arXiv subjects

Alex Sprintson

Publications and source records attributed to Alex Sprintson.

At least 55 records · Page 3Linked to original sources

arXiv2019

Capacity of Single-Server Single-Message Private Information Retrieval with Private Coded Side Information

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 side information messages. Depending on whether the demand is part of the coded side information or not, we consider two different models for the problem. For the model in which the demand does not contribute to the side information, we prove a lower bound on the minimum download cost for all (linear and non-linear) PIR protocols; and for the other model wherein the demand is one of the messages contributing to the side information, we prove a lower bound for all scalar-linear PIR protocols. In addition, we propose novel PIR protocols that achieve these lower bounds.

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arXiv2019

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

In many practical settings, the user needs to retrieve information from a server in a periodic manner, over multiple rounds of communication. In this paper, we discuss the setting in which this information needs to be retrieved privately, such that the identity of all the information retrieved until the current round is protected. This setting can occur in practical situations in which the user needs to retrieve items from the server or a periodic basis, such that the privacy needs to be guaranteed for all the items been retrieved until the current round. We refer to this setting as an \emph{online private information retrieval} as the user does not know the identities of the future items that need to be retrieved from the server. Following the previous line of work by Kadhe \emph{et al.}~we assume that the user knows a random subset of $M$ messages in the database as a side information which are unknown to the server. Focusing on scalar-linear settings, we characterize the \emph{per-round capacity}, i.e., the maximum achievable download rate at each round, and present a coding scheme that achieves this capacity. The key idea of our scheme is to utilize the data downloaded during the current round as a side information for the subsequent rounds. We show for the setting with $K$ messages stored at the server, the per-round capacity of the scalar-linear setting is $C_1= ({M+1})/{K}$ for round $i=1$ and ${C_i= {(2^{i-1}(M+1))}/{KM}}$ for round $i\geq2$, provided that ${K}/({M+1})$ is a power of $2$.

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arXiv2018

On the Capacity of Single-Server Multi-Message Private Information Retrieval with Side Information

We study Private Information Retrieval with Side Information (PIR-SI) in the single-server multi-message setting. In this setting, a user wants to download $D$ messages from a database of $K\geq D$ messages, stored on a single server, without revealing any information about the identities of the demanded messages to the server. The goal of the user is to achieve information-theoretic privacy by leveraging the side information about the database. The side information consists of a random subset of $M$ messages in the database which could have been obtained in advance from other users or from previous interactions with the server. The identities of the messages forming the side information are initially unknown to the server. Our goal is to characterize the capacity of this setting, i.e., the maximum achievable download rate. In our previous work, we have established the PIR-SI capacity for the special case in which the user wants a single message, i.e., $D=1$ and showed that the capacity can be achieved through the Partition and Code (PC) scheme. In this paper, we focus on the case when the user wants multiple messages, i.e., $D>1$. Our first result is that if the user wants more messages than what they have as side information, i.e., $D>M$, then the capacity is $\frac{D}{K-M}$, and it can be achieved using a scheme based on the Generalized Reed-Solomon (GRS) codes. In this case, the user must learn all the messages in the database in order to obtain the desired messages. Our second result shows that this may not be necessary when $D\leq M$, and the capacity in this case can be higher. We present a lower bound on the capacity based on an achievability scheme which we call Generalized Partition and Code (GPC).

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arXiv2018

Capacity of Single-Server Single-Message Private Information Retrieval with Coded Side Information

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 the download cost. In this work, we consider two different settings for the PIR-CSI problem depending on the demanded message being or not being one of the messages contributing to the side information. For each setting, we prove an upper bound on the maximum download rate as a function of the size of the database and the size of the side information, and propose a protocol that achieves the rate upper-bound.

