arXiv subjects

Anoosheh Heidarzadeh

Publications and source records attributed to Anoosheh Heidarzadeh.

At least 19 recordsLinked to original sources

arXiv2026

Secure and Private Structured-Subset Retrieval: Fundamental Limits and Achievable Schemes

This work introduces the \emph{Secure and Private Structured-Subset Retrieval (SPSSR)} problem. In SPSSR, a user wishes to retrieve one subset from an arbitrary family of size-$D$ subsets from $K$ messages replicated across $N$ non-colluding servers that share randomness unknown to the user. The privacy requirement ensures that no server learns which subset is requested, while the security requirement ensures that the user learns nothing about the messages outside the requested subset. This generalizes Symmetric Multi-message Private Information Retrieval (SMPIR), where the candidate demand sets consist of all size-$D$ subsets. We show that, for every candidate demand family, the maximum achievable retrieval rate is equal to ${1-1/N}$. We also show that the minimum ratio between the size of the shared randomness and the message size required to achieve this rate is ${D/(N-1)}$, and that, for balanced linear SPSSR schemes, the minimum required subpacketization level is ${(N-1)/\gcd(D,N-1)}$; both quantities are independent of the demand family. Our converse proof for the maximum achievable retrieval rate applies to arbitrary demand families, unlike the existing proof for SMPIR, which is tailored to the full demand family. For achievability, we construct a single SPSSR scheme that applies uniformly to every demand family, achieves the optimal retrieval rate with the optimal shared-randomness ratio, and requires the optimal subpacketization level among balanced linear schemes. This subpacketization level is no larger than that of known SMPIR schemes in any parameter regime and is smaller in some regimes.

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arXiv2026

Private Structured-Subset Retrieval

We introduce the \emph{Private Structured-Subset Retrieval (PSSR)} problem, where a user retrieves $D$ messages from a database of $K$ messages replicated across $N$ non-colluding servers, and the demand is restricted to a known structured family of $D$-subsets. This formulation generalizes Multi-message Private Information Retrieval (MPIR) and captures settings where the demand space is constrained by application-specific structure. Focusing on balanced ${\{0,1\}}$-linear schemes, a class that includes several best-known MPIR schemes, we derive converse bounds on the maximum retrieval rate and minimum subpacketization level required to achieve any given rate. We also develop an optimization-based framework to construct schemes for general structured demand families, providing flexibility in optimizing the retrieval rate or the subpacketization level. When specialized to the full demand family, this framework recovers known balanced $\{0,1\}$-linear MPIR constructions; for more restricted demand families, it can exploit the demand structure to increase the retrieval rate, reduce the subpacketization level, or both. We demonstrate this through a structured-demand example in which the proposed PSSR scheme simultaneously achieves a higher rate and requires a smaller subpacketization than the best-known MPIR scheme for the same parameters $N$, $K$, and $D$. Our parallel work on contiguous-demand families further illustrates the scope of this framework by yielding rate-optimal schemes with substantially smaller subpacketization and no field-size restrictions, improving upon MPIR-based schemes.

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arXiv2026

Private Contiguous-Block Retrieval

We introduce the \emph{Private Contiguous-Block Retrieval (PCBR)} problem, where a user retrieves a block of $D$ messages with contiguous indices from $K$ replicated messages stored across $N$ non-colluding servers, while hiding the identity of the requested block from each server. This problem is motivated by storage and streaming systems where files are split into ordered segments. Unlike multi-message Private Information Retrieval (MPIR), where any $D$-subset may be requested, PCBR restricts the demand family to contiguous blocks. This relaxation raises a natural question: Can this structure be exploited to improve retrieval efficiency? We answer this question for balanced $\{0,1\}$-linear schemes. We establish an upper bound on the achievable retrieval rate for all problem parameters, derive a lower bound on the subpacketization level required by any scheme achieving the rate upper bound, and construct a rate-optimal scheme whose subpacketization level matches the lower bound for a broad range of problem parameters. Although the optimal PCBR rate coincides with the best-known MPIR rate converse bound, existing MPIR schemes can be suboptimal for PCBR and can require a much larger subpacketization level. In contrast, our scheme exploits the contiguous-block structure to achieve the optimal rate with reduced subpacketization.

