arXiv subjects

Mingyue Ji

Publications and source records attributed to Mingyue Ji.

At least 73 records · Page 4Linked to original sources

arXiv2020

Coded Elastic Computing on Machines with Heterogeneous Storage and Computation Speed

We study the optimal design of heterogeneous Coded Elastic Computing (CEC) where machines have varying computation speeds and storage. CEC introduced by Yang et al. in 2018 is a framework that mitigates the impact of elastic events, where machines can join and leave at arbitrary times. In CEC, data is distributed among machines using a Maximum Distance Separable (MDS) code such that subsets of machines can perform the desired computations. However, state-of-the-art CEC designs only operate on homogeneous networks where machines have the same speeds and storage. This may not be practical. In this work, based on an MDS storage assignment, we develop a novel computation assignment approach for heterogeneous CEC networks to minimize the overall computation time. We first consider the scenario where machines have heterogeneous computing speeds but same storage and then the scenario where both heterogeneities are present. We propose a novel combinatorial optimization formulation and solve it exactly by decomposing it into a convex optimization problem for finding the optimal computation load and a "filling problem" for finding the exact computation assignment. A low-complexity "filling algorithm" is adapted and can be completed within a number of iterations equals at most the number of available machines.

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arXiv2020

A Combinatorial Design for Cascaded Coded Distributed Computing on General Networks

Coding theoretic approached have been developed to significantly reduce the communication load in modern distributed computing system. In particular, coded distributed computing (CDC) introduced by Li et al. can efficiently trade computation resources to reduce the communication load in MapReduce like computing systems. For the more general cascaded CDC, Map computations are repeated at r nodes to significantly reduce the communication load among nodes tasked with computing Q Reduce functions s times. In this paper, we propose a novel low-complexity combinatorial design for cascaded CDC which 1) determines both input file and output function assignments, 2) requires significantly less number of input files and output functions, and 3) operates on heterogeneous networks where nodes have varying storage and computing capabilities. We provide an analytical characterization of the computation-communication tradeoff, from which we show the proposed scheme can outperform the state-of-the-art scheme proposed by Li et al. for the homogeneous networks. Further, when the network is heterogeneous, we show that the performance of the proposed scheme can be better than its homogeneous counterpart. In addition, the proposed scheme is optimal within a constant factor of the information theoretic converse bound while fixing the input file and the output function assignments.

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arXiv2020

A New Combinatorial Coded Design for Heterogeneous Distributed Computing

Coded Distributed Computing (CDC) introduced by Li et al. in 2015 offers an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce and Spark. In particular, increasing the computation load in the Map phase by a factor of r can create coded multicasting opportunities to reduce the communication load in the Shuffle phase by the same factor. However, the CDC scheme is designed for the homogeneous settings, where the storage, computation load and communication load on the computing nodes are the same. In addition, it requires an exponentially large number of input files (data batches), reduce functions and multicasting groups relative to the number of nodes to achieve the promised gain. We address the CDC limitations by proposing a novel CDC approach based on a combinatorial design, which accommodates heterogeneous networks where nodes have varying storage and computing capabilities. In addition, the proposed approach requires an exponentially less number of input files compared to the original CDC scheme proposed by Li et al. Meanwhile, the resulting computation-communication trade-off maintains the multiplicative gain compared to conventional uncoded unicast and asymptotically achieves the optimal performance proposed by Li et al.

