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Register a new userFundamental Limits of Caching for Demand Privacy against Colluding Users
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Qifa Yan
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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This work investigates the problem of demand privacy against colluding users for shared-link coded caching systems, where no subset of users can learn any information about the demands of the remaining users. The notion of privacy used here is stronger than similar notions adopted in past work and is motivated by the practical need to insure privacy regardless of the file distribution. Two scenarios are considered: Single File Retrieval (SFR) and Linear Function Retrieval (LFR), where in the latter case each user demands an arbitrary linear combination of the files at the server. The main contributions of this paper are a novel achievable scheme for LFR, referred as privacy key scheme, and a new information theoretic converse bound for SFR. Clearly, being SFR a special case of LFR, an achievable scheme for LFR works for SFR as well, and a converse for SFR is a valid converse for LFR as well. By comparing the performance of the achievable scheme with the converse bound derived in this paper (for the small cache size regime) and existing converse bounds without privacy constraints (in the remaining memory regime), the communication load of the privacy key scheme turns out to be optimal to within a constant multiplicative gap in all parameter regimes. Numerical results show that the new privacy key scheme outperforms in some regime known schemes based on the idea of virtual users, which also satisfy the stronger notion of user privacy against colluding users adopted here. Moreover, the privacy key scheme enjoys much lower subpacketization than known schemes based on virtual users.
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We consider the coded caching problem with an additional privacy constraint that a user should not get any information about the demands of the other users. We first show that a demand-private scheme for $N$ files and $K$ users can be obtained from a non-private scheme that serves only a subset of the demands for the $N$ files and $NK$ users problem. We further use this fact to construct a demand-private scheme for $N$ files and $K$ users from a particular known non-private scheme for $N$ files and $NK-K+1$ users. It is then demonstrated that, the memory-rate pair $(M,min {N,K}(1-M/N))$, which is achievable for non-private schemes with uncoded transmissions, is also achievable under demand privacy. We further propose a scheme that improves on these ideas by removing some redundant transmissions. The memory-rate trade-off achieved using our schemes is shown to be within a multiplicative factor of 3 from the optimal when $K < N$ and of 8 when $Nleq K$. Finally, we give the exact memory-rate trade-off for demand-private coded caching problems with $Ngeq K=2$.
Coded Caching is an efficient technique to reduce peak hour network traffic. One limitation of known coded caching schemes is that the demands of all users are revealed to their peers in the delivery phase. Schemes that assure privacy for user demands are studied in recent past. Assuming that the users are equipped with caches of small memory sizes, the achievable rate under demand privacy constraints is investigated in this work. We present an MDS code based demand private coded caching scheme with $K$ users and $N$ files that achieves a memory rate pair $left(frac{1}{K(N-1)+1},Nleft(1-frac{1}{K(N-1)+1}right)right)$. The presented memory-rate pair meets the lower bound under demand-privacy requirements, proposed by Yan textit{et al.} in the recent work cite{c13}. By memory sharing this characterizes the exact rate-memory trade-off for the demand private coded caching scheme for cache memory $Min left[0,frac{1}{K(N-1)+1}right]$.
The demand private coded caching problem in a multi-access network with $K$ users and $K$ caches, where each user has access to $L$ neighbouring caches in a cyclic wrap-around manner, is studied. The additional constraint imposed is that one user should not get any information regarding the demands of the remaining users. A lifting construction of demand private multi-access coded caching scheme from conventional, non-private multi-access scheme is introduced. The demand-privacy for a user is ensured by placing some additional textit{keys} in a set of caches called the textit{private set} of that user. For a given $K$ and $L$, a technique is also devised to find the private sets of the users.
Optimal caching of files in a content distribution network (CDN) is a problem of fundamental and growing commercial interest. Although many different caching algorithms are in use today, the fundamental performance limits of network caching algorithms from an online learning point-of-view remain poorly understood to date. In this paper, we resolve this question in the following two settings: (1) a single user connected to a single cache, and (2) a set of users and a set of caches interconnected through a bipartite network. Recently, an online gradient-based coded caching policy was shown to enjoy sub-linear regret. However, due to the lack of known regret lower bounds, the question of the optimality of the proposed policy was left open. In this paper, we settle this question by deriving tight non-asymptotic regret lower bounds in both of the above settings. In addition to that, we propose a new Follow-the-Perturbed-Leader-based uncoded caching policy with near-optimal regret. Technically, the lower-bounds are obtained by relating the online caching problem to the classic probabilistic paradigm of balls-into-bins. Our proofs make extensive use of a new result on the expected load in the most populated half of the bins, which might also be of independent interest. We evaluate the performance of the caching policies by experimenting with the popular MovieLens dataset and conclude the paper with design recommendations and a list of open problems.
In general coding theory, we often assume that error is observed in transferring or storing encoded symbols, while the process of encoding itself is error-free. Motivated by recent applications of coding theory, in this paper, we consider the case where the process of encoding is distributed and prone to error. We introduce the problem of distributed encoding, comprising of $Kinmathbb{N}$ isolated source nodes and $Ninmathbb{N}$ encoding nodes. Each source node has one symbol from a finite field and sends it to all encoding nodes. Each encoding node stores an encoded symbol, as a function of the received symbols. However, some of the source nodes are controlled by the adversary and may send different symbols to different encoding nodes. Depending on the number of adversarial nodes, denoted by $betainmathbb{N}$, and the number of symbols that each one generates, denoted by $vinmathbb{N}$, the process of decoding from the encoded symbols could be impossible. Assume that a decoder connects to an arbitrary subset of $t inmathbb{N}$ encoding nodes and wants to decode the symbols of the honest nodes correctly, without necessarily identifying the sets of honest and adversarial nodes. In this paper, we study $t^*inmathbb{N}$, the minimum of $t$, which is a function of $K$, $N$, $beta$, and $v$. We show that when the encoding nodes use linear coding, $t^*_{textrm{linear}}=K+2beta(v-1)$, if $Nge K+2beta(v-1)$, and $t^*_{textrm{linear}}=N$, if $Nle K+2beta(v-1)$. In order to achieve $t^*_{textrm{linear}}$, we use random linear coding and show that in any feasible solution that the decoder finds, the messages of the honest nodes are decoded correctly. For the converse of the fundamental limit, we show that when the adversary behaves in a particular way, it can always confuse the decoder between two feasible solutions that differ in the message of at least one honest node.
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