arXiv subjects

Kai Wan

Publications and source records attributed to Kai Wan.

At least 91 records · Page 5Linked to original sources

arXiv2020

On the Fundamental Limits of Cache-aided Multiuser Private Information Retrieval

We consider the problem of cache-aided Multiuser Private Information Retrieval (MuPIR) which is an extension of the single-user cache-aided PIR problem to the case of multiple users. In MuPIR, each of the $K_{\rm u}$ cache-equipped users wishes to privately retrieve a message out of $K$ messages from $N$ databases each having access to the entire message library. The privacy constraint requires that any individual database learns nothing about the demands of all users. The users are connected to each database via an error-free shared-link. In this paper, we aim to characterize the optimal trade-off between users' memory and communication load for such systems. Based on the proposed novel approach of \emph{cache-aided interference alignment (CIA)}, first, for the MuPIR problem with $K=2$ messages, $K_{\rm u}=2$ users and $N\ge 2$ databases, we propose achievable retrieval schemes for both uncoded and general cache placement. The CIA approach is optimal when the cache placement is uncoded. For general cache placement, the CIA approach is optimal when $N=2$ and $3$ verified by the computer-aided approach. Second, when $K,K_{\rm u}$ and $N$ are general, we propose a new \emph{product design} (PD) which incorporates the PIR code into the linear caching code. The product design is shown to be order optimal within a multiplicative factor of 8 and is exactly optimal when the user cache memory size is large.

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arXiv2020

On the Tradeoff Between Computation and Communication Costs for Distributed Linearly Separable Computation

This paper studies the distributed linearly separable computation problem, which is a generalization of many existing distributed computing problems such as distributed gradient descent and distributed linear transform. In this problem, a master asks $N$ distributed workers to compute a linearly separable function of $K$ datasets, which is a set of $K_c$ linear combinations of $K$ messages (each message is a function of one dataset). We assign some datasets to each worker, which then computes the corresponding messages and returns some function of these messages, such that from the answers of any $N_r$ out of $N$ workers the master can recover the task function. In the literature, the specific case where $K_c = 1$ or where the computation cost is minimum has been considered. In this paper, we focus on the general case (i.e., general $K_c$ and general computation cost) and aim to find the minimum communication cost. We first propose a novel converse bound on the communication cost under the constraint of the popular cyclic assignment (widely considered in the literature), which assigns the datasets to the workers in a cyclic way. Motivated by the observation that existing strategies for distributed computing fall short of achieving the converse bound, we propose a novel distributed computing scheme for some system parameters. The proposed computing scheme is optimal for any assignment when $K_c$ is large and is optimal under cyclic assignment when the numbers of workers and datasets are equal or $K_c$ is small. In addition, it is order optimal within a factor of 2 under cyclic assignment for the remaining cases.

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arXiv2020

Coded Caching over Multicast Routing Networks

The coded caching scheme originally proposed by Maddah-Ali and Niesen (MAN) transmits coded multicast messages from a server to users equipped with caches via a capacitated shared-link and was shown to be information theoretically optimal within a constant multiplicative factor. This work extends the MAN scheme to a class of two-hop wired-wireless networks including one server connected via fronthaul links to a layer of $H$ helper nodes (access points/base stations), which in turns communicate via a wireless access network to $K$ users, each equipped with its own cache. Two variants are considered, which differ in the modeling of the access segment. Both models should be regarded as abstractions at the network layer for physical scenarios such as local area networks and cellular networks, spatially distributed over a certain coverage area. The key focus of our approach consists of routing MAN-type multicast messages through the network and formulating the optimal routing scheme as an optimization problem that can be solved exactly or for which we give powerful heuristic algorithms. Our approach solves at once many of the open practical problems identified as stumbling blocks for the application of coded caching in practical scenarios, namely: asynchronous streaming sessions, finite file size, scalability of the scheme to large and spatially distributed networks, user mobility and random activity (users joining and leaving the system at arbitrary times), decentralized prefetching of the cache contents, end-to-end encryption of HTTPS requests, which renders the helper nodes oblivious of the user demands.

