arXiv subjects

Alex Sprintson

Publications and source records attributed to Alex Sprintson.

At least 19 recordsLinked to original sources

arXiv2026

Design of MDP Convolutional Codes and Maximally Recoverable Codes Through the Lens of Matrix Completion

The matrix completion problem provides a unifying lens through which many fundamental problems in coding theory can be viewed. In this paper, we investigate Locally Recoverable Codes (LRCs) with Maximal Recoverability (MR) and Maximum Distance Profile (MDP) convolutional codes in the framework of matrix completion. In particular, we present techniques that are general enough to provide constructions for both types of codes. A common feature of our code constructions is the sparsity of their generator matrices and the property that a large number of the entries of the generator matrices are elements of a small subfield of a larger extension field.

cs.IT↗

arXiv2025

A Matrix Completion Approach for the Construction of MDP Convolutional Codes

Maximum Distance Profile (MDP) convolutional codes are an important class of channel codes due to their maximal delay-constrained error correction capabilities. The design of MDP codes has attracted significant attention from the research community. However, only limited attention was given to addressing the complexity of encoding and decoding operations. This paper aims to reduce encoding complexity by constructing partial unit-memory MDP codes with structured and sparse generator matrices. In particular, we present a matrix completion framework that extends a structured superregular matrix (e.g., Cauchy) over a small field to a sparse sliding generator matrix of an MDP code. We show that the proposed construction can reduce the encoding complexity compared to the current state-of-the-art MDP code designs.

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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

On Subset Retrieval and Group Testing Problems with Differential Privacy Constraints

This paper focuses on the design and analysis of privacy-preserving techniques for group testing and infection status retrieval. Our work is motivated by the need to provide accurate information on the status of disease spread among a group of individuals while protecting the privacy of the infection status of any single individual involved. The paper is motivated by practical scenarios, such as controlling the spread of infectious diseases, where individuals might be reluctant to participate in testing if their outcomes are not kept confidential. The paper makes the following contributions. First, we present a differential privacy framework for the subset retrieval problem, which focuses on sharing the infection status of individuals with administrators and decision-makers. We characterize the trade-off between the accuracy of subset retrieval and the degree of privacy guaranteed to the individuals. In particular, we establish tight lower and upper bounds on the achievable level of accuracy subject to the differential privacy constraints. We then formulate the differential privacy framework for the noisy group testing problem in which noise is added either before or after the pooling process. We establish a reduction between the private subset retrieval and noisy group testing problems and show that the converse and achievability schemes for subset retrieval carry over to differentially private group testing.

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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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arXiv2025

Optimizing Leaky Private Information Retrieval Codes to Achieve ${O}(\log K)$ Leakage Ratio Exponent

We study the problem of leaky private information retrieval (L-PIR), where the amount of privacy leakage is measured by the pure differential privacy parameter, referred to as the leakage ratio exponent. Unlike the previous L-PIR scheme proposed by Samy et al., which only adjusted the probability allocation to the clean (low-cost) retrieval pattern, we optimize the probabilities assigned to all the retrieval patterns jointly. It is demonstrated that the optimal retrieval pattern probability distribution is quite sophisticated and has a layered structure: the retrieval patterns associated with the random key values of lower Hamming weights should be assigned higher probabilities. This new scheme provides a significant improvement, leading to an ${O}(\log K)$ leakage ratio exponent with fixed download cost $D$ and number of servers $N$, in contrast to the previous art that only achieves a $\Theta(K)$ exponent, where $K$ is the number of messages.

cs.IR↗

arXiv2024

Secure Distributed Matrix Multiplication with Precomputation

We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show how to construct polynomial schemes for the outer product partitioning which take advantage of the user's ability to precompute, and provide bounds for our technique. We show that precomputation allows for a reduction in the order of the time complexity for the cases where the number of colluding servers is a fixed percentage of the number of servers. Furthermore, with precomputation, any percentage (less than 100%) of collusions can be tolerated, compared to the upper limit of 50% for the case without precomputation.

