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We consider the problem of coded computing, where a computational task is performed in a distributed fashion in the presence of adversarial workers. We propose techniques to break the adversarial toleration threshold barrier previously known in coded computing. More specifically, we leverage list-decoding techniques for folded Reed-Solomon codes and propose novel algorithms to recover the correct codeword using side information. In the coded computing setting, we show how the master node can perform certain carefully designed extra computations to obtain the side information. The workload of computing this side information is negligible compared to the computations done by each worker. This side information is then utilized to prune the output of the list decoder and uniquely recover the true outcome. We further propose folded Lagrange coded computing (FLCC) to incorporate the developed techniques into a specific coded computing setting. Our results show that FLCC outperforms LCC by breaking the barrier on the number of adversaries that can be tolerated. In particular, the corresponding threshold in FLCC is improved by a factor of two asymptotically compared to that of LCC.

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. Based on the compressed CDC technique, we then study a distributed training problem as one of its application. We characterize the communication load for this distributed training problem and show that it is asymptotically optimal.

The growing size of modern datasets necessitates splitting a large scale computation into smaller computations and operate in a distributed manner. Adversaries in a distributed system deliberately send erroneous data in order to affect the computation for their benefit. Boolean functions are the key components of many applications, e.g., verification functions in blockchain systems and design of cryptographic algorithms. We consider the problem of computing a Boolean function in a distributed computing system with particular focus on security against Byzantine workers . Any Boolean function can be modeled as a multivariate polynomial with high degree in general. However, the security threshold (i.e., the maximum number of adversarial workers can be tolerated such that the correct results can be obtained) provided by the recent proposed Lagrange Coded Computing (LCC) can be extremely low if the degree of the polynomial is high. We propose three different schemes called coded Algebraic normal form ( ANF ), coded Disjunctive normal form ( DNF ) and coded polynomial threshold function ( PTF ). The key idea of the proposed schemes is to model it as the concatenation of some low-degree polynomials and threshold functions. In terms of the security threshold, we show that the proposed coded ANF and coded DNF are optimal by providing a matching outer bound.

How to train a machine learning model while keeping the data private and secure? We present CodedPrivateML, a fast and scalable approach to this critical problem. CodedPrivateML keeps both the data and the model information-theoretically private, while allowing efficient parallelization of training across distributed workers. We characterize CodedPrivateML's privacy threshold and prove its convergence for logistic (and linear) regression. Furthermore, via extensive experiments on Amazon EC2, we demonstrate that CodedPrivateML provides significant speedup over cryptographic approaches based on multi-party computing (MPC).

Federated learning enables training a global model from data located at the client nodes, without data sharing and moving client data to a centralized server. Performance of federated learning in a multi-access edge computing (MEC) network suffers from slow convergence due to heterogeneity and stochastic fluctuations in compute power and communication link qualities across clients. We propose a novel coded computing framework, CodedFedL, that injects structured coding redundancy into federated learning for mitigating stragglers and speeding up the training procedure. CodedFedL enables coded computing for non-linear federated learning by efficiently exploiting distributed kernel embedding via random Fourier features that transforms the training task into computationally favourable distributed linear regression. Furthermore, clients generate local parity datasets by coding over their local datasets, while the server combines them to obtain the global parity dataset. Gradient from the global parity dataset compensates for straggling gradients during training, and thereby speeds up convergence. For minimizing the epoch deadline time at the MEC server, we provide a tractable approach for finding the amount of coding redundancy and the number of local data points that a client processes during training, by exploiting the statistical properties of compute as well as communication delays. We also characterize the leakage in data privacy when clients share their local parity datasets with the server. We analyze the convergence rate and iteration complexity of CodedFedL under simplifying assumptions, by treating CodedFedL as a stochastic gradient descent algorithm. Furthermore, we conduct numerical experiments using practical network parameters and benchmark datasets, where CodedFedL speeds up the overall training time by up to $15\times$ in comparison to the benchmark schemes., Final version to appear in the first issue of the IEEE JSAC Series on Machine Learning for Communications and Networks

Coded computing is a new framework to address fundamental issues in large scale distributed computing, by injecting structured randomness and redundancy. We first provide an overview of coded computing and summarize some recent advances. Then we focus on distributed matrix multiplication and consider a common scenario where each worker is assigned a fraction of the multiplication task. In particular, by partitioning two input matrices into $m$ -by- $p$ and $p$ -by- $n$ subblocks, a single multiplication task can be viewed as computing linear combinations of $pmn$ submatrix products, which can be assigned to $pmn$ workers. Such block-partitioning-based designs have been widely studied under the topics of secure, private, and batch computation, where the state of the arts all require computing at least “cubic” ( $pmn$ ) number of submatrix multiplications. Entangled polynomial codes, first presented for straggler mitigation, provides a powerful method for breaking the cubic barrier. It achieves a subcubic recovery threshold, i.e., recovering the final product from any subset of multiplication results with a size order-wise smaller than $pmn$ . We show that entangled polynomial codes can be further extended to also include these three important settings, providing unified frameworks that order-wise reduce the total computational costs by achieving subcubic recovery thresholds.

