Distributed databases often suffer unequal distribution of data among storage nodes, which is known as `data skew'. Data skew arises from a number of causes such as removal of existing storage nodes and addition of new empty nodes to the database. Data skew leads to performance degradations and \textcolor{black}{thus} necessitates `rebalancing' at regular intervals to reduce the amount of skew. We define an $r$-balanced distributed database as a distributed database in which the storage across the nodes has uniform size, and each bit of the data is replicated in $r$ distinct storage nodes. We consider the problem of designing such balanced databases along with associated rebalancing schemes which maintain the $r$-balanced property under node removal and addition operations. We present a class of $r$-balanced databases (parameterized by the number of storage nodes) which have the property of structural invariance, i.e., the databases designed for different number of storage nodes have the same essential structure. For this class of $r$-balanced databases, we present rebalancing schemes which use coded transmissions between storage nodes, and characterize their communication loads under node addition and removal. We show that the communication cost incurred to rebalance our distributed database for node addition and removal is optimal, i.e., it achieves the minimum possible cost among all possible balanced distributed databases and rebalancing schemes.
The performance of replication-based distributed databases is affected due to non-uniform storage across storage nodes (also called \textit{data skew}) and reduction in the replication factor during operation, particularly due to node additions or removals. Data rebalancing refers to the communication involved between the nodes in correcting this data skew, while maintaining the replication factor. For carefully designed distributed databases, transmitting coded symbols during the rebalancing phase has been recently shown to reduce the communication load of rebalancing. In this work, we look a…
Coded Data Rebalancing for Distributed Data Storage Systems with Cyclic Storage
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院数学系）；Instituto de Telecomunicações（电信研究所）；International Institute of Information Technology, Hyderabad（海得拉巴国际信息技术学院）；Indian Institute of Science, Bengaluru（班加罗尔印度理工学院）；Qualcomm, Hyderabad（高通（海得拉巴））
Caching is a technique to reduce the communication load in peak hours by prefetching contents during off-peak hours. An information-theoretic framework for coded caching was introduced by Maddah-Ali and Niesen in a recent work, where it was shown that significant improvement can be obtained compared to uncoded caching. Considerable efforts have been devoted to identify the precise information-theoretic fundamental limits of the coded caching systems, however the difficulty of this task has also become clear. One of the reasons for this difficulty is that the original coded caching setting allo…
Fundamental Limits of Coded Caching: Improved Delivery Rate-Cache Capacity Trade-off
一个集中式编码缓存系统，包括一个服务器提供N个流行的文件，每个大小F位，K个用户通过一个无错误的共享链接，被认为是。假设每个用户都配备有具有容量MF位的本地高速缓存存储器，并且内容可以在低流量时段内主动地高速缓存到这些高速缓存中;然而，无需了解用户需求。在流量高峰期，每个用户从服务器请求单个文件。目标是在所有用户需求组合中，最小化服务器在共享链路上传输的比特数（称为传输速率）。提出了一种新的缓存容量为M=（N-1）/K的编码缓存方案。当K > N >= 3时，该方案比文献中已有的编码缓存方案具有更小的传输速率。此外，我们认为，所提出的方案的交付率是在一个常数乘法因子2的最佳交付率的缓存容量1/K <= M <=（N-1）/K，当K > N >= 3。
Coded caching utilizes proper file subpacketization and coded delivery to make full use of the multicast opportunities in content delivery, to alleviate file transfer load in massive content delivery scenarios. Most existing work considers deterministic environments. An important practical topic is to characterize the impact of the uncertainty from user inactivity on coded caching. We consider a one server cache-enabled network under homogeneous file and network settings in presence of user inactivity. Unlike random or probabilistic caching studied in the literature, deterministic coded cachin…
We consider the coded caching problem with an additional privacy constraint that a user should not get any information about the demands of the other users. We first show that a demand-private scheme for $N$ files and $K$ users can be obtained from a non-private scheme that serves only a subset of the demands for the $N$ files and $NK$ users problem. We further use this fact to construct a demand-private scheme for $N$ files and $K$ users from a particular known non-private scheme for $N$ files and $NK-K+1$ users. It is then demonstrated that, the memory-rate pair $(M,\min \{N,K\}(1-M/N))$, wh…
In the coded caching problem, as originally formulated by Maddah-Ali and Niesen, a server communicates via a noiseless shared broadcast link to multiple users that have local storage capability. In order for a user to decode its demanded file from the coded multicast transmission, the demands of all the users must be globally known, which may violate the privacy of the users. To overcome this privacy problem, Wan and Caire recently proposed several schemes that attain coded multicasting gain while simultaneously guarantee information theoretic privacy of the users' demands. In Device-to-Device…
This paper studies the caching system of multiple cache-enabled users with random demands. Under nonuniform file popularity, we thoroughly characterize the optimal uncoded cache placement structure for the coded caching scheme (CCS). Formulating the cache placement as an optimization problem to minimize the average delivery rate, we identify the file group structure in the optimal solution. We show that, regardless of the file popularity distribution, there are \emph{at most three file groups} in the optimal cache placement{, where files within a group have the same cache placement}. We furthe…
Decentralized coded caching scheme, introduced by Maddah-Ali and Niesen, assumes that the caches are filled with no coordination. This work identifies a decentralized coded caching scheme -- under the assumption of uncoded placement -- for shared cache network, where each cache serves multiple users. Each user has access to only a single cache and the number of caches is less than or equal to the number of users. For this setting, we derive the optimal worst-case delivery time for any user-to-cache association profile where each such profile describes the number of users served by each cache. …