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arXiv2026

On the Subpacketization Level of the Banawan-Ulukus Multi-Message PIR Scheme

This note analyzes a linear recursion that arises in the computation of the subpacketization level for the multi-message PIR scheme of Banawan and Ulukus. We derive an explicit representation for the normalized subpacketization level $L$, whose smallest integer multiple yields the subpacketization level of the scheme, in terms of the number of servers $N$, the total number of messages $K$, and the number of demand messages $D$. The resulting formula shows that $L$ is a polynomial in $N$ with nonnegative coefficients, and its leading term is $N^{K-D+1}/D$.

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arXiv2025

A Low-Complexity Scheme for Multi-Message Private Information Retrieval

Private Information Retrieval (PIR) is a fundamental problem in the broader fields of security and privacy. In recent years, the problem has garnered significant attention from the research community, leading to achievability schemes and converse results for many important PIR settings. This paper focuses on the Multi-message Private Information Retrieval (MPIR) setting, where a user aims to retrieve $D$ messages from a database of $K$ messages, with identical copies of the database available on $N$ remote servers. The user's goal is to maximize the download rate while keeping the identities of the retrieved messages private. Existing approaches to the MPIR problem primarily focus on either scalar-linear solutions or vector-linear solutions, the latter requiring a high degree of subpacketization. Furthermore, prior scalar-linear solutions are restricted to the special case of $N = D+1$. This limitation hinders the practical adoption of these schemes, as real-world applications demand simple, easily implementable solutions that support a broad range of scenarios. In this work, we present a solution for the MPIR problem, which applies to a broader range of system parameters and requires a limited degree of subpacketization. In particular, the proposed scheme applies to all values of $N=DL+1$ for any integer $L\geq 1$, and requires a degree of subpacketization $L$. Our scheme achieves capacity when $D$ divides $K$, and in all other cases, its performance matches or comes within a small additive margin of the best-known scheme that requires a high degree of subpacketization.

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arXiv2025

A Linear Programming Approach to Private Information Retrieval

This work presents an algorithmic framework that uses linear programming to construct \emph{addition-based Private Information Retrieval (AB-PIR)} schemes, where retrieval is performed by downloading only linear combinations of message symbols with coefficients set to 0 or 1. The AB-PIR schemes generalize several existing capacity-achieving PIR schemes and are of practical interest because they use only addition operations -- avoiding multiplication and other complex operations -- and are compatible with any finite field, including binary. Our framework broadens the search space to include all feasible solutions and can be used to construct optimal AB-PIR schemes for the entire range of problem parameters, including the number of servers, the total number of messages, and the number of messages that need to be retrieved. The framework enables us to identify schemes that outperform the previously proposed PIR schemes in certain cases and, in other cases, achieve performance on par with the best-known AB-PIR solutions. Additionally, the schemes generated by our framework can be integrated into existing solutions for several related PIR scenarios, improving their overall performance.

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arXiv2024

Achieving Capacity of PIR with Private Side Information with Low Sub-packetization and without MDS Codes

This paper revisits the problem of multi-server Private Information Retrieval with Private Side Information (PIR-PSI). In this problem, $N$ non-colluding servers store identical copies of $K$ messages, each comprising $L$ symbols from $\mathbb{F}_q$, and a user, who knows $M$ of these messages, wants to retrieve one of the remaining $K-M$ messages. The user's goal is to retrieve the desired message by downloading the minimum amount of information from the servers while revealing no information about the identities of the desired message and side information messages to any server. The capacity of PIR-PSI, defined as the maximum achievable download rate, was previously characterized for all $N$, $K$, and $M$ when $L$ and $q$ are sufficiently large -- specifically, growing exponentially with $K$, to ensure the divisibility of each message into $N^K$ sub-packets and to guarantee the existence of an MDS code with its length and dimension being exponential in $K$. In this work, we propose a new capacity-achieving PIR-PSI scheme that is applicable to all $N$, $K$, $M$, $L$, and $q$ where $N\geq M+1$ and $N-1\mid L$. The proposed scheme operates with a sub-packetization level of $N-1$, independent of $K$, and works over any finite field without requiring an MDS code.