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arXiv2018

A Simple and Efficient Strategy for the Coin Weighing Problem with a Spring Scale

This paper considers a generalized version of the coin weighing problem with a spring scale that lies at the intersection of group testing and compressed sensing problems. Given a collection of $n\geq 2$ coins of total weight $d$ (for a known integer $d$), where the weight of each coin is an unknown integer in the range of $\{0,1,\dots,k\}$ (for a known integer $k\geq 1$), the problem is to determine the weight of each coin by weighing subsets of coins in a spring scale. The goal is to minimize the average number of weighings over all possible weight configurations. For $d=k=1$, an adaptive bisecting weighing strategy is known to be optimal. However, even the case of $d=k=2$, which is the simplest non-trivial case of the problem, is still open. For this case, we propose and analyze a simple and effective adaptive weighing strategy. A numerical evaluation of the exact recursive formulas, derived for the analysis of the proposed strategy, shows that this strategy requires about ${1.365\log_2 n -0.5}$ weighings on average. To the best of our knowledge, this is the first non-trivial achievable upper bound on the minimum expected required number of weighings for the case of $d=k=2$. As $n$ grows unbounded, the proposed strategy, when compared to an optimal strategy within the commonly-used class of nested strategies, requires about $31.75\%$ less number of weighings on average; and in comparison with the information-theoretic lower bound, it requires at most about $8.16\%$ extra number of weighings on average.

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arXiv2018

On the Packet Decoding Delay of Linear Network Coded Wireless Broadcast

We apply linear network coding (LNC) to broadcast a block of data packets from one sender to a set of receivers via lossy wireless channels, assuming each receiver already possesses a subset of these packets and wants the rest. We aim to characterize the average packet decoding delay (APDD), which reflects how soon each individual data packet can be decoded by each receiver on average, and to minimize it while achieving optimal throughput. To this end, we first derive closed-form lower bounds on the expected APDD of all LNC techniques under random packet erasures. We then prove that these bounds are NP-hard to achieve and, thus, that APDD minimization is an NP-hard problem. We then study the performance of some existing LNC techniques, including random linear network coding (RLNC) and instantly decodable network coding (IDNC). We proved that all throughput-optimal LNC techniques can approximate the minimum expected APDD with a ratio between 4/3 and 2. In particular, the ratio of RLNC is exactly 2. We then prove that all IDNC techniques are only heuristics in terms of throughput optimization and {cannot guarantee an APDD approximation ratio for at least a subset of the receivers}. Finally, we propose hyper-graphic linear network coding (HLNC), a novel throughput-optimal and APDD-approximating LNC technique based on a hypergraph model of receivers' packet reception state. We implement it under different availability of receiver feedback, and numerically compare its performance with RLNC and a heuristic general IDNC technique. The results show that the APDD performance of HLNC is better under all tested system settings, even if receiver feedback is only collected intermittently.

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arXiv2018

A Monetary Mechanism for Stabilizing Cooperative Data Exchange with Selfish Users

This paper considers the problem of stabilizing cooperative data exchange with selfish users. In this setting, each user has a subset of packets in the ground set $X$, and wants all other packets in $X$. The users can exchange their packets by broadcasting coded or uncoded packets over a lossless broadcast channel, and monetary transactions are allowed between any pair of users. We define the utility of each user as the sum of two sub-utility functions: (i) the difference between the total payment received by the user and the total transmission rate of the user, and (ii) the difference between the total number of required packets by the user and the total payment made by the user. A rate-vector and payment-matrix pair $(r,p)$ is said to stabilize the grand coalition (i.e., the set of all users) if $(r,p)$ is Pareto optimal over all minor coalitions (i.e., all proper subsets of users who collectively know all packets in $X$). Our goal is to design a stabilizing rate-payment pair with minimum total sum-rate and minimum total sum-payment for any given instance of the problem. In this work, we propose two algorithms that find such a solution. Moreover, we show that both algorithms maximize the sum of utility of all users (over all solutions), and one of the algorithms also maximizes the minimum utility among all users (over all solutions).