We address the worst-user bottleneck of wireless coded caching, which is known to severely diminish cache-aided multicasting gains due to the fundamental worst-channel limitation of multicasting transmission. We consider the quasi-static Rayleigh fading Broadcast Channel, for which we first show that the effective coded caching gain of the XOR-based standard coded-caching scheme completely vanishes in the low-SNR regime. Then, we reveal that this collapse is not intrinsic to coded caching. We do so by presenting a novel scheme that can fully recover the coded caching gains by capitalizing on o…
Coded distributed computing can alleviate the communication load by leveraging the redundant storage and computation resources with coding techniques in distributed computing. In this paper, we study a MapReduce-type distributed computing framework over star topological network, where all the workers exchange information through a common access point. The optimal tradeoff among the normalized number of the stored files (storage load), computed intermediate values (computation load) and transmitted bits in the uplink and downlink (communication loads) are characterized. A coded computing scheme…
Li {\it et al}. introduced coded distributed computing (CDC) scheme to reduce the communication load in general distributed computing frameworks such as MapReduce. They also proposed cascaded CDC schemes where each output function is computed multiple times, and proved that such schemes achieved the fundamental trade-off between computation load and communication load. However, these schemes require exponentially large numbers of input files and output functions when the number of computing nodes gets large. In this paper, by using the structure of placement delivery arrays (PDAs), we construc…
Recently, Muralidhar et al. proposed a novel multi-access system model where each user is connected to multiple caches in a manner that follows the well-known combinatorial topology of combination networks. For such multi-access topology, the same authors proposed an achievable scheme, which stands out for the unprecedented coding gains even with very modest cache resources. In this paper, we identify the fundamental limits of such multi-access setting with exceptional potential, providing an information-theoretic converse which establishes, together with the inner bound by Muralidhar et al., …
We consider the data shuffling problem in a distributed learning system, in which a master node is connected to a set of worker nodes, via a shared link, in order to communicate a set of files to the worker nodes. The master node has access to a database of files. In every shuffling iteration, each worker node processes a new subset of files, and has excess storage to partially cache the remaining files, assuming the cached files are uncoded. The caches of the worker nodes are updated every iteration, and they should be designed to satisfy any possible unknown permutation of the files in subse…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed nodes. The goal is to reduce the average execution time of the computational job. We provide a connection between the problem of characterizing the average execution time of a coded distributed computing system and the problem of analyzing the error probability of codes of length $n$ used over erasure channels. Accordingly, we present closed-form expressions for…
Erasure coding has been recognized as a powerful method to mitigate delays due to slow or straggling nodes in distributed systems. This work shows that erasure coding of data objects can flexibly handle skews in the request rates. Coding can help boost the \emph{service rate region}, that is, increase the overall volume of data access requests that the system can handle. This paper aims to postulate the service rate region as an important consideration in the design of erasure-coded distributed systems. We highlight several open problems that can be grouped into two broad threads: 1) character…
This work studies a well-known shared-cache coded caching scenario where each cache can serve an arbitrary number of users, analyzing the case where there is some knowledge about such number of users (i.e., the topology) during the content placement phase. Under the assumption of regular placement and a cumulative cache size that can be optimized across the different caches, we derive the fundamental limits of performance by introducing a novel cache-size optimization and placement scheme and a novel information-theoretic converse. The converse employs new index coding techniques to bypass tra…
University of Michigan（密歇根大学）；University of Southern California（南加州大学）
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 b…
This work identifies the fundamental limits of Multi-Access Coded Caching (MACC) where each user is connected to multiple caches in a manner that follows a generalized combinatorial topology. This topology stands out as it allows for unprecedented coding gains, even with very modest cache resources. First, we extend the setting and the scheme presented by Muralidhar et al. to a much more general topology that supports both a much denser range of users and the coexistence of users connected to different numbers of caches, all while maintaining the astounding coding gains, here proven to be exac…
The work establishes the exact performance limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. Under the premise that more balanced user-to-cache associations perform better than unbalanced ones, our work provides a statistical analysis of the average performance of such networks, identifying in closed form, the exact optimal average delivery time. To insightfully capture this delay, we derive easy to compute closed-form analytical bounds that prove tight in the limit of a large number $Λ$ of cache …
This work investigates the problem of demand privacy against colluding users for shared-link coded caching systems, where no subset of users can learn any information about the demands of the remaining users. The notion of privacy used here is stronger than similar notions adopted in past work and is motivated by the practical need to insure privacy regardless of the file distribution. Two scenarios are considered: Single File Retrieval (SFR) and Linear Function Retrieval (LFR), where in the latter case each user demands an arbitrary linear combination of the files at the server. The main cont…