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arXiv2024

A New Approach to Harnessing Side Information in Multi-Server Private Information Retrieval

This paper presents new solutions for Private Information Retrieval (PIR) with side information. This problem is motivated by PIR settings in which a client has side information about the data held by the servers and would like to leverage this information in order to improve the download rate. The problem of PIR with side information has been the subject of several recent studies that presented achievability schemes as well as converses for both multi-server and single-server settings. However, the solutions for the multi-server settings adapted from the solutions for the single-server setting in a rather straightforward manner, relying on the concept of super-messages. Such solutions require an exponential degree of sub-packetization (in terms of the number of messages). This paper makes the following contributions. First, we revisit the PIR problem with side information and present a new approach to leverage side information in the context of PIR. The key idea of our approach is a randomized algorithm to determine the linear combinations of the sub-packets that need to be recovered from each server. In addition, our approach takes advantage of the fact that the identity of the side information messages does not need to be kept private, and, as a result, the information retrieval scheme does not need to be symmetric. Second, we present schemes for PIR with side information that achieve a higher rate than previously proposed solutions and require a significantly lower degree of sub-packetization (linear in the number of servers). Our scheme not only achieves the highest known download rate for the problem at hand but also invalidates a previously claimed converse bound on the maximum achievable download rate.

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arXiv2022

Multi-Message Private Information Retrieval: A Scalar Linear Solution

In recent years, the Multi-message Private Information Retrieval (MPIR) problem has received significant attention from the research community. In this problem, a user wants to privately retrieve $D$ messages out of $K$ messages whose identical copies are stored on $N$ remote servers, while maximizing the download rate. The MPIR schemes can find applications in many practical scenarios and can serve as an important building block for private computation and private machine learning applications. The existing solutions for MPIR require a large degree of subpacketization, which can result in large overheads, high complexity, and impose constraints on the system parameters. These factors can limit practical applications of the existing solutions. In this paper, we present a methodology for the design of scalar-linear MPIR schemes. Such schemes are easy to implement in practical systems as they do not require partitioning of messages into smaller size sub-messages and do not impose any constraints on the minimum required size of the messages. Focusing on the case of $N=D+1$, we show that when $D$ divides $K$, our scheme achieves the capacity, where the capacity is defined as the maximum achievable download rate. When the divisibility condition does not hold, the performance of our scheme is the same or within a small additive margin compared to the best known scheme that requires a high degree of subpacketization.

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arXiv2022

Single-Server Private Information Retrieval with Side Information Under Arbitrary Popularity Profiles

This paper introduces a generalization of the Private Information Retrieval with Side Information (PIR-SI) problem called Popularity-Aware PIR-SI (PA-PIR-SI). The PA-PIR-SI problem includes one or more remote servers storing copies of a dataset of $K$ messages, and a user who knows $M$ out of $K$ messages -- the identities of which are unknown to the server -- as a prior side information, and wishes to retrieve one of the remaining $K-M$ messages. The goal of the user is to minimize the amount of information they must download from the server while revealing no information about the identity of the desired message. In contrast to PIR-SI, in PA-PIR-SI, the dataset messages are not assumed to be equally popular. That is, given the $M$ side information messages, each of the remaining $K-M$ messages is not necessarily equally likely to be the message desired by the user. In this work, we focus on the single-server setting of PA-PIR-SI, and establish lower and upper bounds on the capacity of this setting -- defined as the maximum possible achievable download rate. Our upper bound holds for any message popularity profile, and is the same as the capacity of single-server PIR-SI. We prove the lower bound by presenting a PA-PIR-SI scheme which takes a novel probabilistic approach -- carefully designed based on the popularity profile -- to integrate two existing PIR-SI schemes. The rate of our scheme is strictly higher than that of the only existing PIR-SI scheme applicable to the PA-PIR-SI setting.

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arXiv2022

Sparse Random Khatri-Rao Product Codes for Distributed Matrix Multiplication

We introduce two generalizations to the paradigm of using Random Khatri-Rao Product (RKRP) codes for distributed matrix multiplication. We first introduce a class of codes called Sparse Random Khatri-Rao Product (SRKRP) codes which have sparse generator matrices. SRKRP codes result in lower encoding, computation and communication costs than RKRP codes when the input matrices are sparse, while they exhibit similar numerical stability to other state of the art schemes. We empirically study the relationship between the probability of the generator matrix (restricted to the set of non-stragglers) of a randomly chosen SRKRP code being rank deficient and various parameters of the coding scheme including the degree of sparsity of the generator matrix and the number of non-stragglers. Secondly, we show that if the master node can perform a very small number of matrix product computations in addition to the computations performed by the workers, the failure probability can be substantially improved.