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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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arXiv2023

Flow Correlator: A Flow Table Cache Management Strategy

Switching, routing, and security functions are the backbone of packet processing networks. Fast and efficient processing of packets requires maintaining the state of a large number of transient network connections. In particular, modern stateful firewalls, security monitoring devices, and software-defined networking (SDN) programmable dataplanes require maintaining stateful flow tables. These flow tables often grow much larger than can be expected to fit within on-chip memory, requiring a managed caching layer to maintain performance. This paper focuses on improving the efficiency of caching, an important architectural component of the packet processing data planes. We present a novel predictive approach to network flow table cache management. Our approach leverages a Hashed Perceptron binary classifier as well as an iterative approach to feature selection and ranking to improve the reliability and performance of the data plane caches. We validate the efficiency of the proposed techniques through extensive experimentation using real-world data sets. Our numerical results demonstrate that our techniques improve the reliability and performance of flow-centric packet processing architectures.

cs.NI↗

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

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

Group Testing on General Set-Systems

Group testing is one of the fundamental problems in coding theory and combinatorics in which one is to identify a subset of contaminated items from a given ground set. There has been renewed interest in group testing recently due to its applications in diagnostic virology, including pool testing for the novel coronavirus. The majority of existing works on group testing focus on the \emph{uniform} setting in which any subset of size $d$ from a ground set $V$ of size $n$ is potentially contaminated. In this work, we consider a {\em generalized} version of group testing with an arbitrary set-system of potentially contaminated sets. The generalized problem is characterized by a hypergraph $H=(V,E)$, where $V$ represents the ground set and edges $e\in E$ represent potentially contaminated sets. The problem of generalized group testing is motivated by practical settings in which not all subsets of a given size $d$ may be potentially contaminated, rather, due to social dynamics, geographical limitations, or other considerations, there exist subsets that can be readily ruled out. For example, in the context of pool testing, the edge set $E$ may consist of families, work teams, or students in a classroom, i.e., subsets likely to be mutually contaminated. The goal in studying the generalized setting is to leverage the additional knowledge characterized by $H=(V,E)$ to significantly reduce the number of required tests. The paper considers both adaptive and non-adaptive group testing and makes the following contributions. First, for the non-adaptive setting, we show that finding an optimal solution for the generalized version of group testing is NP-hard. For this setting, we present a solution that requires $O(d\log{|E|})$ tests, where $d$ is the maximum size of a set $e \in E$. Our solutions generalize those given for the traditional setting and are shown to be of order-optimal size $O(\log{|E|})$ for hypergraphs with edges that have ``large'' symmetric differences. For the adaptive setting, when edges in $E$ are of size exactly $d$, we present a solution of size $O(\log{|E|}+d\log^2{d})$ that comes close to the lower bound of $Ω(\log{|E|} + d)$.

cs.IT↗

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.

cs.IT↗

arXiv2021

Multi-Server Private Linear Transformation with Joint Privacy

This paper focuses on the Private Linear Transformation (PLT) problem in the multi-server scenario. In this problem, there are $N$ servers, each of which stores an identical copy of a database consisting of $K$ independent messages, and there is a user who wishes to compute $L$ independent linear combinations of a subset of $D$ messages in the database while leaking no information to the servers about the identity of the entire set of these $D$ messages required for the computation. We focus on the setting in which the coefficient matrix of the desired $L$ linear combinations generates a Maximum Distance Separable (MDS) code. We characterize the capacity of the PLT problem, defined as the supremum of all achievable download rates, for all parameters $N, K, D \geq 1$ and $L=1$, i.e., when the user wishes to compute one linear combination of $D$ messages. Moreover, we establish an upper bound on the capacity of PLT problem for all parameters $N, K, D, L \geq 1$, and leveraging some known capacity results, we show the tightness of this bound in the following regimes: (i) the case when there is a single server (i.e., $N=1$), (ii) the case when $L=1$, and (iii) the case when $L=D$.

cs.IT↗

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.

cs.IT↗

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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