arXiv subjects

Jesús Gómez-Vilardebó

Publications and source records attributed to Jesús Gómez-Vilardebó.

4 recordsLinked to original sources

arXiv2024

Generalized Multivariate Polynomial Codes for Distributed Matrix-Matrix Multiplication

Supporting multiple partial computations efficiently at each of the workers is a keystone in distributed coded computing in order to speed up computations and to fully exploit the resources of heterogeneous workers in terms of communication, storage, or computation capabilities. Multivariate polynomial coding schemes have recently been shown to deliver faster results for distributed matrix-matrix multiplication compared to conventional univariate polynomial coding schemes by supporting multiple partial coded computations at each worker at reduced communication costs. In this work, we extend multivariate coding schemes to also support arbitrary matrix partitions. Generalized matrix partitions have been proved useful to trade-off between computation speed and communication costs in distributed (univariate) coded computing. We first formulate the computation latency-communication trade-off in terms of the computation complexity and communication overheads required by coded computing approaches as compared to a single server uncoded computing system. Then, we propose two novel multivariate coded computing schemes supporting arbitrary matrix partitions. The proposed schemes are shown to improve the studied trade-off as compared to univariate schemes.

cs.IT↗

arXiv2021

On the Fundamental Limits of Coded Caching Systems with Restricted Demand Types

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 allows all possible multiple demand types during delivery, which in fact introduces tension in the coding strategy. In this paper, we seek to develop a better understanding of the fundamental limits of coded caching by investigating systems with certain demand type restrictions. We first consider the canonical three-user three-file system, and show that, contrary to popular beliefs, the worst demand type is not the one in which all three files are requested. Motivated by these findings, we focus on coded caching systems where every file must be requested by at least one user. A novel coding scheme is proposed, which can provide new operating points that are not covered by any previously known schemes.

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arXiv2017

Fundamental Limits of Caching: Improved Bounds with Coded Prefetching

We consider a cache network in which a single server is connected to multiple users via a shared error free link. The server has access to a database with $N$ files of equal length $F$, and serves $K$ users each with a cache memory of $MF$ bits. A novel centralized coded caching scheme is proposed for scenarios with more users than files $N\leq K$ and cache capacities satisfying $\frac{1}{K}\leq M\leq\frac{N}{K}$. The proposed scheme outperforms the best rate-memory region known in the literature if $N\leq K\leq\frac{N^{2}+1}{2}$.

cs.IT↗

arXiv2016

Wireless Content Caching for Small Cell and D2D Networks

The fifth generation wireless networks must provide fast and reliable connectivity while coping with the ongoing traffic growth. It is of paramount importance that the required resources, such as energy and bandwidth, do not scale with traffic. While the aggregate network traffic is growing at an unprecedented rate, users tend to request the same popular contents at different time instants. Therefore, caching the most popular contents at the network edge is a promising solution to reduce the traffic and the energy consumption over the backhaul links. In this paper, two scenarios are considered, where caching is performed either at a small base station, or directly at the user terminals, which communicate using \ac{D2D} communications. In both scenarios, joint design of the transmission and caching policies is studied when the user demands are known in advance. This joint design offers two different caching gains, namely, the \textit{pre-downloading} and \textit{local caching gains}. It is shown that the finite cache capacity limits the attainable gains, and creates an inherent tradeoff between the two types of gains. In this context, a continuous time optimization problem is formulated to determine the optimal transmission and caching policies that minimize a generic cost function, such as energy, bandwidth, or throughput. The jointly optimal solution is obtained by demonstrating that caching files at a constant rate is optimal, which allows to reformulate the problem as a finite-dimensional convex program. The numerical results show that the proposed joint transmission and caching policy dramatically reduces the total cost, which is particularised to the total energy consumption at the \ac{MBS}, as well as to the total economical cost for the service provider, when users demand economical incentives for delivering content to other users over the D2D links.

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