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arXiv2022

The Linear Capacity of Single-Server Individually-Private Information Retrieval with Side Information

This paper considers the problem of single-server Individually-Private Information Retrieval with side information (IPIR). In this problem, there is a remote server that stores a dataset of $K$ messages, and there is a user that initially knows $M$ of these messages, and wants to retrieve $D$ other messages belonging to the dataset. The goal of the user is to retrieve the $D$ desired messages by downloading the minimum amount of information from the server while revealing no information about whether an individual message is one of the $D$ desired messages. In this work, we focus on linear IPIR schemes, i.e., the IPIR schemes in which the user downloads only linear combinations of the original messages from the server. We prove a converse bound on the download rate of any linear IPIR scheme for all $K,D,M$, and show the achievability of this bound for all $K,D,M$ satisfying a certain divisibility condition. Our results characterize the linear capacity of IPIR, which is defined as the maximum achievable download rate over all linear IPIR schemes, for a wide range of values of $K,D,M$.

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arXiv2022

Noisy Group Testing with Side Information

Group testing has recently attracted significant attention from the research community due to its applications in diagnostic virology. An instance of the group testing problem includes a ground set of individuals which includes a small subset of infected individuals. The group testing procedure consists of a number of tests, such that each test indicates whether or not a given subset of individuals includes one or more infected individuals. The goal of the group testing procedure is to identify the subset of infected individuals with the minimum number of tests. Motivated by practical scenarios, such as testing for viral diseases, this paper focuses on the following group testing settings: (i) the group testing procedure is noisy, i.e., the outcome of the group testing procedure can be flipped with a certain probability; (ii) there is a certain amount of side information on the distribution of the infected individuals available to the group testing algorithm. The paper makes the following contributions. First, we propose a probabilistic model, referred to as an interaction model, that captures the side information about the probability distribution of the infected individuals. Next, we present a decoding scheme, based on the belief propagation, that leverages the interaction model to improve the decoding accuracy. Our results indicate that the proposed algorithm achieves higher success probability and lower false-negative and false-positive rates when compared to the traditional belief propagation especially in the high noise regime.

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arXiv2022

The Role of Reusable and Single-Use Side Information in Private Information Retrieval

This paper introduces the problem of Private Information Retrieval with Reusable and Single-use Side Information (PIR-RSSI). In this problem, one or more remote servers store identical copies of a set of $K$ messages, and there is a user that initially knows $M$ of these messages, and wants to privately retrieve one other message from the set of $K$ messages. The objective is to design a retrieval scheme in which the user downloads the minimum amount of information from the server(s) while the identity of the message wanted by the user and the identities of an $M_1$-subset of the $M$ messages known by the user (referred to as reusable side information) are protected, but the identities of the remaining $M_2=M-M_1$ messages known by the user (referred to as single-use side information) do not need to be protected. The PIR-RSSI problem reduces to the classical Private Information Retrieval (PIR) problem when ${M_1=M_2=0}$, and reduces to the problem of PIR with Private Side Information or PIR with Side Information when ${M_1\geq 1,M_2=0}$ or ${M_1=0,M_2\geq 1}$, respectively. In this work, we focus on the single-server setting of the PIR-RSSI problem. We characterize the capacity of this setting for the cases of ${M_1=1,M_2\geq 1}$ and ${M_1\geq 1,M_2=1}$, where the capacity is defined as the maximum achievable download rate over all PIR-RSSI schemes. Our results show that for sufficiently small values of $K$, the single-use side information messages can help in reducing the download cost only if they are kept private; and for larger values of $K$, the reusable side information messages cannot help in reducing the download cost.

