受一个开放问题和猜想的启发，本研究探讨了最近由Heidarzadeh等人提出的具有私有编码边信息的单服务器私有信息检索（PIR-PCSI）问题。PIR-PCSI的目标是允许用户高效地检索期望的消息$\bm{W}_{\bm{\theta}}$，该消息是存储在服务器上的$K$个独立消息之一，同时利用消息的均匀选择的规模为$M$的子集（$\bm{\mathcal{S}}\subset[K]$）的线性组合的私有边信息。设置PIR-PCSI-I和PIR-PCSI-II分别对应于约束$\bm{\theta}$从$[K]\setminus\bm{\mathcal{S}}$和$\bm{\mathcal{S}}$中均匀生成。在每种情况下，$(\bm{\theta},\bm{\mathcal{S}})$必须对服务器保密。容量定义为在消息和字段大小上，可达速率（每次下载位中检索到的期望消息位数）的上确界，并由Heidarzadeh等人对PIR-PCSI-I一般情况以及PIR-PCSI-II在$M>(K+1)/2$时表征为$(K-M+1)^{-1}$。对于$2\leq M\leq (K+1)/2$，PIR-PCSI-II的容量仍未解决，并且猜想即使在这种情况下容量也为$(K-M+1)^{-1}$。我们证明对于$2 \leq M \leq \frac{K+1}{2}$，PIR-PCSI-II的容量等于$2/K$，这严格大于猜想值，并且在此参数范围内不依赖于$M$。值得注意的是，发现一半的边信息是冗余的。我们还刻画了容量下确界（对字段取下确界而非上确界），以及具有私有系数的容量。结果被推广到PIR-PCSI-I（$\theta\in[K]\setminus\mathcal{S}$）和PIR-PCSI（$\theta\in[K]$）设置。
英文摘要：
Motivated by an open problem and a conjecture, this work studies the problem of single server private information retrieval with private coded side information (PIR-PCSI) that was recently introduced by Heidarzadeh et al. The goal of PIR-PCSI is to allow a user to efficiently retrieve a desired message $\bm{W}_{\bmθ}$, which is one of $K$ independent messages that are stored at a server, while utilizing private side information of a linear combination of a uniformly chosen size-$M$ subset ($\bm{\mathcal{S}}\subset[K]$) of messages. The settings PIR-PCSI-I and PIR-PCSI-II correspond to the constraints that $\bmθ$ is generated uniformly from $[K]\setminus\bm{\mathcal{S}}$, and $\bm{\mathcal{S}}$, respectively. In each case, $(\bmθ,\bm{\mathcal{S}})$ must be kept private from the server. The capacity is defined as the supremum over message and field sizes, of achievable rates (number of bits of desired message retrieved per bit of download) and is characterized by Heidarzadeh et al. for PIR-PCSI-I in general, and for PIR-PCSI-II for $M>(K+1)/2$ as $(K-M+1)^{-1}$. For $2\leq M\leq (K+1)/2$ the capacity of PIR-PCSI-II remains open, and it is conjectured that even in this case the capacity is $(K-M+1)^{-1}$. We show the capacity of PIR-PCSI-II is equal to $2/K$ for $2 \leq M \leq \frac{K+1}{2}$, which is strictly larger than the conjectured value, and does not depend on $M$ within this parameter regime. Remarkably, half the side-information is found to be redundant. We also characterize the infimum capacity (infimum over fields instead of supremum), and the capacity with private coefficients. The results are generalized to PIR-PCSI-I ($θ\in[K]\setminus\mathcal{S}$) and PIR-PCSI ($θ\in[K]$) settings.