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arXiv2017

A Fast and Accurate Failure Frequency Approximation for $k$-Terminal Reliability Systems

This paper considers the problem of approximating the failure frequency of large-scale composite $k$-terminal reliability systems. In such systems, the nodes ($k$ of which are terminals) are connected through components which are subject to random failure and repair processes. At any time, a system failure occurs if the surviving system fails to connect all the k terminals together. We assume that each component's up-times and down-times follow statistically independent stationary random processes, and these processes are statistically independent across the components. In this setting, the exact computation of failure frequency is known to be computationally intractable (NP-hard). In this work, we present an algorithm to approximate the failure frequency for any given multiplicative error factor that runs in polynomial time in the number of (minimal) cutsets. Moreover, for the special case of all-terminal reliability systems, i.e., where all nodes are terminals, we propose an algorithm for approximating the failure frequency within an arbitrary multiplicative error that runs in polynomial time in the number of nodes (which can be much smaller than the number of cutsets). In addition, our simulation results confirm that the proposed method is much faster and more accurate than the Monte Carlo simulation technique for approximating the failure frequency.

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arXiv2017

Universally Weakly Secure Coset Coding Schemes for Minimum Storage Regenerating (MSR) Codes

We consider the problem of designing codes for distributed storage that protect user data against eavesdroppers that can gain access to network links as well as individual nodes. Our goal is to achieve weak security (also known as block security) that requires that the eavesdroppers would not be able to decode individual files or combinations of a small number of files. The standard approach for achieving block security is to use a joint design scheme that consists of (inner) storage code and the (outer) coset code. However, jointly designing the codes requires that the user, who pre-processes and stores the files, should know the underlying storage code in order to design the (outer) linear transformation for achieving weak security. In many practical scenarios, such as storing the files on the third party cloud storage system, it may not be possible for the user to know the underlying storage code. In this work, we present universal schemes that separate the outer code design from the storage code design for minimum storage regenerating codes (MSR). Our schemes allow the independent design of the storage code and the outer code. Our schemes use small field size and can be used in a broad range of practical settings.

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arXiv2017

Private Information Retrieval with Side Information

We study the problem of Private Information Retrieval (PIR) in the presence of prior side information. The problem setup includes a database of $K$ independent messages possibly replicated on several servers, and a user that needs to retrieve one of these messages. In addition, the user has some prior side information in the form of a subset of $M$ messages, not containing the desired message and unknown to the servers. This problem is motivated by practical settings in which the user can obtain side information opportunistically from other users or has previously downloaded some messages using classical PIR schemes. The objective of the user is to retrieve the required message without revealing its identity while minimizing the amount of data downloaded from the servers. We focus on achieving information-theoretic privacy in two scenarios: (i) the user wants to protect jointly its demand and side information; (ii) the user wants to protect only the information about its demand, but not the side information. To highlight the role of side information, we focus first on the case of a single server (single database). In the first scenario, we prove that the minimum download cost is $K-M$ messages, and in the second scenario it is $\lceil \frac{K}{M+1}\rceil$ messages, which should be compared to $K$ messages, the minimum download cost in the case of no side information. Then, we extend some of our results to the case of the database replicated on multiple servers. Our proof techniques relate PIR with side information to the index coding problem. We leverage this connection to prove converse results, as well as to design achievability schemes.

