Search

We study two problems of private matrix multiplication, over a distributed computing system consisting of a master node, and multiple servers that collectively store a family of public matrices using Maximum-Distance-Separable (MDS) codes. In the first problem of Private and Secure Matrix Multiplication (PSMM) from colluding servers, the master intends to compute the product of its confidential matrix $\mathbf{A}$ with a target matrix stored on the servers, without revealing any information about $\mathbf{A}$ and the index of target matrix to some colluding servers. In the second problem of Fully Private Matrix Multiplication (FPMM) from colluding servers, the matrix $\mathbf{A}$ is also selected from another family of public matrices stored at the servers in MDS form. In this case, the indices of the two target matrices should both be kept private from colluding servers. We develop novel strategies for the two PSMM and FPMM problems, which simultaneously guarantee information-theoretic data/index privacy and computation correctness. We compare the proposed PSMM strategy with a previous PSMM strategy with a weaker privacy guarantee (non-colluding servers), and demonstrate substantial improvements over the previous strategy in terms of communication and computation overheads. Moreover, compared with a baseline FPMM strategy that uses the idea of Private Information Retrieval (PIR) to directly retrieve the desired matrix multiplication, the proposed FPMM strategy significantly reduces storage overhead, but slightly incurs large communication and computation overheads., 16 pages, 6 figures

We propose SwiftAgg+, a novel secure aggregation protocol for federated learning systems, where a central server aggregates local models of $N \in \mathbb{N}$ distributed users, each of size $L \in \mathbb{N}$, trained on their local data, in a privacy-preserving manner. SwiftAgg+ can significantly reduce the communication overheads without any compromise on security, and achieve optimal communication loads within diminishing gaps. Specifically, in presence of at most $D=o(N)$ dropout users, SwiftAgg+ achieves a per-user communication load of $(1+\mathcal{O}(\frac{1}{N}))L$ symbols and a server communication load of $(1+\mathcal{O}(\frac{1}{N}))L$ symbols, with a worst-case information-theoretic security guarantee, against any subset of up to $T=o(N)$ semi-honest users who may also collude with the curious server. Moreover, the proposed SwiftAgg+ allows for a flexible trade-off between communication loads and the number of active communication links. In particular, for $T, Comment: arXiv admin note: substantial text overlap with arXiv:2202.04169

We propose SwiftAgg, a novel secure aggregation protocol for federated learning systems, where a central server aggregates local models of $N$ distributed users, each of size $L$, trained on their local data, in a privacy-preserving manner. Compared with state-of-the-art secure aggregation protocols, SwiftAgg significantly reduces the communication overheads without any compromise on security. Specifically, in presence of at most $D$ dropout users, SwiftAgg achieves a users-to-server communication load of $(T+1)L$ and a users-to-users communication load of up to $(N-1)(T+D+1)L$, with a worst-case information-theoretic security guarantee, against any subset of up to $T$ semi-honest users who may also collude with the curious server. The key idea of SwiftAgg is to partition the users into groups of size $D+T+1$, then in the first phase, secret sharing and aggregation of the individual models are performed within each group, and then in the second phase, model aggregation is performed on $D+T+1$ sequences of users across the groups. If a user in a sequence drops out in the second phase, the rest of the sequence remain silent. This design allows only a subset of users to communicate with each other, and only the users in a single group to directly communicate with the server, eliminating the requirements of 1) all-to-all communication network across users; and 2) all users communicating with the server, for other secure aggregation protocols. This helps to substantially slash the communication costs of the system.