This article proposes a coded distributed graph processing framework to alleviate the communication bottleneck in large-scale distributed graph processing. In particular, we propose a topology-aware coded computing (TACC) algorithm that has two novel salient features: (i) a topology-aware graph allocation strategy, and (ii) a coded aggregation scheme that combines the intermediate computations for graph processing while constructing coded messages. The proposed setup results in a trade-off between computation and communication, in that increasing the computation load at the distributed parties can in turn reduce the communication load. We demonstrate the effectiveness of the TACC algorithm by comparing the communication load with existing setups on both Erdos-Renyi and Barabasi-Albert type random graphs, as well as real-world Google web graph for PageRank computations. In particular, we show that the proposed coding strategy can lead to up to $82\%$ reduction in communication load and up to $46\%$ reduction in overall execution time, when compared to the state-of-the-art and implemented on the Amazon EC2 cloud compute platform.

Federated learning can be a promising solution for enabling IoT cybersecurity (i.e., anomaly detection in the IoT environment) while preserving data privacy and mitigating the high communication/storage overhead (e.g., high-frequency data from time-series sensors) of centralized over-the-cloud approaches. In this paper, to further push forward this direction with a comprehensive study in both algorithm and system design, we build FedIoT platform that contains FedDetect algorithm for on-device anomaly data detection and a system design for realistic evaluation of federated learning on IoT devices. Furthermore, the proposed FedDetect learning framework improves the performance by utilizing a local adaptive optimizer (e.g., Adam) and a cross-round learning rate scheduler. In a network of realistic IoT devices (Raspberry PI), we evaluate FedIoT platform and FedDetect algorithm in both model and system performance. Our results demonstrate the efficacy of federated learning in detecting a wider range of attack types occurred at multiple devices. The system efficiency analysis indicates that both end-to-end training time and memory cost are affordable and promising for resource-constrained IoT devices. The source code is publicly available at https://github.com/FedML-AI/FedIoT.

The state-of-the-art approaches to privacy-preserving coded computing rely on quantizing the data into a finite field, so that Shamir's secret sharing can be employed. Such coded computing solutions, however, are not properly scalable with the size of dataset, mainly due to computation overflows. To address such a critical issue, we propose a novel extension of certain coded computing schemes to the analog domain. This includes distributed polynomial evaluation and Lagrange coded computing (LCC) that are widely used in the literature. All the operations in the proposed protocols are done over the infinite fields of R/C but for practical implementations floating-point numbers are used. We characterize the privacy of data in our proposed protocols, against any subset of colluding servers up to a certain size, in terms of the distinguishing security (DS) and the mutual information security (MIS) metrics. Also, the accuracy of outcome is characterized in a practical setting assuming operations are performed using floating-point numbers. Consequently, fundamental trade-offs between the accuracy of the outcome and their privacy level are observed in the analog domain and are numerically evaluated. Moreover, we implement analog LCC (ALCC) to perform matrix-matrix multiplication over a batch of matrices. It is observed that ALCC is superior compared to LCC, implemented using fixed-point numbers, assuming both schemes use an equal number of bits to represent data symbols.

With recent advancements in edge computing capabilities, there has been a significant increase in utilizing the edge cloud for event-driven and time-sensitive computations. However, large-scale edge computing networks can suffer substantially from unpredictable and unreliable computing resources which can result in high variability of service quality. Thus, it is crucial to design efficient task scheduling policies that guarantee quality of service and the timeliness of computation queries. In this paper, we study the problem of computation offloading over unknown edge cloud networks with a sequence of timely computation jobs. Motivated by the MapReduce computation paradigm, we assume each computation job can be partitioned to smaller Map functions that are processed at the edge, and the Reduce function is computed at the user after the Map results are collected from the edge nodes. We model the service quality (success probability of returning result back to the user within deadline) of each edge device as function of context (collection of factors that affect edge devices). The user decides the computations to offload to each device with the goal of receiving a recoverable set of computation results in the given deadline. Our goal is to design an efficient edge computing policy in the dark without the knowledge of the context or computation capabilities of each device. By leveraging the \emph{coded computing} framework in order to tackle failures or stragglers in computation, we formulate this problem using contextual-combinatorial multi-armed bandits (CC-MAB), and aim to maximize the cumulative expected reward. We propose an online learning policy called \emph{online coded edge computing policy}, which provably achieves asymptotically-optimal performance in terms of regret loss compared with the optimal offline policy for the proposed CC-MAB problem.

We consider the problem of interference management in wireless cellular networks with caches at both base stations and receivers and we characterize the degrees-of-freedom (DoF) per cell to within an additive gap of 1 and a multiplicative gap of 2 for all system parameters, under one-shot linear schemes. Our result indicates that the one-shot linear DoF per cell scales linearly with the total amount of cache that is available within each cell. A similar phenomenon had been previously observed for the case of fully-connected wireless networks. Hence, our result demonstrates that it also holds in cellular networks, despite the presence of path loss and fading which results in partial connectivity of the network topology. To establish the result, we propose a randomized and decentralized cache placement and a delivery scheme which, on one hand, utilizes the overlap of contents at base station caches to zero-force part of their outgoing interference, and on the other hand, uses the receiver caches to create coded multicasting opportunities, so that the receivers can eliminate the remaining interference due to undesired packets. We also provide a converse argument to show that our achievable one-shot linear DoF per cell is within an additive gap of 1 and a multiplicative gap of 2 of its optimal value.