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arXiv2020

A New Design Framework on Device-to-Device Coded Caching with Optimal Rate and Significantly Less Subpacketizations

In this paper, we propose a new design framework on Device-to-Device (D2D) coded caching networks with optimal rate but significantly less file subpacketizations compared to that of the well-known D2D coded caching scheme proposed by Ji, Caire and Molisch (JCM). The proposed design framework is referred to as the {\em Packet Type-based (PTB) design}, where D2D users are first partitioned into multiple groups, which leads to a so-called {\em raw packet saving gain}. Then the corresponding multicasting group types and packet types are specified based on the prescribed node partition. By a careful selection of transmitters within each multicasting group, a so-called {\em further splitting ratio gain} can also be achieved. By the joint effect of the {\em raw packet saving gain} and the {\em further splitting ratio gain}, an order-wise subpacketization reduction can be achieved compared to the JCM scheme while preserving the optimal rate for large system parameter regimes. In addition, as the first time presented in the literature according to our knowledge, we find that unequal subpacketizaton is a key to achieve a subpacketization gain when the number of users is odd. As a by-product, instead of directly translating shared link caching schemes to D2D caching schemes, at least for the sake of subpackeitzations, a new design framework is indeed needed.

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arXiv2020

Topological Coded Distributed Computing

This paper considers the MapReduce-like coded distributed computing framework originally proposed by Li et al., which uses coding techniques when distributed computing servers exchange their computed intermediate values, in order to reduce the overall traffic load. Their original model servers are connected via an error-free common communication bus allowing broadcast transmissions. However, this assumption is one of the major limitations in practice since the practical cloud computing network topologies are far more involved than a simple single bus. We formulate a topological coded distributed computing problem, where the distributed servers communicate with each other through some switch network. By using a special instance of fat-tree topologies, referred to as t-ary fat-tree proposed by Al-Fares et al. which can be built by some cheap switches, we propose a coded distributed computing scheme to achieve the minimum max-link communication load defined as the maximum load over all links.

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arXiv2020

Cache-Aided Modulation for Heterogeneous Coded Caching over a Gaussian Broadcast Channel

Coded caching is an information theoretic scheme to reduce high peak hours traffic by partially prefetching files in the users local storage during low peak hours. This paper considers heterogeneous decentralized caching systems where cache of users and content library files may have distinct sizes. The server communicates with the users through a Gaussian broadcast channel. The main contribution of this paper is a novel modulation strategy to map the multicast messages generated in the coded caching delivery phase to the symbols of a signal constellation, such that users can leverage their cached content to demodulate the desired symbols with higher reliability. For the sake of simplicity, in this paper we focus only on uncoded modulation and symbol-by-symbol error probability. However, our scheme in conjunction with multilevel coded modulation can be extended to channel coding over a larger block lengths.

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arXiv2020

Fundamental Limits of Decentralized Data Shuffling

Data shuffling of training data among different computing nodes (workers) has been identified as a core element to improve the statistical performance of modern large-scale machine learning algorithms. Data shuffling is often considered as one of the most significant bottlenecks in such systems due to the heavy communication load. Under a master-worker architecture (where a master has access to the entire dataset and only communication between the master and the workers is allowed) coding has been recently proved to considerably reduce the communication load. This work considers a different communication paradigm referred to as decentralized data shuffling, where workers are allowed to communicate with one another via a shared link. The decentralized data shuffling problem has two phases: workers communicate with each other during the data shuffling phase, and then workers update their stored content during the storage phase. The main challenge is to derive novel converse bounds and achievable schemes for decentralized data shuffling by considering the asymmetry of the workers' storages (i.e., workers are constrained to store different files in their storages based on the problem setting), in order to characterize the fundamental limits of this problem. For the case of uncoded storage (i.e., each worker directly stores a subset of bits of the dataset), this paper proposes converse and achievable bounds (based on distributed interference alignment and distributed clique-covering strategies) that are within a factor of 3/2 of one another. The proposed schemes are also exactly optimal under the constraint of uncoded storage for either large storage size or at most four workers in the system.