The problem of $X$-secure $T$-colluding symmetric Private Polynomial Computation (PPC) from coded storage system with $B$ Byzantine and $U$ unresponsive servers is studied in this paper. Specifically, a dataset consisting of $M$ files is stored across $N$ distributed servers according to $(N,K+X)$ Maximum Distance Separable (MDS) codes such that any group of up to $X$ colluding servers can not learn anything about the data files. A user wishes to privately evaluate one out of a set of candidate polynomial functions over the $M$ files from the system, while guaranteeing that any $T$ colluding servers can not learn anything about the identity of the desired function and the user can not learn anything about the $M$ data files more than the desired polynomial function evaluations, in the presence of $B$ Byzantine servers that can send arbitrary responses maliciously to confuse the user and $U$ unresponsive servers that will not respond any information at all. A novel symmetric PPC scheme using Lagrange encoding is proposed. This scheme achieves a PPC rate of $1-\frac{G(K+X-1)+T+2B}{N-U}$ with secrecy rate $\frac{G(K+X-1)+T}{N-(G(K+X-1)+T+2B+U)}$ and finite field size $N+\max\{K,N-(G(K+X-1)+T+2B+U)\}$, where $G$ is the maximum degree over all the candidate polynomial functions. Moreover, to further measure the efficiency of PPC schemes, upload cost, query complexity, server computation complexity and decoding complexity required to implement the scheme are analyzed. Remarkably, the PPC setup studied in this paper generalizes all the previous MDS coded PPC setups and the degraded schemes strictly outperform the best known schemes in terms of (asymptotical) PPC rate, which is the main concern of the PPC schemes.

How can we optimally trade extra computing power to reduce the communication load in distributed computing? We answer this question by characterizing a fundamental tradeoff between computation and communication in distributed computing, i.e., the two are inversely proportional to each other. More specifically, a general distributed computing framework, motivated by commonly used structures like MapReduce, is considered, where the overall computation is decomposed into computing a set of "Map" and "Reduce" functions distributedly across multiple computing nodes. A coded scheme, named "Coded Distributed Computing" (CDC), is proposed to demonstrate that increasing the computation load of the Map functions by a factor of $r$ (i.e., evaluating each function at $r$ carefully chosen nodes) can create novel coding opportunities that reduce the communication load by the same factor. An information-theoretic lower bound on the communication load is also provided, which matches the communication load achieved by the CDC scheme. As a result, the optimal computation-communication tradeoff in distributed computing is exactly characterized. Finally, the coding techniques of CDC is applied to the Hadoop TeraSort benchmark to develop a novel CodedTeraSort algorithm, which is empirically demonstrated to speed up the overall job execution by $1.97\times$ - $3.39\times$, for typical settings of interest., To appear in IEEE Transactions on Information Theory

We consider a wireless distributed computing system, in which multiple mobile users, connected wirelessly through an access point, collaborate to perform a computation task. In particular, users communicate with each other via the access point to exchange their locally computed intermediate computation results, which is known as data shuffling. We propose a scalable framework for this system, in which the required communication bandwidth for data shuffling does not increase with the number of users in the network. The key idea is to utilize a particular repetitive pattern of placing the dataset (thus a particular repetitive pattern of intermediate computations), in order to provide coding opportunities at both the users and the access point, which reduce the required uplink communication bandwidth from users to access point and the downlink communication bandwidth from access point to users by factors that grow linearly with the number of users. We also demonstrate that the proposed dataset placement and coded shuffling schemes are optimal (i.e., achieve the minimum required shuffling load) for both a centralized setting and a decentralized setting, by developing tight information-theoretic lower bounds., Comment: To appear in IEEE/ACM Transactions on Networking

We introduce an information-theoretic framework, named Coded State Machine (CSM), to securely and efficiently execute multiple state machines on untrusted network nodes, some of which are Byzantine. The standard method of solving this problem is using State Machine Replication, which achieves high security at the cost of low efficiency. We propose CSM, which achieves the optimal linear scaling in storage efficiency, throughput, and security simultaneously with the size of the network. The storage efficiency is scaled via the design of Lagrange coded states and coded input commands that require the same storage size as their origins. The computational efficiency is scaled using a novel delegation algorithm, called INTERMIX, which is an information-theoretically verifiable matrix-vector multiplication algorithm of independent interest. Using INTERMIX, the network nodes securely delegate their coding operations to a single worker node, and a small group of randomly selected auditor nodes verify its correctness, so that computational efficiency can scale almost linearly with the network size, without compromising on security.