Graph-based methods have been quite successful in solving unsupervised and semi-supervised learning problems, as they provide a means to capture the underlying geometry of the dataset. It is often desirable for the constructed graph to satisfy two properties: first, data points that are similar in the feature space should be strongly connected on the graph, and second, the class label information should vary smoothly with respect to the graph, where smoothness is measured using the spectral properties of the graph Laplacian matrix. Recent works have justified some of these smoothness conditions by showing that they are strongly linked to the semi-supervised smoothness assumption and its variants. In this work, we reinforce this connection by viewing the problem from a graph sampling theoretic perspective, where class indicator functions are treated as bandlimited graph signals (in the eigenvector basis of the graph Laplacian) and label prediction as a bandlimited reconstruction problem. Our approach involves analyzing the bandwidth of class indicator signals generated from statistical data models with separable and nonseparable classes. These models are quite general and mimic the nature of most real-world datasets. Our results show that in the asymptotic limit, the bandwidth of any class indicator is also closely related to the geometry of the dataset. This allows one to theoretically justify the assumption of bandlimitedness of class indicator signals, thereby providing a sampling theoretic interpretation of graph-based semi-supervised classification.

We consider a basic caching system, where a single server with a database of N files (e.g. movies) is connected to a set of K users through a shared bottleneck link. Each user has a local cache memory with a size of M files. The system operates in two phases: a placement phase, where each cache memory is populated up to its size from the database, and a following delivery phase, where each user requests a file from the database, and the server is responsible for delivering the requested contents. The objective is to design the two phases to minimize the load (peak or average) of the bottleneck link. We characterize the rate-memory tradeoff of the above caching system within a factor of 2.00884 for both the peak rate and the average rate (under uniform file popularity), where the best proved characterization in the current literature gives a factor of 4 and 4.7 respectively. Moreover, in the practically important case where the number of files (N) is large, we exactly characterize the tradeoff for systems with no more than 5 users, and characterize the tradeoff within a factor of 2 otherwise. We establish these results by developing novel information theoretic outer-bounds for the caching problem, which improves the state of the art and gives tight characterization in various cases.

MLaaS (ML-as-a-Service) offerings by cloud computing platforms are becoming increasingly popular. Hosting pre-trained machine learning models in the cloud enables elastic scalability as the demand grows. But providing low latency and reducing the latency variance is a key requirement. Variance is harder to control in a cloud deployment due to uncertain-ties in resource allocations across many virtual instances. We propose the collage inference technique, which uses a novel convolutional neural network model, collage-cnn, to provide low-cost redundancy. A collage-cnn model takes a collage image formed by combining multiple images and performs multi-image classification in one shot, albeit at slightly lower accuracy. We augment a collection of traditional single image classifier models with a single collage-cnn classifier, which acts as their low-cost redundant backup. Collage-cnn provides backup classification results if any single image classification requests experience a slowdown. Deploying the collage-cnn models in the cloud, we demonstrate that the 99th percentile tail latency of inference can be reduced by 1.2x to 2x compared to replication-based approaches while providing high accuracy. Variation in inference latency can be reduced by 1.8x to 15x.

A distributed computing scenario is considered, where the computational power of a set of worker nodes is used to perform a certain computation task over a dataset that is dispersed among the workers. Lagrange coded computing (LCC), proposed by Yu et al. , leverages the well-known Lagrange polynomial to perform polynomial evaluation of the dataset in such a scenario in an efficient parallel fashion while keeping the privacy of data amidst possible collusion of workers. This solution relies on quantizing the data into a finite field, so that Shamir’s secret sharing, as one of its main building blocks, can be employed. Such a solution, however, is not properly scalable with the size of dataset, mainly due to computation overflows. To address such a critical issue, we propose a novel extension of LCC to the analog domain, referred to as analog LCC (ALCC). All the operations in the proposed ALCC protocol are done over the infinite fields of ${ \mathbb R}/ { \mathbb C}$ but for practical implementations floating-point numbers are used. We characterize the privacy of data in ALCC, against any subset of colluding workers up to a certain size, in terms of the distinguishing security (DS) and the mutual information security (MIS) metrics. Also, the accuracy of outcome is characterized in a practical setting assuming operations are performed using floating-point numbers. Consequently, a fundamental trade-off between the accuracy of the outcome of ALCC and its privacy level is observed and is numerically evaluated. Moreover, we implement the proposed scheme to perform matrix-matrix multiplication over a batch of matrices. It is observed that ALCC is superior compared to the state-of-the-art LCC, implemented using fixed-point numbers, assuming both schemes use an equal number of bits to represent data symbols.

Recently, there has been a significant increase in utilizing the cloud networks for event-driven and time-sensitive computations. However, large-scale distributed computing networks can suffer substantially from unpredictable and unreliable computing resources which can result in high variability of service quality. Thus, it is crucial to design efficient task scheduling policies that guarantee quality of service and the timeliness of computation queries. In this paper, we study the problem of computation offloading over unknown cloud networks with a sequence of timely computation jobs. We model the service quality (success probability of returning result back to the user within deadline) of each worker as function of context (collection of factors that affect workers). The user decides the computations to offload to each worker with the goal of receiving a recoverable set of computation results in the given deadline. Our goal is to design an efficient computing policy in the dark without the knowledge of the context or computation capabilities of each worker. By leveraging the coded computing framework in order to tackle failures or stragglers in computation, we formulate this problem using contextual-combinatorial multi-armed bandits (CC-MAB), and aim to maximize the cumulative expected reward. We propose an online learning policy called online coded computing policy, which provably achieves asymptotically-optimal performance in terms of regret loss compared with the optimal offline policy.