We introduce a variation of coded computation that ensures data security and master's privacy against workers, which is referred to as private secure coded computation. In private secure coded computation, the master needs to compute a function of its own dataset and one of the datasets in a library exclusively shared by external workers. After recovering the desired function, the workers must not be able to know which dataset in the library was desired by the master or obtain any information about the master's own data. We propose a private secure coded computation scheme for matrix multiplic…
In a distributed computing system for the master-worker framework, an erasure code can mitigate the effects of slow workers, also called stragglers. The distributed computing system combined with coding is referred to as coded computation. We introduce a variation of coded computation that protects the master's privacy from the workers, which is referred to as private coded computation. In private coded computation, the master needs to compute a function of its own dataset and one of the datasets in a library exclusively shared by the external workers. After the master recovers the result of t…
Recently Hachem et al. formulated a multiaccess coded caching model which consists of a central server connected to $K$ users via an error-free shared link, and $K$ cache-nodes. Each cache-node is equipped with a local cache and each user can access $L$ neighbouring cache-nodes with a cyclic wrap-around fashion. In this paper, we take the privacy of the users' demands into consideration, i.e., each user can only get its required file and can not get any information about the demands of other users. By storing some private keys at the cache-nodes, we propose a novel transformation approach to t…
We consider the problem of designing PIR scheme on coded data when certain nodes are unresponsive. We provide the construction of $ν$-robust PIR schemes that can tolerate up to $ν$ unresponsive nodes. These schemes are adaptive and universally optimal in the sense of achieving (asymptotically) optimal download cost for any number of unresponsive nodes up to $ν$.
Cache-aided content delivery is studied in a multi-server system with $P$ servers and $K$ users, each equipped with a local cache memory. In the delivery phase, each user connects randomly to any $ρ$ out of $P$ servers. Thanks to the availability of multiple servers, which model small-cell base stations (SBSs), demands can be satisfied with reduced storage capacity at each server and reduced delivery rate per server; however, this also leads to reduced multicasting opportunities compared to the single-server scenario. A joint storage and proactive caching scheme is proposed, which exploits cod…
We consider private polynomial computation (PPC) over noncolluding coded databases. In such a setting a user wishes to compute a multivariate polynomial of degree at most $g$ over $f$ variables (or messages) stored in multiple databases while revealing no information about the desired polynomial to the databases. We construct two novel PPC schemes, where the first is a generalization of our previous work in private linear computation for coded databases. In this scheme we consider Reed-Solomon coded databases with Lagrange encoding, which leverages ideas from recently proposed star-product pri…
Coded caching has been widely used in the wireless network for shifting the some transmissions during the peak traffic times to the off-peak traffic times. Multi-server coded caching, which can share responsibility for the total amount of transmission in the wireless network during the peak traffic times by means of the collaboration among these servers, can be seen everywhere in our life. The three servers setting (two data servers and one parity check server) is used in practice, e.g. redundant array of independent disks-4. In this scenario, there are total $N$ files which are equally stored…
We study the problem of private function retrieval (PFR) in a distributed storage system. In PFR the user wishes to retrieve a linear combination of $M$ messages stored in non-colluding $(N,K)$ MDS coded databases while revealing no information about the coefficients of the intended linear combination to any of the individual databases. We present an achievable scheme for MDS coded PFR with a rate that matches the capacity for coded private information retrieval derived recently, $R=(1+R_c+R_c^2+\dots+R_c^{M-1})^{-1}=\frac{1-R_c}{1-R_c^M}$, where $R_c=\frac{K}{N}$ is the rate of the MDS code. …
We present a general framework for Private Information Retrieval (PIR) from arbitrary coded databases, that allows one to adjust the rate of the scheme according to the suspected number of colluding servers. If the storage code is a generalized Reed-Solomon code of length n and dimension k, we design PIR schemes which simultaneously protect against t colluding servers and provide PIR rate 1-(k+t-1)/n, for all t between 1 and n-k. This interpolates between the previously studied cases of t=1 and k=1 and asymptotically achieves the known capacity bounds in both of these cases, as the size of the…
The problem of private information retrieval gets renewed attentions in recent years due to its information-theoretic reformulation and applications in distributed storage systems. PIR capacity is the maximal number of bits privately retrieved per one bit of downloaded bit. The capacity has been fully solved for some degenerating cases. For a general case where the database is both coded and colluded, the exact capacity remains unknown. We build a general private information retrieval scheme for MDS coded databases with colluding servers. Our scheme achieves the rate $(1+R+R^2+\cdots+R^{M-1})$…
The distributed coded caching problem has been studied extensively in the recent past. While the known coded caching schemes achieve an improved transmission rate, they violate the privacy of the users since in these schemes the demand of one user is revealed to others in the delivery phase. In this paper, we consider the coded caching problem under the constraint that the demands of the other users remain information theoretically secret from each user. We first show that the memory-rate pair $(M,\min \{N,K\}(1-M/N))$ is achievable under information theoretic demand privacy, while using broad…
The problem of Private Information Retrieval (PIR) from coded storage systems with colluding, byzantine, and unresponsive servers is considered. An explicit scheme using an $[n,k]$ Reed-Solomon storage code is designed, protecting against $t$-collusion and handling up to $b$ byzantine and $r$ unresponsive servers, when $n>k+t+2b+r-1$. This scheme achieves a PIR rate of $\frac{n-r-(k+2b+t-1)}{n-r}$. In the case where the capacity is known, namely when $k=1$, it is asymptotically capacity-achieving as the number of files grows. Lastly, the scheme is adapted to symmetric PIR.