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arXiv2021

Scheduling Improves the Performance of Belief Propagation for Noisy Group Testing

This paper considers the noisy group testing problem where among a large population of items some are defective. The goal is to identify all defective items by testing groups of items, with the minimum possible number of tests. The focus of this work is on the practical settings with a limited number of items rather than the asymptotic regime. In the current literature, belief propagation has been shown to be effective in recovering defective items from the test results. In this work, we adopt two variants of the belief propagation algorithm for the noisy group testing problem. These algorithms have been used successfully in the decoding of low-density parity-check codes. We perform an experimental study and using extensive simulations we show that these algorithms achieve higher success probability, lower false-negative, and false-positive rates compared to the traditional belief propagation algorithm. For instance, our results show that the proposed algorithms can reduce the false-negative rate by about $50\%$ (or more) when compared to the traditional BP algorithm, under the combinatorial model. Moreover, under the probabilistic model, this reduction in the false-negative rate increases to about $80\%$ for the tested cases.

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arXiv2021

Multi-Server Private Linear Computation with Joint and Individual Privacy Guarantees

This paper considers the problem of multi-server Private Linear Computation, under the joint and individual privacy guarantees. In this problem, identical copies of a dataset comprised of $K$ messages are stored on $N$ non-colluding servers, and a user wishes to obtain one linear combination of a $D$-subset of messages belonging to the dataset. The goal is to design a scheme for performing the computation such that the total amount of information downloaded from the servers is minimized, while the privacy of the $D$ messages required for the computation is protected. When joint privacy is required, the identities of all of these $D$ messages must be kept private jointly, and when individual privacy is required, the identity of every one of these $D$ messages must be kept private individually. In this work, we characterize the capacity, which is defined as the maximum achievable download rate, under both joint and individual privacy requirements. In particular, we show that when joint privacy is required the capacity is given by ${(1+1/N+\dots+1/N^{K-D})^{-1}}$, and when individual privacy is required the capacity is given by ${(1+1/N+\dots+1/N^{\lceil K/D\rceil-1})^{-1}}$ assuming that $D$ divides $K$, or $K\pmod D$ divides $D$. Our converse proofs are based on reduction from two variants of the multi-server Private Information Retrieval problem in the presence of side information. Our achievability schemes build up on our recently proposed schemes for single-server Private Linear Transformation and the multi-server private computation scheme proposed by Sun and Jafar. Using similar proof techniques, we also establish upper and lower bounds on the capacity for the cases in which the user wants to compute $L$ (potentially more than one) linear combinations.

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arXiv2021

Single-Server Private Linear Transformation: The Joint Privacy Case

This paper introduces the problem of Private Linear Transformation (PLT) which generalizes the problems of private information retrieval and private linear computation. The PLT problem includes one or more remote server(s) storing (identical copies of) $K$ messages and a user who wants to compute $L$ independent linear combinations of a $D$-subset of messages. The objective of the user is to perform the computation by downloading minimum possible amount of information from the server(s), while protecting the identities of the $D$ messages required for the computation. In this work, we focus on the single-server setting of the PLT problem when the identities of the $D$ messages required for the computation must be protected jointly. We consider two different models, depending on whether the coefficient matrix of the required $L$ linear combinations generates a Maximum Distance Separable (MDS) code. We prove that the capacity for both models is given by $L/(K-D+L)$, where the capacity is defined as the supremum of all achievable download rates. Our converse proofs are based on linear-algebraic and information-theoretic arguments that establish connections between PLT schemes and linear codes. We also present an achievability scheme for each of the models being considered.

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arXiv2021

Single-Server Private Linear Transformation: The Individual Privacy Case

This paper considers the single-server Private Linear Transformation (PLT) problem with individual privacy guarantees. In this problem, there is a user that wishes to obtain $L$ independent linear combinations of a $D$-subset of messages belonging to a dataset of $K$ messages stored on a single server. The goal is to minimize the download cost while keeping the identity of each message required for the computation individually private. The individual privacy requirement ensures that the identity of each individual message required for the computation is kept private. This is in contrast to the stricter notion of joint privacy that protects the entire set of identities of all messages used for the computation, including the correlations between these identities. The notion of individual privacy captures a broad set of practical applications. For example, such notion is relevant when the dataset contains information about individuals, each of them requires privacy guarantees for their data access patterns. We focus on the setting in which the required linear transformation is associated with a maximum distance separable (MDS) matrix. In particular, we require that the matrix of coefficients pertaining to the required linear combinations is the generator matrix of an MDS code. We establish lower and upper bounds on the capacity of PLT with individual privacy, where the capacity is defined as the supremum of all achievable download rates. We show that our bounds are tight under certain conditions.

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