Cloud computing platforms have created the possibility for computationally limited users to delegate demanding tasks to strong but untrusted servers. Verifiable computing algorithms help build trust in such interactions by enabling the server to provide a proof of correctness of his results which the user can check very efficiently. In this paper, we present a doubly-efficient interactive algorithm for verifiable polynomial evaluation. Unlike the mainstream literature on verifiable computing, the soundness of our algorithm is information-theoretic and cannot be broken by a computationally unbounded server. By relying on basic properties of error correcting codes, our algorithm enforces a dishonest server to provide false results to problems which become progressively easier to verify. After roughly logd rounds, the user can verify the response of the server against a look-up table that has been pre-computed during an initialization phase. For a polynomial of degree d, we achieve a user complexity of $O\left( {{d^\varepsilon }} \right)$, a server complexity of $O\left( {{d^{1 + \varepsilon }}} \right)$, a round complexity of O(logd) and an initialization complexity of $O\left( {{d^{1 + \varepsilon }}} \right)$.

In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into m-by-p and p-by-n subblocks, a single multiplication task can be viewed as computing linear combinations of pmn submatrix products, which can be assigned to pmn workers. Such block-partitioning based designs have been widely studied under the topics of secure, private, and batch computation, where the state of the arts all require computing at least "cubic" (pmn) number of submatrix multiplications. Entangled polynomial codes, first presented for straggler mitigation, provides a powerful method for breaking the cubic barrier. It achieves a subcubic recovery threshold, meaning that the final product can be recovered from any subset of multiplication results with a size order-wise smaller than pmn. In this work, we show that entangled polynomial codes can be further extended to also include these three important settings, and provide a unified framework that order-wise reduces the total computational costs upon the state of the arts by achieving subcubic recovery thresholds.

Federated learning is a distributed framework for training machine learning models over the data residing at mobile devices, while protecting the privacy of individual users. A major bottleneck in scaling federated learning to a large number of users is the overhead of secure model aggregation across many users. In particular, the overhead of the state-of-the-art protocols for secure model aggregation grows quadratically with the number of users. In this article, we propose the first secure aggregation framework, named Turbo-Aggregate, that in a network with $N$ users achieves a secure aggregation overhead of $O(N\log {N})$ , as opposed to $O(N^{2})$ , while tolerating up to a user dropout rate of 50%. Turbo-Aggregate employs a multi-group circular strategy for efficient model aggregation, and leverages additive secret sharing and novel coding techniques for injecting aggregation redundancy in order to handle user dropouts while guaranteeing user privacy. We experimentally demonstrate that Turbo-Aggregate achieves a total running time that grows almost linear in the number of users, and provides up to $40\times $ speedup over the state-of-the-art protocols with up to $N=200$ users. Our experiments also demonstrate the impact of model size and bandwidth on the performance of Turbo-Aggregate.

In this paper, we propose coded Merkle tree (CMT), a novel hash accumulator that offers a constant-cost protection against data availability attacks in blockchains, even if the majority of the network nodes are malicious. A CMT is constructed using a family of sparse erasure codes on each layer, and is recovered by iteratively applying a peeling-decoding technique that enables a compact proof for data availability attack on any layer. Our algorithm enables any node to verify the full availability of any data block generated by the system by just downloading a \(\varTheta (1)\) byte block hash commitment and randomly sampling \(\varTheta (\log b)\) bytes, where b is the size of the data block. With the help of only one connected honest node in the system, our method also allows any node to verify any tampering of the coded Merkle tree by just downloading \(\varTheta (\log b)\) bytes. We provide a modular library for CMT in Rust and Python and demonstrate its efficacy inside the Parity Bitcoin client.

Secure federated learning is a privacy-preserving framework to improve machine learning models by training over large volumes of data collected by mobile users. This is achieved through an iterative process where, at each iteration, users update a global model using their local datasets. Each user then masks its local update via random keys, and the masked models are aggregated at a central server to compute the global model for the next iteration. As the local updates are protected by random masks, the server cannot observe their true values. This presents a major challenge for the resilience of the model against adversarial (Byzantine) users, who can manipulate the global model by modifying their local updates or datasets. Towards addressing this challenge, this paper presents the first single-server Byzantine-resilient secure aggregation framework (BREA) for secure federated learning. BREA is based on an integrated stochastic quantization, verifiable outlier detection, and secure model aggregation approach to guarantee Byzantine-resilience, privacy, and convergence simultaneously. We provide theoretical convergence and privacy guarantees and characterize the fundamental trade-offs in terms of the network size, user dropouts, and privacy protection. Our experiments demonstrate convergence in the presence of Byzantine users, and comparable accuracy to conventional federated learning benchmarks.

We consider a basic cache network, in which a single server is connected to multiple users via a shared bottleneck link. The server has a database of files (content). Each user has an isolated memory that can be used to cache content in a prefetching phase. In a following delivery phase, each user requests a file from the database, and the server needs to deliver users’ demands as efficiently as possible by taking into account their cache contents. We focus on an important and commonly used class of prefetching schemes, where the caches are filled with uncoded data. We provide the exact characterization of the rate-memory tradeoff for this problem, by deriving both the minimum average rate (for a uniform file popularity) and the minimum peak rate required on the bottleneck link for a given cache size available at each user. In particular, we propose a novel caching scheme, which strictly improves the state of the art by exploiting commonality among user demands. We then demonstrate the exact optimality of our proposed scheme through a matching converse, by dividing the set of all demands into types, and showing that the placement phase in the proposed caching scheme is universally optimal for all types. Using these techniques, we also fully characterize the rate-memory tradeoff for a decentralized setting, in which users fill out their cache content without any coordination.