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},N\left(1-\fr…
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 $(M,\min \{N,K\}(1-M/N))$, wh…
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…
This work investigates a system where each user aims to retrieve a scalar linear function of the files of a library, which are Maximum Distance Separable coded and stored at multiple distributed servers. The system needs to guarantee robust decoding in the sense that each user must decode its demanded function with signals received from any subset of servers whose cardinality exceeds a threshold. In addition, (a) the content of the library must be kept secure from a wiretapper who obtains all the signals from the servers;(b) any subset of users together can not obtain any information about the…
We study the problem of single-server single-message Private Information Retrieval with Private Coded Side Information (PIR-PCSI). In this problem, there is a server that stores a database, and a user who knows a random linear combination of a random subset of messages in the database. The number of messages contributing to the user's side information is known to the server a priori, whereas their indices and coefficients are unknown to the server a priori. The user wants to retrieve a message from the server (with minimum download cost), while protecting the identities of both the demand and …
A private information retrieval (PIR) scheme on coded storage systems with colluding, byzantine, and non-responsive servers is presented. Furthermore, the scheme can also be used for symmetric PIR in the same setting. An explicit scheme using an $[n,k]$ generalized Reed-Solomon storage code is designed, protecting against $t$-collusion and handling up to $b$ byzantine and $r$ non-responsive servers, when $n\geq n'= (ν+1) k+t+2b+r-1$, for some integer $ν\geq 1$. This scheme achieves a PIR rate of $1-\frac{k+2b+t+r-1}{n'}$. In the case where the capacity is known, namely when $k=1$, it is asympt…
Private computation in a distributed storage system (DSS) is a generalization of the private information retrieval (PIR) problem. In such setting a user wishes to compute a function of $f$ messages stored in $n$ noncolluding coded databases, i.e., databases storing data encoded with an $[n,k]$ linear storage code, while revealing no information about the desired function to the databases. We consider the problem of private polynomial computation (PPC). In PPC, a user wishes to compute a multivariate polynomial of degree at most $g$ over $f$ variables (or messages) stored in multiple databases.…
Private information retrieval scheme for coded data storage is considered in this paper. We focus on the case where the size of each data record is large and hence only the download cost (but not the upload cost for transmitting retrieval queries) is of interest. We prove that the tradeoff between storage cost and retrieval/download cost depends on the number of data records in the system. We also propose a fairly general class of linear storage codes and retrieval schemes and derive conditions under which our retrieval schemes are error-free and private. Tradeoffs between the storage cost and…
In private information delivery (PID) problem, there are $K$ messages stored across $N$ servers, each capable of storing $M$ messages and a user. Servers want to convey one of the $K$ messages to the user without revealing the identity (index) of the message conveyed. The capacity of PID problem is defined as maximum number of bits of the desired message that can be conveyed privately, per bit of total communication, to the user. For the restricted case of replicated systems, where coded messages or splitting one message into several servers is not allowed, the capacity of PID has been charact…
In a distributed storage system, private information retrieval (PIR) guarantees that a user retrieves one file from the system without revealing any information about the identity of its interested file to any individual server. In this paper, we investigate $(N,K,M)$ coded sever model of PIR, where each of $M$ files is distributed to the $N$ servers in the form of $(N,K)$ maximum distance separable (MDS) code for some $N>K$ and $M>1$. As a result, we propose a new capacity-achieving $(N,K,M)$ coded linear PIR scheme such that it can be implemented with file length $\frac{K(N-K)}{\gcd(N,K)}$, …
Consider the problem of private information retrieval (PIR) over a distributed storage system where $M$ records are stored across $N$ servers by using an $[N,K]$ MDS code. For simplicity, this problem is usually referred as the coded PIR problem. In 2016, Banawan and Ulukus designed the first capacity-achieving coded PIR scheme with sub-packetization $KN^{M}$ and access number $MKN^{M}$, where capacity characterizes the minimal download size for retrieving per unit of data, and sub-packetization and access number are two metrics closely related to implementation complexity. In this paper, we f…