Communication overhead is one of the major performance bottlenecks in large-scale distributed computing systems, in particular for machine learning applications. Conventionally, compression techniques are used to reduce the load of communication by combining intermediate results of the same computation task as much as possible. Recently, via the development of coded distributed computing (CDC), it has been shown that it is possible to enable coding opportunities across intermediate results of different computation tasks to further reduce the communication load. We propose a new scheme, named compressed coded distributed computing (in short, compressed CDC), which jointly exploits the above two techniques (i.e., combining the intermediate results of the same computation and coding across the intermediate results of different computations) to significantly reduce the communication load for computations with linear aggregation (reduction) of intermediate results in the final stage that are prevalent in machine learning (e.g., distributed training algorithms where partial gradients are computed distributedly and then averaged in the final stage). In particular, compressed CDC first compresses/combines several intermediate results for a single computation, and then utilizes multiple such combined packets to create a coded multicast packet that is simultaneously useful for multiple computations. We characterize the achievable communication load of compressed CDC and show that it substantially outperforms both combining methods and CDC scheme., Comment: A shorter version to appear in ISIT 2018

Today’s blockchain designs suffer from a trilemma claiming that no blockchain system can simultaneously achieve decentralization, security, and performance scalability. For current blockchain systems, as more nodes join the network, the efficiency of the system (computation, communication, and storage) stays constant at best. A leading idea for enabling blockchains to scale efficiency is the notion of sharding: different subsets of nodes handle different portions of the blockchain, thereby reducing the load for each individual node. However, existing sharding proposals achieve efficiency scaling by compromising on trust - corrupting the nodes in a given shard will lead to the permanent loss of the corresponding portion of data. In this paper, we settle the trilemma by demonstrating a new protocol for coded storage and computation in blockchains. In particular, we propose PolyShard : “polynomially coded sharding” scheme that achieves information-theoretic upper bounds on the efficiency of the storage, system throughput, as well as on trust, thus enabling a truly scalable system. We provide simulation results that numerically demonstrate the performance improvement over state of the arts, and the scalability of the PolyShard system. Finally, we discuss potential enhancements, and highlight practical considerations in building such a system.

We consider a mobile edge computing problem, in which mobile users offload their computation tasks to computing nodes (e.g., base stations) at the network edge. The edge nodes compute the requested functions and communicate the computed results to the users via wireless links. For this problem, we propose a Universal Coded Edge Computing (UCEC) scheme for linear functions to simultaneously minimize the load of computation at the edge nodes, and maximize the physical-layer communication efficiency towards the mobile users. In the proposed UCEC scheme, edge nodes create coded inputs of the users, from which they compute coded output results. Then, the edge nodes utilize the computed coded results to create communication messages that zero-force all the interference signals over the air at each user. Specifically, the proposed scheme is universal since the coded computations performed at the edge nodes are oblivious of the channel states during the communication process from the edge nodes to the users., To Appear in ISIT 2017

Redundancy is abundant in Fog networks (i.e., many computing and storage points) and grows linearly with network size. We demonstrate the transformational role of coding in Fog computing for leveraging such redundancy to substantially reduce the bandwidth consumption and latency of computing. In particular, we discuss two recently proposed coding concepts, namely Minimum Bandwidth Codes and Minimum Latency Codes, and illustrate their impacts in Fog computing. We also review a unified coding framework that includes the above two coding techniques as special cases, and enables a tradeoff between computation latency and communication load to optimize system performance. At the end, we will discuss several open problems and future research directions., To appear in IEEE Communications Magazine, Issue on Fog Computing and Networking

We focus on sorting, which is the building block of many machine learning algorithms, and propose a novel distributed sorting algorithm, named Coded TeraSort, which substantially improves the execution time of the TeraSort benchmark in Hadoop MapReduce. The key idea of Coded TeraSort is to impose structured redundancy in data, in order to enable in-network coding opportunities that overcome the data shuffling bottleneck of TeraSort. We empirically evaluate the performance of CodedTeraSort algorithm on Amazon EC2 clusters, and demonstrate that it achieves 1.97x - 3.39x speedup, compared with TeraSort, for typical settings of interest., to appear in proceedings of 2017 International Workshop on Parallel and Distributed Computing for Large Scale Machine Learning and Big Data Analytics