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arXiv2017

An Algebraic-Combinatorial Proof Technique for the GM-MDS Conjecture

This paper considers the problem of designing maximum distance separable (MDS) codes over small fields with constraints on the support of their generator matrices. For any given $m\times n$ binary matrix $M$, the GM-MDS conjecture, due to Dau et al., states that if $M$ satisfies the so-called MDS condition, then for any field $\mathbb{F}$ of size $q\geq n+m-1$, there exists an $[n,m]_q$ MDS code whose generator matrix $G$, with entries in $\mathbb{F}$, fits $M$ (i.e., $M$ is the support matrix of $G$). Despite all the attempts by the coding theory community, this conjecture remains still open in general. It was shown, independently by Yan et al. and Dau et al., that the GM-MDS conjecture holds if the following conjecture, referred to as the TM-MDS conjecture, holds: if $M$ satisfies the MDS condition, then the determinant of a transformation matrix $T$, such that $TV$ fits $M$, is not identically zero, where $V$ is a Vandermonde matrix with distinct parameters. In this work, we generalize the TM-MDS conjecture, and present an algebraic-combinatorial approach based on polynomial-degree reduction for proving this conjecture. Our proof technique's strength is based primarily on reducing inherent combinatorics in the proof. We demonstrate the strength of our technique by proving the TM-MDS conjecture for the cases where the number of rows ($m$) of $M$ is upper bounded by $5$. For this class of special cases of $M$ where the only additional constraint is on $m$, only cases with $m\leq 4$ were previously proven theoretically, and the previously used proof techniques are not applicable to cases with $m > 4$.

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arXiv2017

Successive Local and Successive Global Omniscience

This paper considers two generalizations of the cooperative data exchange problem, referred to as the successive local omniscience (SLO) and the successive global omniscience (SGO). The users are divided into $\ell$ nested sub-groups. Each user initially knows a subset of packets in a ground set $X$ of size $k$, and all users wish to learn all packets in $X$. The users exchange their packets by broadcasting coded or uncoded packets. In SLO or SGO, in the $l$th ($1\leq l\leq \ell$) round of transmissions, the $l$th smallest sub-group of users need to learn all packets they collectively hold or all packets in $X$, respectively. The problem is to find the minimum sum-rate (i.e., the total transmission rate by all users) for each round, subject to minimizing the sum-rate for the previous round. To solve this problem, we use a linear-programming approach. For the cases in which the packets are randomly distributed among users, we construct a system of linear equations whose solution characterizes the minimum sum-rate for each round with high probability as $k$ tends to infinity. Moreover, for the special case of two nested groups, we derive closed-form expressions, which hold with high probability as $k$ tends to infinity, for the minimum sum-rate for each round.

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arXiv2016

Codes with Unequal Locality

For a code $\code$, its $i$-th symbol is said to have locality $r$ if its value can be recovered by accessing some other $r$ symbols of $\code$. Locally repairable codes (LRCs) are the family of codes such that every symbol has locality $r$. In this paper, we focus on (linear) codes whose individual symbols can be partitioned into disjoint subsets such that the symbols in one subset have different locality than the symbols in other. We call such codes as "codes with unequal locality". For codes with "unequal information locality", we compute a tight upper bound on the minimum distance as a function of number of information symbols of each locality. We demonstrate that the construction of Pyramid codes can be adapted to design codes with unequal information locality that achieve the minimum distance bound. This result generalizes the classical result of Gopalan et al. for codes with unequal locality. Next, we consider codes with "unequal all symbol locality", and establish an upper bound on the minimum distance as a function of number of symbols of each locality. We show that the construction based on rank-metric codes by Silberstein et al. can be adapted to obtain codes with unequal all symbol locality that achieve the minimum distance bound. Finally, we introduce the concept of "locality requirement" on a code, which can be viewed as a recoverability requirement on symbols. Information locality requirement on a code essentially specifies the minimum number of information symbols of different localities that must be present in the code. We present a greedy algorithm that assigns localities to information symbols so as to maximize the minimum distance among all codes that satisfy a given locality requirement.