The work by Maddah-Ali and Niesen demonstrated the benefits in reducing the transmission rate in a noiseless broadcast network by joint design of caching and delivery schemes. In their setup, each user learns the demands of all other users in the delivery phase. In this paper, we introduce the problem of demand private coded caching where we impose a privacy requirement that no user learns any information about the demands of other users. We provide an achievable scheme and compare its performance using the existing lower bounds on the achievable rates under no privacy setting. For this settin…
In Private Information Retrieval (PIR), one wants to download a file from a database without revealing to the database which file is being downloaded. Much attention has been paid to the case of the database being encoded across several servers, subsets of which can collude to attempt to deduce the requested file. With the goal of studying the achievable PIR rates in realistic scenarios, we generalize results for coded data from the case of all subsets of servers of size $t$ colluding, to arbitrary subsets of the servers. We investigate the effectiveness of previous strategies in this new scen…
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…
Recent work by Maddah-Ali and Niesen introduced coded caching which demonstrated the benefits of joint design of storage and transmission policies in content delivery networks. They studied a setup where a server communicates with a set of users, each equipped with a local cache, over a shared error-free link and proposed an order-optimal caching and delivery scheme. In this paper, we introduce the problem of secretive coded caching where we impose the additional constraint that a user should not be able to learn anything, from either the content stored in its cache or the server transmissions…
The problem of symmetric private information retrieval (SPIR) from a coded database which is distributively stored among colluding servers is studied. Specifically, the database comprises $K$ files, which are stored among $N$ servers using an $(N,M)$-MDS storage code. A user wants to retrieve one file from the database by communicating with the $N$ servers, without revealing the identity of the desired file to any server. Furthermore, the user shall learn nothing about the other $K-1$ files in the database. In the $T$-colluding SPIR problem (hence called TSPIR), any $T$ out of $N$ servers may …
In this paper, we consider multiple cache-enabled clients connected to multiple servers through an intermediate network. We design several topology-aware coding strategies for such networks. Based on topology richness of the intermediate network, and types of coding operations at internal nodes, we define three classes of networks, namely, dedicated, flexible, and linear networks. For each class, we propose an achievable coding scheme, analyze its coding delay, and also, compare it with an information theoretic lower bound. For flexible networks, we show that our scheme is order-optimal in ter…
This paper considers the problem of single-server single-message private information retrieval with coded side information (PIR-CSI). In this problem, there is a server storing a database, and a user which knows a linear combination of a subset of messages in the database as a side information. The number of messages contributing to the side information is known to the server, but the indices and the coefficients of these messages are unknown to the server. The user wishes to download a message from the server privately, i.e., without revealing which message it is requesting, while minimizing …
Cache-aided content delivery is studied in a multi-server system with $P$ servers and $K$ users, each equipped with a local cache memory. In the delivery phase, each user connects randomly to any $ρ$ out of $P$ servers. Thanks to the availability of multiple servers, which model small base stations with limited storage capacity, user demands can be satisfied with reduced storage capacity at each server and reduced delivery rate per server; however, this also leads to reduced multicasting opportunities compared to a single server serving all the users simultaneously. A joint storage and proacti…
Private information retrieval (PIR) is the problem of privately retrieving one out of $M$ original files from $N$ severs, i.e., each individual server learns nothing about the file that the user is requesting. Usually, the $M$ files are replicated or encoded by a maximum distance separable (MDS) code and then stored across the $N$ servers. Compared to mere replication, MDS coded servers can significantly reduce the storage overhead. Particularly, PIR from minimum storage regenerating (MSR) coded servers can simultaneously reduce the repair bandwidth when repairing failed servers. Existing PIR …
MapReduce is a commonly used framework for executing data-intensive jobs on distributed server clusters. We introduce a variant implementation of MapReduce, namely "Coded MapReduce", to substantially reduce the inter-server communication load for the shuffling phase of MapReduce, and thus accelerating its execution. The proposed Coded MapReduce exploits the repetitive mapping of data blocks at different servers to create coding opportunities in the shuffling phase to exchange (key,value) pairs among servers much more efficiently. We demonstrate that Coded MapReduce can cut down the total inter…