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arXiv2020

Heterogeneous Computation Assignments in Coded Elastic Computing

We study the optimal design of a heterogeneous coded elastic computing (CEC) network where machines have varying relative computation speeds. CEC introduced by Yang {\it et al.} is a framework which mitigates the impact of elastic events, where machines join and leave the network. A set of data is distributed among storage constrained machines using a Maximum Distance Separable (MDS) code such that any subset of machines of a specific size can perform the desired computations. This design eliminates the need to re-distribute the data after each elastic event. In this work, we develop a process for an arbitrary heterogeneous computing network to minimize the overall computation time by defining an optimal computation load, or number of computations assigned to each machine. We then present an algorithm to define a specific computation assignment among the machines that makes use of the MDS code and meets the optimal computation load.

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arXiv2020

On Optimal Load-Memory Tradeoff of Cache-Aided Scalar Linear Function Retrieval

Coded caching has the potential to greatly reduce network traffic by leveraging the cheap and abundant storage available in end-user devices so as to create multicast opportunities in the delivery phase. In the seminal work by Maddah-Ali and Niesen (MAN), the shared-link coded caching problem was formulated, where each user demands one file (i.e., single file retrieval). This paper generalizes the MAN problem so as to allow users to request scalar linear functions of the files. This paper proposes a novel coded delivery scheme that, based on MAN uncoded cache placement, is shown to allow for the decoding of arbitrary scalar linear functions of the files (on arbitrary finite fields). Interestingly, and quite surprisingly, it is shown that the load for cache-aided scalar linear function retrieval depends on the number of linearly independent functions that are demanded, akin to the cache-aided single-file retrieval problem where the load depends on the number of distinct file requests. The proposed scheme is optimal under the constraint of uncoded cache placement, in terms of worst-case load, and within a factor 2 otherwise. The key idea of this paper can be extended to all scenarios which the original MAN scheme has been extended to, including demand-private and/or device-to-device settings.

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arXiv2019

Private Information Retrieval from Heterogeneous Uncoded Storage Constrained Databases with Reduced Sub-Messages

We propose capacity-achieving schemes for private information retrieval (PIR) from uncoded databases (DBs) with both homogeneous and heterogeneous storage constraints. In the PIR setting, a user queries a set of DBs to privately download a message, where privacy implies that no one DB can infer which message the user desires. In general, a PIR scheme is comprised of storage placement and delivery designs. Previous works have derived the capacity, or infimum download cost, of PIR with uncoded storage placement and also sufficient conditions of a storage placement design to meet capacity. However, the currently proposed storage placement designs require splitting each message into an exponential number of sub-messages with respect to the number of DBs. In this work, when DBs have the same storage constraint, we propose two simple storage placement designs that satisfy the capacity conditions. Then, for more general heterogeneous storage constraints, we translate the storage placement design process into a "filling problem". We design an iterative algorithm to solve the filling problem where, in each iteration, messages are partitioned into sub-messages and stored at subsets of DBs. All of our proposed storage placement designs require a number of sub-messages per message at most equal to the number of DBs.

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arXiv2019

Towards Practical File Packetizations in Wireless Device-to-Device Caching Networks

We consider wireless device-to-device (D2D) caching networks with single-hop transmissions. Previous work has demonstrated that caching and coded multicasting can significantly increase per user throughput. However, the state-of-the-art coded caching schemes for D2D networks are generally impractical because content files are partitioned into an exponential number of packets with respect to the number of users if both library and memory sizes are fixed. In this paper, we present two combinatorial approaches of D2D coded caching network design with reduced packetizations and desired throughput gain compared to the conventional uncoded unicasting. The first approach uses a "hypercube" design, where each user caches a "hyperplane" in this hypercube and the intersections of "hyperplanes" represent coded multicasting codewords. In addition, we extend the hypercube approach to a decentralized design. The second approach uses the Ruzsa-Szeméredi graph to define the cache placement. Disjoint matchings on this graph represent coded multicasting codewords. Both approaches yield an exponential reduction of packetizations while providing a per-user throughput that is comparable to the state-of-the-art designs in the literature. Furthermore, we apply spatial reuse to the new D2D network designs to further reduce the required packetizations and significantly improve per user throughput for some parameter regimes.