We study the Gaussian multiple-input multiple-output multiple-eavesdropper wiretap channel where a transmitter wishes to communicate a confidential message to a legitimate receiver in the presence of eavesdroppers. Each node in the network is equipped with an arbitrary number of antennas. Furthermore, channels are time varying, and there is no channel state information available at the transmitter (CSIT) with respect to eavesdroppers' channels; and transmitter only has access to delayed CSIT of the channel to the legitimate receiver. The secure degrees of freedom (SDoF) for such a network has only been characterized for special cases, and is unknown in general. We completely characterize the SDoF of this network for all antenna configurations. In particular, we strictly improve the state-of-the-art achievable scheme for this network by proposing more efficient artificial noise alignment at the receivers. Furthermore, we develop a tight upper bound by utilizing three important inequalities that provide lower bounds on the received signal dimensions at receivers which supply delayed CSIT or no CSIT. These inequalities together allow for analysis of signal dimensions in networks with heterogeneous CSIT; and as a result, we present a converse proof that leads to characterization of SDoF for all possible antenna configurations.

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 study the symmetric degrees-of-freedom (DoF) of partially connected interference networks under linear coding strategies at transmitters without channel state information beyond topology. We assume that the receivers are equipped with reconfigurable antennas that can switch among their preset modes. In such a network setting, we characterize the class of network topologies in which half linear symmetric DoF is achievable. Moreover, we derive a general upper bound on the linear symmetric DoF for arbitrary network topologies. We also show that this upper bound is tight if the transmitters have at most two co-interferers., Comment: This work will be presented in part at the 2016 IEEE International Symposium on Information Theory (ISIT)

Computing is the next frontier for information theory. Intellectually, the goal of coded computing has been of interest from the days of von Neumann and Shannon. von Neumann examined this issue in his 1956 paper “Probabilistic Logics and the Synthesis of Reliable Organisms From Unreliable Components,” which was in turn motivated intellectually by Shannon’s 1948 paper, and by the application of understanding reliability of seemingly noisy biological systems. While the original biological application remains ill-understood, the recent increasing use of decentralized and distributed computing architectures, as well as increasingly noisy technologies at a device level, have motivated a resurgence of interest in the problem.

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 study the fundamental limits of communications over multi-layer wireless networks where each node has only limited knowledge of the channel state information. In particular, we consider the scenario in which each source-destination pair has only enough information to perform optimally when other pairs do not interfere. Beyond that, the only other information available at each node is the global network connectivity. We propose a transmission strategy that solely relies on the available limited knowledge and combines coding with interference avoidance. We show that our proposed strategy goes well beyond the performance of interference avoidance techniques. We present an algebraic framework for the proposed transmission strategy based on which we provide a guarantee of the achievable rate. For several network topologies, we prove the optimality of our proposed strategy by providing information-theoretic outer-bounds.

We introduce the blind index coding (BIC) problem, in which a single sender communicates distinct messages to multiple users over a shared channel. Each user has partial knowledge of each message as side information. However, unlike classic index coding, in BIC, the sender is uncertain of what side information is available to each user. In particular, the sender only knows the amount of bits in each user's side information but not its content. This problem can arise naturally in caching and wireless networks. In order to blindly exploit side information in the BIC problem, we develop a hybrid coding scheme that XORs uncoded bits of a subset of messages with random combinations of bits from other messages. This scheme allows us to strike the right balance between maximizing the transmission rate to each user and minimizing the interference leakage to others. We also develop a general outer bound, which relies on a strong data processing inequality to effectively capture the senders uncertainty about the users' side information. Additionally, we consider the case where communication takes place over a shared wireless medium, modeled by an erasure broadcast channel, and show that surprisingly, combining repetition coding with hybrid coding improves the achievable rate region and outperforms alternative strategies of coping with channel erasure and while blindly exploiting side information., Parts of this paper were presented at ISIT 2015 and ICC 2015

We study the degrees of freedom (DoFs) of the multiple-input multiple-output X-channel (MIMO XC) with delayed channel state information at the transmitters (delayed CSITs), assuming linear coding strategies at the transmitters. We present two results: 1) the linear sum DoF for MIMO XC with general antenna configurations and 2) the linear DoF region for MIMO XC with symmetric antennas. The converse for each result is based on developing a novel rank-ratio inequality that characterizes the maximum ratio between the dimensions of received linear subspaces at the two multiple-antenna receivers. The achievability of the linear sum DoF is based on a three-phase strategy, in which during the first two phases only the transmitter with fewer antennas exploits delayed CSIT in order to minimize the dimension of its signal at the unintended receiver. During the third phase, both transmitters use delayed CSIT to send linear combinations of past transmissions, such that each receiver receives a superposition of desired message data and known interference, thus simultaneously serving both receivers. We also derive other linear DoF outer bounds for the MIMO XC that, in addition to the outer bounds from the sum DoF converse and the proposed transmission strategy, allow us to characterize the linear DoF region for symmetric antenna configurations.

We study the impact of heterogeneity of channel-state-information available at the transmitters (CSIT) on the capacity of broadcast channels with a multiple-antenna transmitter and $k$ single-antenna receivers (MISO BC). In particular, we consider the $k$-user MISO BC, where the CSIT with respect to each receiver can be either instantaneous/perfect, delayed, or not available; and we study the impact of this heterogeneity of CSIT on the degrees-of-freedom (DoF) of such network. We first focus on the $3$-user MISO BC; and we completely characterize the DoF region for all possible heterogeneous CSIT configurations, assuming linear encoding strategies at the transmitters. The result shows that the state-of-the-art achievable schemes in the literature are indeed sum-DoF optimal, when restricted to linear encoding schemes. To prove the result, we develop a novel bound, called Interference Decomposition Bound, which provides a lower bound on the interference dimension at a receiver which supplies delayed CSIT based on the average dimension of constituents of that interference, thereby decomposing the interference into its individual components. Furthermore, we extend our outer bound on the DoF region to the general $k$-user MISO BC, and demonstrate that it leads to an approximate characterization of linear sum-DoF to within an additive gap of $0.5$ for a broad range of CSIT configurations. Moreover, for the special case where only one receiver supplies delayed CSIT, we completely characterize the linear sum-DoF., submitted to IEEE Transactions on Information Theory; shorter version will be presented at IEEE ISIT, 2015