MapReduce is a widely used framework for distributed computing. Data shuffling between the Map phase and Reduce phase of a job involves a large amount of data transfer across servers, which in turn accounts for increase in job completion time. Recently, Coded MapReduce has been proposed to offer savings with respect to the communication cost incurred in data shuffling. This is achieved by creating coded multicast opportunities for shuffling through repeating Map tasks at multiple servers. We consider a server-rack architecture for MapReduce and in this architecture, propose to divide the total…
In this work, two practical concepts related to private information retrieval (PIR) are introduced and coined full support-rank PIR and strongly linear PIR. Being of full support-rank is a technical, yet natural condition required to prove a converse result for a capacity expression and satisfied by almost all currently known capacity-achieving schemes, while strong linearity is a practical requirement enabling implementation over small finite fields with low subpacketization degree. Then, the capacity of MDS-coded, linear, full support-rank PIR in the presence of colluding servers is derived,…
We consider private information retrieval (PIR) for distributed storage systems (DSSs) with noncolluding nodes where data is stored using a non maximum distance separable (MDS) linear code. It was recently shown that if data is stored using a particular class of non-MDS linear codes, the MDS-PIR capacity, i.e., the maximum possible PIR rate for MDS-coded DSSs, can be achieved. For this class of codes, we prove that the PIR capacity is indeed equal to the MDS-PIR capacity, giving the first family of non-MDS codes for which the PIR capacity is known. For other codes, we provide asymmetric PIR pr…
The problem of $X$-secure $T$-private information retrieval from MDS coded storage is studied in this paper, where the user wishes to privately retrieve one out of $K$ independent messages that are distributed over $N$ servers according to an MDS code. It is guaranteed that any group of up to $X$ colluding servers learn nothing about the messages and that any group of up to $T$ colluding servers learn nothing about the identity of desired message. A lower bound of achievable rates is proved by presenting a novel scheme based on \emph{cross-subspace alignment} and a successive decoding with int…
In this paper, we study the problem of \emph{private and secure distributed matrix multiplication (PSDMM)}, where a user having a private matrix $A$ and $N$ non-colluding servers sharing a library of $L$ ($L>1$) matrices $B^{(0)}, B^{(1)},\ldots,B^{(L-1)}$, for which the user wishes to compute $AB^{(θ)}$ for some $θ\in [0, L)$ without revealing any information of the matrix $A$ to the servers, and keeping the index $θ$ private to the servers. Previous work is limited to the case that the shared library (\textit{i.e.,} the matrices $B^{(0)}, B^{(1)},\ldots,B^{(L-1)}$) is stored across the serve…
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 shared-link caching model, Maddah-Ali and Niesen (MAN) proposed a two-phase (placement and delivery) coded caching strategy, which is order optimal within a constant factor. However, in the MAN coded caching scheme, each user can obtain the information about the demands of other users, i.e., the MAN coded caching scheme is inherently prone to tampering and spying the activity/demands of other users. In this paper…
Edge computing is emerging as a new paradigm to allow processing data near the edge of the network, where the data is typically generated and collected. This enables critical computations at the edge in applications such as Internet of Things (IoT), in which an increasing number of devices (sensors, cameras, health monitoring devices, etc.) collect data that needs to be processed through computationally intensive algorithms with stringent reliability, security and latency constraints. Our key tool is the theory of coded computation, which advocates mixing data in computationally intensive task…
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 …
Coded caching is a technique that leverages locally cached contents at the users to reduce the network's peak-time communication load. Coded caching achieves significant performance gains compared to uncoded caching schemes and is thus a promising technique to boost performance in future networks. In the original model introduced by Maddah-Ali and Niesen (MAN), a server stores multiple files and is connected to multiple cache-aided users through an error-free shared link; once the local caches have been filled and all users have sent their demand to the server, the server can start sending cod…
Private Information Retrieval (PIR) was first proposed by B. Chor, O. Goldreich, E. Kushilevitz and M. Sudan in their 1995 FOCS paper. For MDS coded distributed storage system private information retrieval was proposed and the capacity of PIR schemes for MDS coded distributed storage was studied. Star product PIR schemes from general coded distributed storage system with colluding servers were constructed over general finite fields. These star product schemes has no restriction on the sizes of fields and can be constructed for coded distributed storage across large number of servers. In this p…