Today's data centers have an abundance of computing resources, hosting server clusters consisting of as many as tens or hundreds of thousands of machines. To execute a complex computing task over a data center, it is natural to distribute computations across many nodes to take advantage of parallel processing. However, as we allocate more and more computing resources to a computation task and further distribute the computations, large amounts of (partially) computed data must be moved between consecutive stages of computation tasks among the nodes, hence the communication load can become the bottleneck. In this paper, we study the optimal allocation of computing resources in distributed computing, in order to minimize the total execution time in distributed computing accounting for both the duration of computation and communication phases. In particular, we consider a general MapReduce-type distributed computing framework, in which the computation is decomposed into three stages: \emph{Map}, \emph{Shuffle}, and \emph{Reduce}. We focus on a recently proposed \emph{Coded Distributed Computing} approach for MapReduce and study the optimal allocation of computing resources in this framework. For all values of problem parameters, we characterize the optimal number of servers that should be used for distributed processing, provide the optimal placements of the Map and Reduce tasks, and propose an optimal coded data shuffling scheme, in order to minimize the total execution time. To prove the optimality of the proposed scheme, we first derive a matching information-theoretic converse on the execution time, then we prove that among all possible resource allocation schemes that achieve the minimum execution time, our proposed scheme uses the exactly minimum possible number of servers.

Modern learning algorithms use gradient descent updates to train inferential models that best explain data. Scaling these approaches to massive data sizes requires proper distributed gradient descent schemes where distributed worker nodes compute partial gradients based on their partial and local data sets, and send the results to a master node where all the computations are aggregated into a full gradient and the learning model is updated. However, a major performance bottleneck that arises is that some of the worker nodes may run slow. These nodes a.k.a. stragglers can significantly slow down computation as the slowest node may dictate the overall computational time. We propose a distributed computing scheme, called Batched Coupon's Collector (BCC) to alleviate the effect of stragglers in gradient methods. We prove that our BCC scheme is robust to a near optimal number of random stragglers. We also empirically demonstrate that our proposed BCC scheme reduces the run-time by up to 85.4% over Amazon EC2 clusters when compared with other straggler mitigation strategies. We also generalize the proposed BCC scheme to minimize the completion time when implementing gradient descent-based algorithms over heterogeneous worker nodes.

We propose a unified coded framework for distributed computing with straggling servers, by introducing a tradeoff between "latency of computation" and "load of communication" for some linear computation tasks. We show that the coded scheme of [1]-[3] that repeats the intermediate computations to create coded multicasting opportunities to reduce communication load, and the coded scheme of [4], [5] that generates redundant intermediate computations to combat against straggling servers can be viewed as special instances of the proposed framework, by considering two extremes of this tradeoff: minimizing either the load of communication or the latency of computation individually. Furthermore, the latency-load tradeoff achieved by the proposed coded framework allows to systematically operate at any point on that tradeoff to perform distributed computing tasks. We also prove an information-theoretic lower bound on the latency-load tradeoff, which is shown to be within a constant multiplicative gap from the achieved tradeoff at the two end points., a shorter version to appear in NetCod 2016

In this paper, we study the communication problem from rovers on Mars' surface to Mars-orbiting satellites. We first justify that, to a good extent, the rover-to-orbiter communication problem can be modelled as communication over a $2 \times 2$ X-channel with the network topology varying over time. For such a fading X-channel where transmitters are only aware of the time-varying topology but not the time-varying channel state (i.e., no CSIT), we propose coding strategies that code across topologies, and develop upper bounds on the sum degrees-of-freedom (DoF) that is shown to be tight under certain pattern of the topology variation. Furthermore we demonstrate that the proposed scheme approximately achieves the ergodic sum-capacity of the network. Using the proposed coding scheme, we numerically evaluate the ergodic rate gain over a time-division-multiple-access (TDMA) scheme for Rayleigh and Rice fading channels. We also numerically demonstrate that with practical orbital parameters, a 9.6% DoF gain, as well as more than 11.6% throughput gain can be achieved for a rover-to-orbiter communication network., 13 pages, 6 figures. Accepted by IEEE Transactions on Communications