This paper proposes a privacy-aware framework for distributed semi-supervised learning. In particular, we consider a semi-supervised learning problem where the training data is distributed among multiple data-owners, who wish to protect the privacy of their individual datasets from the other parties during training. We propose a novel framework for protecting the privacy of individual datasets while achieving good accuracy. Then, we characterize the privacy of our framework, by defining a metric that quantifies the number of candidate data points that are consistent with information shared by data-owners. The number of candidates (and thus the privacy) decreases as more information is shared between data-owners, leading to a privacy-utility (accuracy) trade-off. Our experiments show a significant increase in classification accuracy compared to local training, i.e., using the individual datasets only, while the complexity of our approach is significantly lower than that of other benchmarks, such as secure multi-party computing or homomorphic encryption.

In modern distributed computing systems, unpredictable and unreliable infrastructures result in high variability of computing resources. Meanwhile, there is significantly increasing demand for timely and event-driven services with deadline constraints. Motivated by measurements over Amazon EC2 clusters, we consider a two-state Markov model for variability of computing speed in cloud networks. In this model, each worker can be either in a good state or a bad state in terms of the computation speed, and the transition between these states is modeled as a Markov chain which is unknown to the scheduler. We then consider a Coded Computing framework, in which the data is possibly encoded and stored at the worker nodes in order to provide robustness against nodes that may be in a bad state. With timely computation requests submitted to the system with computation deadlines, our goal is to design the optimal computation-load allocation scheme and the optimal data encoding scheme that maximize the timely computation throughput (i.e, the average number of computation tasks that are accomplished before their deadline). Our main result is the development of a dynamic computation strategy called Lagrange Estimate-and Allocate (LEA) strategy, which achieves the optimal timely computation throughput. It is shown that compared to the static allocation strategy, LEA increases the timely computation throughput by 1.4X - 17.5X in various scenarios via simulations and by 1.27X - 6.5X in experiments over Amazon EC2 clusters, to appear in MobiHoc 2019

We consider the problem of distributedly computing a general class of functions, referred to as gradient-type computation, while maintaining the privacy of the input dataset. Gradient-type computation evaluates the sum of some "partial gradients", defined as polynomials of subsets of the input. It underlies many algorithms in machine learning and data analytics. We propose Harmonic Coding, which universally computes any gradient-type function, while requiring the minimum possible number of workers. Harmonic Coding strictly improves computing schemes developed based on prior works, such as Shamir’s secret sharing and Lagrange Coded Computing, by injecting coded redundancy using harmonic progression. It enables the computing results of the workers to be interpreted as the sum of partial gradients and some redundant results, which then allows the cancellation of non-gradient terms in the decoding process. By proving a matching converse, we demonstrate the optimality of Harmonic Coding, even compared to the schemes that are non-universal (i.e., can be designed based on a specific gradient-type function).

We study the problem of verifiable polynomial evaluation in the user-server and multi-party setups. We propose INTERPOL, an information-theoretically verifiable algorithm that allows a user to delegate the evaluation of a polynomial to a server, and verify the correctness of the results with high probability and in sublinear complexity. Compared to the existing approaches which typically rely on cryptographic assumptions, INTERPOL stands out in that it does not assume any computational limitation on the server. INTERPOL relies on decomposition of polynomial evaluation into two matrix multiplications, and injection of computation redundancy in the form of locally computed parities with secret coefficients for verification. Furthermore, by generalizing INTERPOL to a multiparty setting consisting of a network of n untrusted nodes, where each node is interested in evaluating the same polynomial, we demonstrate that we can achieve an overall computational complexity comparable to a trusted setup, while guaranteeing information-theoretic verification at each node.

Scaling up distributed machine learning systems face two major bottlenecks – delays due to stragglers and limited communication bandwidth. Recently, a number of coding theoretic strategies have been proposed for mitigating these bottlenecks. In particular, the Gradient Coding (GC) scheme was proposed to speed up distributed gradient descent algorithm in a synchronous master-worker setting by providing robustness to stragglers. A major drawback of the master-worker architecture for distributed learning is however, the bandwidth contention at the master, which can significantly deteriorate the performance as the cluster size increases. In this paper, we propose a new framework named Tree Gradient Coding (TGC) for distributed gradient aggregation, which parallelizes communication over a tree topology while providing straggler robustness. As our main contribution, we characterize the minimum computation load for TGC for a given tree topology and straggler resiliency, and design a tree gradient coding algorithm that achieves this optimal computation load. Furthermore, we provide results from experiments over Amazon EC2, where TGC speeds up the training time by up to 18.8× in comparison to GC.