In this paper we determine the delivery time for a multi-server coded caching problem when the cache size of each user is small. We propose an achievable scheme based on coded cache content placement, and employ zero-forcing techniques at the content delivery phase. Surprisingly, in contrast to previous multi-server results which were proved to be order-optimal within a multiplicative factor of 2, for the low memory regime we prove that our achievable scheme is optimal. Moreover, we compare the performance of our scheme with the uncoded solution, and show our proposal improvement over the unco…
This paper considers the MapReduce-like coded distributed computing framework originally proposed by Li et al., which uses coding techniques when distributed computing servers exchange their computed intermediate values, in order to reduce the overall traffic load. Their original model servers are connected via an error-free common communication bus allowing broadcast transmissions. However, this assumption is one of the major limitations in practice since the practical cloud computing network topologies are far more involved than a simple single bus. We formulate a topological coded distribut…
Coded caching is a recently proposed technique for dealing with large scale content distribution over the Internet. As in conventional caching, it leverages the presence of local caches at the end users. However, it considers coding in the caches and/or coded transmission from the central server and demonstrates that huge savings in transmission rate are possible when the server and the end users are connected via a single shared link. In this work, we consider a more general topology where there is a layer of relay nodes between the server and the users, e.g., combination networks studied in …
We consider constructing capacity-achieving linear codes with minimum message size for private information retrieval (PIR) from $N$ non-colluding databases, where each message is coded using maximum distance separable (MDS) codes, such that it can be recovered from accessing the contents of any $T$ databases. It is shown that the minimum message size (sometimes also referred to as the sub-packetization factor) is significantly, in fact exponentially, lower than previously believed. More precisely, when $K>T/\textbf{gcd}(N,T)$ where $K$ is the total number of messages in the system and $\textbf…
Content delivery networks store information distributed across multiple servers, so as to balance the load and avoid unrecoverable losses in case of node or disk failures. Coded caching has been shown to be a useful technique which can reduce peak traffic rates by pre-fetching popular content at the end users and encoding transmissions so that different users can extract different information from the same packet. On one hand, distributed storage limits the capability of combining content from different servers into a single message, causing performance losses in coded caching schemes. But, on…
The problem of Multi-user Blind $X$-secure $T$-colluding Symmetric Private Information Retrieval from Maximum Distance Separable (MDS) coded storage system with $B$ Byzantine and $U$ unresponsive servers (U-B-MDS-MB-XTSPIR) is studied in this paper. Specifically, a database consisting of multiple files, each labeled by $M$ indices, is stored at the distributed system with $N$ servers according to $(N,K+X)$ MDS codes over $\mathbb{F}_q$ such that any group of up to $X$ colluding servers learn nothing about the data files. There are $M$ users, in which each user $m,m=1,\ldots,M$ privately select…
We study the role of coded side information in single-server Private Information Retrieval (PIR). An instance of the single-server PIR problem includes a server that stores a database of $K$ independently and uniformly distributed messages, and a user who wants to retrieve one of these messages from the server. We consider settings in which the user initially has access to a coded side information which includes a linear combination of a subset of $M$ messages in the database. We assume that the identities of the $M$ messages that form the support set of the coded side information as well as t…
Private Computation (PC), recently introduced by Sun and Jafar, is a generalization of Private Information Retrieval (PIR) in which a user wishes to privately compute an arbitrary function of data stored across several servers. We construct a PC scheme which accounts for server collusion, coded data, and non-linear functions. For data replicated over several possibly colluding servers, our scheme computes arbitrary functions of the data with rate equal to the asymptotic capacity of PIR for this setup. For systematically encoded data stored over colluding servers, we privately compute arbitrary…
We study private information retrieval (PIR) on coded data with possibly colluding servers. Devising PIR schemes with optimal download rate in the case of collusion and coded data is still open in general. We provide a lifting operation that can transform what we call one-shot PIR schemes for two messages into schemes for any number of messages. We apply this lifting operation on existing PIR schemes and describe two immediate implications. First, we obtain novel PIR schemes with improved download rate in the case of MDS coded data and server collusion. Second, we provide a simplified descript…