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arXiv2019

On the Fundamental Limits of Fog-RAN Cache-aided Networks with Downlink and Sidelink Communications

Maddah-Ali and Niesen (MAN) in 2014 showed that coded caching in single bottleneck-link broadcast networks allows serving an arbitrarily large number of cache-equipped users with a total link load (bits per unit time) that does not scale with the number of users. Since then, the general topic of coded caching has generated enormous interest both from the information theoretic and (network) coding theoretic viewpoint, and from the viewpoint of applications. Building on the MAN work, this paper considers a particular network topology referred to as cache-aided Fog Radio Access Network (Fog-RAN), that includes a Macro-cell Base Station (MBS) co-located with the content server, several cache-equipped Small-cell Base Stations (SBSs), and many users without caches. Some users are served directly by the MBS broadcast downlink, while other users are served by the SBSs. The SBSs can also exchange data via rounds of direct communication via a side channel, referred to as "sidelink". For this novel Fog-RAN model, the fundamental tradeoff among (a) the amount of cache memory at the SBSs, (b) the load on the downlink (from MBS to directly served users and SBSs), and (c) the aggregate load on the sidelink is studied, under the standard worst-case demand scenario. Several existing results are recovered as special cases of this network model and byproduct results of independent interest are given. Finally, the role of topology-aware versus topology-agnostic caching is discussed.

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arXiv2019

Performance of Caching-Based D2D Video Distribution with Measured Popularity Distributions

On-demand video accounts for the majority of wireless data traffic. Video distribution schemes based on caching combined with device-to-device (D2D) communications promise order-of-magnitude greater spectral efficiency for video delivery, but hinge on the principle of `concentrated demand distributions.' This paper presents, for the first time, the analysis and evaluations of the throughput--outage tradeoff of such schemes based on measured cellular demand distributions. In particular, we use a dataset with more than 100 million requests from the BBC iPlayer, a popular video streaming service in the U.K., as the foundation of the analysis and evaluations. We present an achievable scaling law based on the practical popularity distribution, and show that such scaling law is identical to those reported in the literature. We find that also for the numerical evaluations based on a realistic setup, order-of-magnitude improvements can be achieved. Our results indicate that the benefits promised by the caching-based D2D in the literature could be retained for cellular networks in practice.

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arXiv2019

Coded Distributed Computing with Heterogeneous Function Assignments

Coded distributed computing (CDC) introduced by Li et. al. is an effective technique to trade computation load for communication load in a MapReduce framework. CDC achieves an optimal trade-off by duplicating map computations at $r$ computing nodes to yield multicasting opportunities such that $r$ nodes are served simultaneously in the Shuffle phase. However, in general, the state-of-the-art CDC scheme is mainly designed only for homogeneous networks, where the computing nodes are assumed to have the same storage, computation and communication capabilities. In this work, we explore two novel approaches of heterogeneous CDC design. First, we study CDC schemes which operate on multiple, collaborating homogeneous computing networks. Second, we allow heterogeneous function assignment in the CDC design, where nodes are assigned a varying number of reduce functions. Finally, we propose an expandable heterogeneous CDC scheme where $r-1$ nodes are served simultaneously in the Shuffle phase. In comparison to the state-of-the-art homogeneous CDC scheme with an equivalent computation load, we find our newly proposed heterogeneous CDC scheme has a smaller communication load in some cases.

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arXiv2019

Markov Decision Policies for Dynamic Video Delivery in Wireless Caching Networks

This paper proposes a video delivery strategy for dynamic streaming services which maximizes time-average streaming quality under a playback delay constraint in wireless caching networks. The network where popular videos encoded by scalable video coding are already stored in randomly distributed caching nodes is considered under adaptive video streaming concepts, and distance-based interference management is investigated in this paper. In this network model, a streaming user makes delay-constrained decisions depending on stochastic network states: 1) caching node for video delivery, 2) video quality, and 3) the quantity of video chunks to receive. Since wireless link activation for video delivery may introduce delays, different timescales for updating caching node association, video quality adaptation, and chunk amounts are considered. After associating with a caching node for video delivery, the streaming user chooses combinations of quality and chunk amounts in the small timescale. The dynamic decision making process for video quality and chunk amounts at each slot is modeled using Markov decision process, and the caching node decision is made based on the framework of Lyapunov optimization. Our intensive simulations verify that the proposed video delivery algorithm works reliably and also can control the tradeoff between video quality and playback latency.