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arXiv2015

Cooperative Data Exchange with Unreliable Clients

Consider a set of clients in a broadcast network, each of which holds a subset of packets in the ground set X. In the (coded) cooperative data exchange problem, the clients need to recover all packets in X by exchanging coded packets over a lossless broadcast channel. Several previous works analyzed this problem under the assumption that each client initially holds a random subset of packets in X. In this paper we consider a generalization of this problem for settings in which an unknown (but of a certain size) subset of clients are unreliable and their packet transmissions are subject to arbitrary erasures. For the special case of one unreliable client, we derive a closed-form expression for the minimum number of transmissions required for each reliable client to obtain all packets held by other reliable clients (with probability approaching 1 as the number of packets tends to infinity). Furthermore, for the cases with more than one unreliable client, we provide an approximation solution in which the number of transmissions per packet is within an arbitrarily small additive factor from the value of the optimal solution.

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arXiv2015

ÆtherFlow: Principled Wireless Support in SDN

Software Defined Networking (SDN) drastically changes the meaning and process of designing, building, testing, and operating networks. The current support for wireless net- working in SDN technologies has lagged behind its development and deployment for wired networks. The purpose of this work is to bring principled support for wireless access networks so that they can receive the same level of programmability as wireline interfaces. Specifically we aim to integrate wireless protocols into the general SDN framework by proposing a new set of abstractions in wireless devices and the interfaces to manipulate them. We validate our approach by implementing our design as an extension of an existing OpenFlow data plane and deploying it in an IEEE 802.11 access point. We demonstrate the viability of software-defined wireless access networks by developing and testing a wireless handoff application. The results of the exper- iment show that our framework is capable of providing new capabilities in an efficient manner.

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arXiv2015

Coding against a Limited-view Adversary: The Effect of Causality and Feedback

We consider the problem of communication over a multi-path network in the presence of a causal adversary. The limited-view causal adversary is able to eavesdrop on a subset of links and also jam on a potentially overlapping subset of links based on the current and past information. To ensure that the communication takes place reliably and secretly, resilient network codes with necessary redundancy are needed. We study two adversarial models - additive and overwrite jamming and we optionally assume passive feedback from decoder to encoder, i.e., the encoder sees everything that the decoder sees. The problem assumes transmissions are in the large alphabet regime. For both jamming models, we find the capacity under four scenarios - reliability without feedback, reliability and secrecy without feedback, reliability with passive feedback, reliability and secrecy with passive feedback. We observe that, in comparison to the non-causal setting, the capacity with a causal adversary is strictly increased for a wide variety of parameter settings and present our intuition through several examples.

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arXiv2015

The Benefit of Limited Feedback to Generation-Based Random Linear Network Coding in Wireless Broadcast

Random linear network coding (RLNC) is asymptotically throughput optimal in the wireless broadcast of a block of packets from a sender to a set of receivers, but suffers from heavy computational load and packet decoding delay. To mitigate this problem while maintaining good throughput, we partition the packet block into disjoint generations after broadcasting the packets uncoded once and collecting one round of feedback about receivers' packet reception state. We prove the NP-hardness of the optimal partitioning problem by using a hypergraph coloring approach, and develop an efficient heuristic algorithm for its solution. Simulations show that our algorithm outperforms existing solutions.

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arXiv2015

On Minimizing the Average Packet Decoding Delay in Wireless Network Coded Broadcast

We consider a setting in which a sender wishes to broadcast a block of K data packets to a set of wireless receivers, where each of the receivers has a subset of the data packets already available to it (e.g., from prior transmissions) and wants the rest of the packets. Our goal is to find a linear network coding scheme that yields the minimum average packet decoding delay (APDD), i.e., the average time it takes for a receiver to decode a data packet. Our contributions can be summarized as follows. First, we prove that this problem is NP-hard by presenting a reduction from the hypergraph coloring problem. Next, we show that %\alexn{an MDS-based solution or} a random linear network coding (RLNC) provides an approximate solution to this problem with approximation ratio $2$ with high probability. Next, we present a methodology for designing specialized approximation algorithms for this problem that outperform RLNC solutions while maintaining the same throughput. In a special case of practical interest with a small number of wanted packets our solution can achieve an approximation ratio (4-2/K)/3. Finally, we conduct an experimental study that demonstrates the advantages of the presented methodology.

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