function of KK, NN, rr. For a fixed KK, NN, we develop converses and achievability schemes for the Dβˆ—(r)D^*(r) curve. The largest additive gap between our achievability and the converse bounds is 16\frac{1}{6}. Our results show that the download cost can be reduced beyond memory-sharing if the databases are unaware of the cached content. Second, we consider the same setting under a more restricted model where the databases know the user cache content partially. The user receives an uncoded fraction rr from each of the KK stored messages, with the rN\frac{r}{N} fraction of it coming from the nnth database. The side information obtained from the nnth database is known by the nnth database and is unknown by the remaining databases. We investigate the optimal normalized download cost Dβˆ—(r)D^*(r), and develop converses and achievability schemes for Dβˆ—(r)D^*(r). The largest additive gap between our achievability and the converse bounds is 532\frac{5}{32} for this case. We observe that the achievable download cost here is larger than that in the previous case due to the partial knowledge of the databases regarding the cache content. Third, we consider the problem of PIR with private side information (PSI) when the cache content is partially known by the databases. Here, a cache-enabled user of cache-size MM possesses side information in the form of full messages that are partially known by the databases. The user wishes to download a desired message privately while keeping the identities of the side information messages that the user did not prefetch from a database private against that database. We characterize the exact capacity of PIR with PSI under partially known PSI condition. We show that the capacity of PIR with partially known PSI is the same as the capacity of PIR with fully unknown PSI. Fourth, we consider PIR with PSI under storage constraints where a cache-enabled user of cache-size SS possesses side information in the form MM messages that are unknown to the databases, where M>SM>S. We address the problem of which uncoded parts of MM messages the user should keep in its constrained cache of size SS in order to minimize the download cost during PIR subject to PSI. We characterize the exact capacity of this PIR-PSI problem under the storage constraint SS. We show that a uniform caching scheme which caches equal amounts from all messages achieves the lowest normalized download cost. Fifth, we consider the PIR problem from decentralized uncoded caching databases. Here, the contents of the databases are not fixed a priori, and we design the probability distribution adopted by each database in the decentralized caching phase in order to minimize the expected normalized download cost in the retrieval phase. We characterize the exact capacity of this problem, and show that uniform and random caching results in the lowest normalized download cost. Next, we focus on security of communication by designing practical coding schemes to achieve the information-theoretically achievable random-coding based secrecy rates. By applying two recently developed techniques for polar codes, namely, universal polar coding and polar coding for asymmetric channels, we propose a polar coding scheme to achieve the secrecy capacity of the general wiretap channel. We then apply this coding scheme to achieve the best-known secrecy rates for the multiple access wiretap channel, and the broadcast and interference channels with confidential messages

    Single-Server Single-Message Online Private Information Retrieval with Side Information

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    In many practical settings, the user needs to retrieve information from a server in a periodic manner, over multiple rounds of communication. In this paper, we discuss the setting in which this information needs to be retrieved privately, such that the identity of all the information retrieved until the current round is protected. This setting can occur in practical situations in which the user needs to retrieve items from the server or a periodic basis, such that the privacy needs to be guaranteed for all the items been retrieved until the current round. We refer to this setting as an \emph{online private information retrieval} as the user does not know the identities of the future items that need to be retrieved from the server. Following the previous line of work by Kadhe \emph{et al.}~we assume that the user knows a random subset of MM messages in the database as a side information which are unknown to the server. Focusing on scalar-linear settings, we characterize the \emph{per-round capacity}, i.e., the maximum achievable download rate at each round, and present a coding scheme that achieves this capacity. The key idea of our scheme is to utilize the data downloaded during the current round as a side information for the subsequent rounds. We show for the setting with KK messages stored at the server, the per-round capacity of the scalar-linear setting is C1=(M+1)/KC_1= ({M+1})/{K} for round i=1i=1 and Ci=(2iβˆ’1(M+1))/KM{C_i= {(2^{i-1}(M+1))}/{KM}} for round iβ‰₯2i\geq2, provided that K/(M+1){K}/({M+1}) is a power of 22.Comment: 7 pages; This work is a long version of an article submitted to IEEE for possible publicatio

    An MDS-PIR Capacity-Achieving Protocol for Distributed Storage Using Non-MDS Linear Codes

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    We propose a private information retrieval (PIR) protocol for distributed storage systems with noncolluding nodes where data is stored using an arbitrary linear code. An expression for the PIR rate, i.e., the ratio of the amount of retrieved data per unit of downloaded data, is derived, and a necessary and a sufficient condition for codes to achieve the maximum distance separable (MDS) PIR capacity are given. The necessary condition is based on the generalized Hamming weights of the storage code, while the sufficient condition is based on code automorphisms. We show that cyclic codes and Reed-Muller codes satisfy the sufficient condition and are thus MDS-PIR capacity-achieving.Comment: To be presented at 2018 IEEE International Symposium on Information Theory (ISIT). arXiv admin note: substantial text overlap with arXiv:1712.0389
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