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arXiv2020

On Coded Caching with Private Demands

Caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the user's local cache memory without knowledge of later demands. For the shared-link caching model, Maddah-Ali and Niesen (MAN) proposed a two-phase (placement and delivery) coded caching strategy, which is order optimal within a constant factor. However, in the MAN coded caching scheme, each user can obtain the information about the demands of other users, i.e., the MAN coded caching scheme is inherently prone to tampering and spying the activity/demands of other users. In this paper, we formulate an information-theoretic shared-link caching model with private demands, where there are K cache-aided users (which can cache up to M files) connected to a central server with access to N files. Each user requests L files. Our objective is to design a two-phase private caching scheme with minimum load while preserving the information-theoretic privacy of the demands of each user with respect to other users. We propose two novel private coded caching schemes with the general underlying idea, which is to satisfy the users' requests by generating a set of coded multicast messages that is symmetric with respect to the library files. In the first scheme, we introduce a number of virtual users such that each L-subset of files is demanded by K real or virtual (effective) users and use the MAN delivery to generate multicast messages. This scheme incurs in an extremely large sub-packetization. Then, we propose a second scheme based on a novel MDS-coded cache placement. In this case, we generate multicast messages where each multicast message contains one MDS-coded symbol from each file in the library and thus is again symmetric over all the files from the viewpoint of each user. The proposed schemes are generally order optimal except for the case where N > LK and M< N/K.

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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

An Index Coding Approach to Caching with Uncoded Cache Placement

Caching is an efficient way to reduce network traffic congestion during peak hours, by storing some content at the user's local cache memory, even without knowledge of user's later demands. Maddah-Ali and Niesen proposed a two-phase (placement phase and delivery phase) coded caching strategy for broadcast channels with cache-aided users. This paper investigates the same model under the constraint that content is placed uncoded within the caches, that is, when bits of the files are simply copied within the caches. When the cache contents are uncoded and the users' demands are revealed, the caching problem can be connected to an index coding problem. This paper focuses on deriving fundamental performance limits for the caching problem by using tools for the index coding problem that were either known or are newly developed in this work. First, a converse bound for the caching problem under the constraint of uncoded cache placement is proposed based on the "acyclic index coding converse bound". This converse bound is proved to be achievable by the Maddah-Ali and Niesen's scheme when the number of files is not less than the number of users, and by a newly derived index coding achievable scheme otherwise. The proposed index coding achievable scheme is based on distributed source coding and strictly improves on the widely used "composite (index) coding" achievable bound and its improvements, and is of independent interest. An important consequence of the findings of this paper is that advancements on the coded caching problem posed by Maddah-Ali and Niesen are thus only possible by considering strategies with coded placement phase. A recent work by Yu et al. has however shown that coded cache placement can at most half the network load compared to the results presented in this paper.

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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

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

Routing-Based Delivery in Combination-Type Networks with Random Topology

The coded caching scheme proposed by Maddah-Ali and Niesen (MAN) transmits coded multicast messages to users equipped with caches and it is known to be optimal within a constant factor. This work extends this caching scheme to two-hop relay networks with one main server with access to a library of $N$ files, and $H$ relays communicating with $K$ users with cache, each of which is connected to a random subset of relays. This topology can be considered as a generalized version of a celebrated family of networks, referred to as combination networks. Our approach is simply based on routing MAN packets through the network. The optimization of the routing can be formulated as a Linear Program (LP). In addition, to reduce the computation complexity, a dynamic algorithm is proposed to approach the LP solution. Numerical simulations show that the proposed scheme outperforms the existing caching schemes for this class of networks.

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arXiv2019

Merging the Bernoulli-Gaussian and Symmetric Alpha-Stable Models for Impulsive Noises in Narrowband Power Line Channels

To model impulsive noise in power line channels, both the Bernoulli-Gaussian model and the symmetric alpha-stable model are usually applied. Towards a merge of existing noise measurement databases and a simplification of communication system design, the compatibility between the two models is of interest. In this paper, we show that they can be approximately converted to each other under certain constrains, although never generally unified. Based on this, we propose a fast model conversion.

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arXiv2018

MIMO-OFDM Scheme design for Medium Voltage Underground Cables based Power Line Communication

Power line communication (PLC) provides intelligent electrical functions such as power quality measurement, fault surveys, and remote control of electrical network. However, most of research works have been done in low voltage (LV) scenario due to the fast development of in-home PLC. The aim of this paper is to design a MIMO-OFDM based transmission link under medium voltage (MV) underground power line channel and evaluate the performance. The MIMO channel is modeled as a modified multipath model in the presence of impulsive noise and background noise. Unlike most literatures on MIMO power line transmission, we adopt spatial multiplexing instead of diversity to increase the transmission rate in this paper. The turbo coding method originally designed for LV power line communication is used in the proposed transmission system. By comparing the BER performance of MIMO-OFDM system with and without the turbo coding, we evaluate its applicability in MV power line communication. The effect of frequency band varying on the PLC system's performance is also investigated.