Lagrange Coded Computing (LCC) is a recently proposed technique for resilient, secure, and private computation of arbitrary polynomials in distributed environments. By mapping such computations to composition of polynomials, LCC allows the master node to complete the computation by accessing a minimal number of workers and downloading all of their content, thus providing resiliency to the remaining stragglers. However, in the most common case in which the number of stragglers is less than in the worst case scenario, much of the computational power of the system remains unexploited. To amend this issue, in this paper we expand LCC by studying a fundamental trade-off between download and access, and present two contributions. In the first contribution, it is shown that without any modification to the encoding process, the master can decode the computations by accessing a larger number of nodes, however downloading less information from each node in comparison with LCC (i.e., trading access for download). This scheme relies on decoding a particular polynomial in the ideal that is generated by the polynomials of interest, a technique we call Ideal Decoding. This new scheme also improves LCC in the sense that for systems with adversaries, the overall downloaded bandwidth is smaller than in LCC. In the second contribution we study a real-time model of this trade-off, in which the data from the workers is downloaded sequentially. By clustering nodes of similar delays and encoding the function with Universally Decodable Matrices, the master can decode once sufficient data is downloaded from every cluster, regardless of the internal delays within that cluster. This allows the master to utilize the partial work that is done by stragglers, rather than to ignore it, a feature that most past works in coded computing are lacking.

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.

This paper considers the graph signal sampling problem when some of the selected samples are lost or unavailable due to sensor failures or adversarial erasures. We formulate a robust graph signal sampling problem where only a subset of selected samples are received, and the goal is to maximize the worst-case performance. We propose a novel greedy robust sample selection algorithm and study its performance guarantees. Our numerical results demonstrate the performance improvement of the proposed algorithm over the existing schemes.

While performing distributed computations in today's cloud-based platforms, execution speed variations among compute nodes can significantly reduce the performance and create bottlenecks like stragglers. Coded computation techniques leverage coding theory to inject computational redundancy and mitigate stragglers in distributed computations. In this paper, we propose a dynamic workload distribution strategy for coded computation called Slack Squeeze Coded Computation ($S^2C^2$). $S^2C^2$ squeezes the compute slack (i.e., overhead) that is built into the coded computing frameworks by efficiently assigning work for all fast and slow nodes according to their speeds and without needing to re-distribute data. We implement an LSTM-based speed prediction algorithm to predict speeds of compute nodes. We evaluate $S^2C^2$ on linear algebraic algorithms, gradient descent, graph ranking, and graph filtering algorithms. We demonstrate 19% to 39% reduction in total computation latency using $S^2C^2$ compared to job replication and coded computation. We further show how $S^2C^2$ can be applied beyond matrix-vector multiplication., 13 pages, SC 2019

We focus on the commonly used synchronous Gradient Descent paradigm for large-scale distributed learning, for which there has been a growing interest to develop efficient and robust gradient aggregation strategies that overcome two key system bottlenecks: communication bandwidth and stragglers' delays. In particular, Ring-AllReduce (RAR) design has been proposed to avoid bandwidth bottleneck at any particular node by allowing each worker to only communicate with its neighbors that are arranged in a logical ring. On the other hand, Gradient Coding (GC) has been recently proposed to mitigate stragglers in a master-worker topology by allowing carefully designed redundant allocation of the data set to the workers. We propose a joint communication topology design and data set allocation strategy, named CodedReduce (CR), that combines the best of both RAR and GC. That is, it parallelizes the communications over a tree topology leading to efficient bandwidth utilization, and carefully designs a redundant data set allocation and coding strategy at the nodes to make the proposed gradient aggregation scheme robust to stragglers. In particular, we quantify the communication parallelization gain and resiliency of the proposed CR scheme, and prove its optimality when the communication topology is a regular tree. Moreover, we characterize the expected run-time of CR and show order-wise speedups compared to the benchmark schemes. Finally, we empirically evaluate the performance of our proposed CR design over Amazon EC2 and demonstrate that it achieves speedups of up to 27.2x and 7.0x, respectively over the benchmarks GC and RAR., Final version to appear in IEEE Transactions on Networking

We consider the problem of secure and private multiparty computation (MPC), in which the goal is to compute a general polynomial function distributedly over several workers, while keeping them oblivious to the content of the dataset, and preventing them from maliciously affecting the computation result. We demonstrate the role of Lagrange Coded Computing (LCC), a recently proposed coded computing technique that can be applied to general polynomial computations, on enabling secure and private MPC. We show that LCC offers both private and secure computation simultaneously, and is universal in the sense that all polynomials up to a certain degree can be computed on the same encoding. We also demonstrate that LCC achieves an optimal tradeoff between privacy and security, and requires a minimal amount of added randomness for privacy. Compared to prevalent algorithms in MPC (in particular the celebrated BGW scheme), we show that LCC significantly improves the storage, communication, and secret-sharing overhead needed for MPC.

We consider the problem of massive matrix multiplication, which underlies many data analytic applications, in a large-scale distributed system comprising a group of worker nodes. We target the stragglers' delay performance bottleneck, which is due to the unpredictable latency in waiting for slowest nodes (or stragglers) to finish their tasks. We propose a novel coding strategy, named \emph{entangled polynomial code}, for designing the intermediate computations at the worker nodes in order to minimize the recovery threshold (i.e., the number of workers that we need to wait for in order to compute the final output). We demonstrate the optimality of entangled polynomial code in several cases, and show that it provides orderwise improvement over the conventional schemes for straggler mitigation. Furthermore, we characterize the optimal recovery threshold among all linear coding strategies within a factor of $2$ using \emph{bilinear complexity}, by developing an improved version of the entangled polynomial code. In particular, while evaluating bilinear complexity is a well-known challenging problem, we show that optimal recovery threshold for linear coding strategies can be approximated within a factor of $2$ of this fundamental quantity. On the other hand, the improved version of the entangled polynomial code enables further and orderwise reduction in the recovery threshold, compared to its basic version. Finally, we show that the techniques developed in this paper can also be extended to several other problems such as coded convolution and fault-tolerant computing, leading to tight characterizations.