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arXiv2019

Throughput-Outage Analysis and Evaluation of Cache-Aided D2D Networks with Measured Popularity Distributions

Caching of video files on user devices, combined with file exchange through device-to-device (D2D) communications is a promising method for increasing the throughput of wireless networks. Previous theoretical investigations showed that throughput can be increased by orders of magnitude, but assumed a Zipf distribution for modeling the popularity distribution, which was based on observations in {\em wired} networks. Thus the question whether cache-aided D2D video distribution can provide in practice the benefits promised by existing theoretical literature remains open. To answer this question, we provide new results specifically for popularity distributions of video requests of mobile users. Based on an extensive real-world dataset, we adopt a generalized distribution, known as Mandelbrot-Zipf (MZipf) distribution. We first show that this popularity distribution can fit the practical data well. Using this distribution, we analyze the throughput--outage tradeoff of the cache-aided D2D network and show that the scaling law is identical to the case of Zipf popularity distribution when the MZipf distribution is sufficiently skewed, implying that the benefits previously promised in the literature could indeed be realized in practice. To support the theory, practical evaluations using numerical experiments are provided, and show that the cache-aided D2D can outperform the conventional unicasting from base stations.

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arXiv2019

Cascaded Coded Distributed Computing on Heterogeneous Networks

Coded distributed computing (CDC) introduced by Li et al. in 2015 offers an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce. For the more general cascaded CDC, Map computations are repeated at $r$ nodes to significantly reduce the communication load among nodes tasked with computing $Q$ Reduce functions $s$ times. While an achievable cascaded CDC scheme was proposed, it only operates on homogeneous networks, where the storage, computation load and communication load of each computing node is the same. In this paper, we address this limitation by proposing a novel combinatorial design which operates on heterogeneous networks where nodes have varying storage and computing capabilities. We provide an analytical characterization of the computation-communication trade-off and show that it is optimal within a constant factor and could outperform the state-of-the-art homogeneous schemes.

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arXiv2019

A New Design of Private Information Retrieval for Storage Constrained Databases

Private information retrieval (PIR) allows a user to download one of $K$ messages from $N$ databases without revealing to any database which of the $K$ messages is being downloaded. In general, the databases can be storage constrained where each database can only store up to $μK L$ bits where $\frac{1}{N} \leq μ\leq 1$ and $L$ is the size of each message in bits. Let $t= μN$, a recent work showed that the capacity of Storage Constrained PIR (SC-PIR) is $\left( 1+ \frac{1}{t} + \frac{1}{t^2} + \cdots + \frac{1}{t^{K-1}} \right)^{-1}$, which is achieved by a storage placement scheme inspired by the content placement scheme in the literature of coded caching and the original PIR scheme. Not surprisingly, this achievable scheme requires that each message is $L = {N \choose t}t^K$ bits in length, which can be impractical. In this paper, without trying to make the connection between SC-PIR and coded caching problems, based on a general connection between the Full Storage PIR (FS-PIR) problem ($μ= 1$) and SC-PIR problem, we propose a new SC-PIR design idea using novel storage placement schemes. The proposed schemes significantly reduce the message size requirement while still meeting the capacity of SC-PIR. In particular, the proposed SC-PIR schemes require the size of each file to be only $L = Nt^{K-1}$ compared to the state-of-the-art $L = {N \choose t}t^K$. Hence, we conclude that PIR may not meet coded caching when the size of $L$ is constrained.

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