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arXiv2018

Caching in Combination Networks: Novel Multicast Message Generation and Delivery by Leveraging the Network Topology

Maddah-Ali and Niesen's original coded caching scheme for shared-link broadcast networks is now known to be optimal to within a factor two, and has been applied to other types of networks. For practical reasons, this paper considers that a server communicates to cache-aided users through $H$ intermediate relays. In particular, it focuses on combination networks where each of the $K = \binom{H}{r}$ users is connected to a distinct $r$-subsets of relays. By leveraging the symmetric topology of the network, this paper proposes a novel method to general multicast messages and to deliver them to the users. By numerical evaluations, the proposed scheme is shown to reduce the download time compared to the schemes available in the literature. The idea is then extended to decentralized combination networks, more general relay networks, and combination networks with cache-aided relays and users. Also in these cases the proposed scheme outperforms known ones.

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arXiv2018

On Combination Networks with Cache-aided Relays and Users

Caching is an efficient way to reduce peak hour network traffic congestion by storing some contents at the user's cache without knowledge of later demands. Coded caching strategy was originally proposed by Maddah-Ali and Niesen to give an additional coded caching gain compared the conventional uncoded scheme. Under practical consideration, the caching model was recently considered in relay network, in particular the combination network, where the central server communicates with $K=\binom{H}{r}$ users (each is with a cache of $M$ files) through $H$ immediate relays, and each user is connected to a different $r-$subsets of relays. Several inner bounds and outer bounds were proposed for combination networks with end-user-caches. This paper extends the recent work by the authors on centralized combination networks with end-user caches to a more general setting, where both relays and users have caches. In contrast to the existing schemes in which the packets transmitted from the server are independent of the cached contents of relays, we propose a novel caching scheme by creating an additional coded caching gain to the transmitted load from the server with the help of the cached contents in relays. We also show that the proposed scheme outperforms the state-of-the-art approaches.

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arXiv2018

On the Benefits of Asymmetric Coded Cache Placement in Combination Networks with End-User Caches

This paper investigates the fundamental tradeoff between cache size and download time in the (H;r;M;N) combination network, where a server with N files is connected to H relays (without caches) and each of the K:=\binom{H}{r} users (with caches of size M files) is connected to a different subset of r relays. Existing schemes fall within two categories: either use the uncoded symmetric cache placement originally proposed for the shared-link model and design delivery phase dependent on the network topology, or effectively divide the combination network into H independent shared-link networks each serving \binom{H-1}{r-1} users; in either case, the placement phase is independent of network topology. In this paper, a novel strategy is proposed where the coded cache placement is dependent on network topology. The proposed scheme is shown to be information theoretically optimal for large cache size. In addition, when not exactly optimal, the proposed scheme can also outperform existing schemes.

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arXiv2018

Caching in Combination Networks: A Novel Delivery by Leveraging the Network Topology

Maddah-Ali and Niesen (MAN) in 2014 surprisingly showed that it is possible to serve an arbitrarily large number of cache-equipped users with a constant number of transmissions by using coded caching in shared-link broadcast networks. This paper studies the tradeoff between the user's cache size and the file download time for combination networks, where users with caches communicate with the servers through intermediate relays. Motivated by the so-called separation approach, it is assumed that placement and multicast message generation are done according to the MAN original scheme and regardless of the network topology. The main contribution of this paper is the design of a novel two-phase delivery scheme that, accounting to the network topology, outperforms schemes available in the literature. The key idea is to create additional (compared to MAN) multicasting opportunities: in the first phase coded messages are sent with the goal of increasing the amount of `side information' at the users, which is then leveraged during the second phase. The download time with the novel scheme is shown to be proportional to 1=H (with H being the number or relays) and to be order optimal under the constraint of uncoded placement for some parameter regimes.

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arXiv2018

A Novel Asymmetric Coded Placement in Combination Networks with end-user Caches

The tradeoff between the user's memory size and the worst-case download time in the $(H,r,M,N)$ combination network is studied, where a central server communicates with $K$ users through $H$ immediate relays, and each user has local cache of size $M$ files and is connected to a different subset of $r$ relays. The main contribution of this paper is the design of a coded caching scheme with asymmetric coded placement by leveraging coordination among the relays, which was not exploited in past work. Mathematical analysis and numerical results show that the proposed schemes outperform existing schemes.

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