A new class of caching schemes, called coded caching, can significantly reduce the communication bandwidth requirement for satisfying users' demands by utilizing the multicasting gain among multiple users. Most existing works assume that the users follow the prescriptions for content placement made by the system. However, users may prefer to decide what files to cache or discard some part of their caches due to lack of space. In order to address this issue, we study a caching system where the content placement phase has been already carried out by the users arbitrarily. More specifically, we consider a network consisting of a file server connected through a shared link to $K$ users, each equipped with a cache. Given arbitrary content placement by the users, the goal is to find a coded multicast strategy for the server that minimizes the load of the shared link. We first formulate the optimal coded multicast design problem as an Integer Linear Program (ILP). Using a connection with the weighted set cover problem, we propose an approximation algorithm for solving this problem. We show that our proposed algorithm provides $(1 + \log K)$-approximation for the optimal coded multicast design problem, while the approximation ratio for the existing coded delivery schemes is linear in $K$. Numerical simulations show that our proposed algorithm provides a considerable bandwidth reduction over the existing coded delivery schemes for uniformly-random generated content placement.

There is a growing interest in development of in-network dispersed computing paradigms that leverage the computing capabilities of heterogeneous resources dispersed across the network for processing massive amount of data is collected at the edge of the network. We consider the problem of task scheduling for such networks, in a dynamic setting in which arriving computation jobs are modeled as chains, with nodes representing tasks, and edges representing precedence constraints among tasks. In our proposed model, motivated by significant communication costs in dispersed computing environments, the communication times are taken into account. More specifically, we consider a network where servers are capable of serving all task types, and sending the results of processed tasks from one server to another server results in some communication delay that makes the design of optimal scheduling policy significantly more challenging than classical queueing networks. As the main contributions of the paper, we first characterize the capacity region of the network, then propose a novel virtual queueing network encoding the state of the network. Finally, we propose a Max-Weight type scheduling policy, and considering the virtual queueing network in the fluid limit, we use a Lyapunov argument to show that the policy is throughput-optimal., accepted to appear in IEEE/ACM Transactions on Networking

Solving a large-scale system of linear equations is a key step at the heart of many algorithms in scientific computing, machine learning, and beyond. When the problem dimension is large, computational and/or memory constraints make it desirable, or even necessary, to perform the task in a distributed fashion. In this paper, we consider a common scenario in which a taskmaster intends to solve a large-scale system of linear equations by distributing subsets of the equations among a number of computing machines/cores. We propose a new algorithm called Accelerated Projection-based Consensus , in which at each iteration every machine updates its solution by adding a scaled version of the projection of an error signal onto the nullspace of its system of equations, and the taskmaster conducts an averaging over the solutions with momentum. The convergence behavior of the proposed algorithm is analyzed in detail and analytically shown to compare favorably with the convergence rate of alternative distributed methods, namely distributed gradient descent, distributed versions of Nesterov's accelerated gradient descent and heavy-ball method, the block Cimmino method, and Alternating Direction Method of Multipliers. On randomly chosen linear systems, as well as on real-world data sets, the proposed method offers significant speed-up relative to all the aforementioned methods. Finally, our analysis suggests a novel variation of the distributed heavy-ball method, which employs a particular distributed preconditioning and achieves the same theoretical convergence rate as that in the proposed consensus-based method.

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

Dealing with the shear size and complexity of today’s massive data sets requires computational platforms that can analyze data in a parallelized and distributed fashion. A major bottleneck that arises in such modern distributed computing environments 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. A recent computational framework, called encoded optimization, creates redundancy in the data to mitigate the effect of stragglers. In this paper, we develop novel mathematical understanding for this framework demonstrating its effectiveness in much broader settings than was previously understood. We also analyze the convergence behavior of iterative encoded optimization algorithms, allowing us to characterize fundamental trade-offs between convergence rate, size of data set, accuracy, computational load (or data redundancy) and straggler toleration in this framework.

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.

Performance of distributed graph processing systems significantly suffers from 'communication bottleneck' as a large number of messages are exchanged among servers at each step of the computation. Motivated by graph based MapReduce, we propose a coded computing framework that leverages computation redundancy to alleviate the communication bottleneck in distributed graph processing. We develop a novel 'coding' scheme that systematically injects structured redundancy in computation phase to enable 'coded' multicasting opportunities during message exchange between servers, reducing communication load substantially in large-scale graph processing. For theoretical analysis, we consider random graph models, and prove that our proposed scheme enables an (asymptotically) inverse-linear trade-off between 'computation load' and 'average communication load' for two popular random graph models -- Erdos-Renyi model, and power law model. Particularly, for a given computation load r, (i.e. when each graph vertex is carefully stored at r servers), the proposed scheme slashes the average communication load by (nearly) a multiplicative factor of r. For the Erdos-Renyi model, our proposed scheme is optimal asymptotically as the graph size increases by providing an information-theoretic converse. To illustrate the benefits of our scheme in practice, we implement PageRank over Amazon EC2, using artificial as well as real-world datasets, demonstrating significant gains over conventional PageRank. We also specialize our scheme and extend our theoretical results to two other random graph models -- random bi-partite model, and stochastic block model. They asymptotically enable inverse-linear trade-offs between computation and communication loads in distributed graph processing for these popular random graph models as well. We complement the achievability results with converse bounds for both of these models., Comment: Accepted for publication in the IEEE Transactions on Information Theory