arXiv subjects

Jaime Llorca

Publications and source records attributed to Jaime Llorca.

42 records · Page 3Linked to original sources

arXiv2015

An Efficient Multiple-Groupcast Coded Multicasting Scheme for Finite Fractional Caching

Coded multicasting has been shown to improve the caching performance of content delivery networks with multiple caches downstream of a common multicast link. However, the schemes that have been shown to achieve order-optimal perfor- mance require content items to be partitioned into a number of packets that grows exponentially with the number of users [1]. In this paper, we first extend the analysis of the achievable scheme in [2] to the case of heterogeneous cache sizes and demand distribu- tions, providing an achievable scheme and an upper bound on the limiting average performance when the number of packets goes to infinity while the remaining system parameters are kept constant. We then show how the scheme achieving this upper bound can very quickly loose its multiplicative caching gain for finite content packetization. To overcome this limitation, we design a novel polynomial-time algorithm based on greedy local graph-coloring that, while keeping the same content packetization, recovers a significant part of the multiplicative caching gain. Our results show that the achievable schemes proposed to date to quantify the limiting performance, must be properly designed for practical finite system parameters.

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arXiv2015

Caching-Aided Coded Multicasting with Multiple Random Requests

The capacity of caching networks has received considerable attention in the past few years. A particularly studied setting is the shared link caching network, in which a single source with access to a file library communicates with multiple users, each having the capability to store segments (packets) of the library files, over a shared multicast link. Each user requests one file from the library according to a common demand distribution and the server sends a coded multicast message to satisfy all users at once. The problem consists of finding the smallest possible average codeword length to satisfy such requests. In this paper, we consider the generalization to the case where each user places L >= 1 independent requests according to the same common demand distribution. We propose an achievable scheme based on random vector (packetized) caching placement and multiple groupcast index coding, shown to be order-optimal in the asymptotic regime in which the number of packets per file B goes to infinity. We then show that the scalar (B = 1) version of the proposed scheme can still preserve order-optimality when the number of per-user requests L is large enough. Our results provide the first order-optimal characterization of the shared link caching network with multiple random requests, revealing the key effects of L on the performance of caching-aided coded multicast schemes.

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arXiv2015

Finite Length Analysis of Caching-Aided Coded Multicasting

In this work, we study a noiseless broadcast link serving $K$ users whose requests arise from a library of $N$ files. Every user is equipped with a cache of size $M$ files each. It has been shown that by splitting all the files into packets and placing individual packets in a random independent manner across all the caches, it requires at most $N/M$ file transmissions for any set of demands from the library. The achievable delivery scheme involves linearly combining packets of different files following a greedy clique cover solution to the underlying index coding problem. This remarkable multiplicative gain of random placement and coded delivery has been established in the asymptotic regime when the number of packets per file $F$ scales to infinity. In this work, we initiate the finite-length analysis of random caching schemes when the number of packets $F$ is a function of the system parameters $M,N,K$. Specifically, we show that existing random placement and clique cover delivery schemes that achieve optimality in the asymptotic regime can have at most a multiplicative gain of $2$ if the number of packets is sub-exponential. Further, for any clique cover based coded delivery and a large class of random caching schemes, that includes the existing ones, we show that the number of packets required to get a multiplicative gain of $\frac{4}{3}g$ is at least $O((N/M)^g)$. We exhibit a random placement and an efficient clique cover based coded delivery scheme that approximately achieves this lower bound. We also provide tight concentration results that show that the average (over the random caching involved) number of transmissions concentrates very well requiring only polynomial number of packets in the rest of the parameters.

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arXiv2015

Order-Optimal Rate of Caching and Coded Multicasting with Random Demands

We consider the canonical {\em shared link network} formed by a source node, hosting a library of $m$ information messages (files), connected via a noiseless common link to $n$ destination nodes (users), each with a cache of size M files. Users request files at random and independently, according to a given a-priori demand distribution $\qv$. A coding scheme for this network consists of a caching placement (i.e., a mapping of the library files into the user caches) and delivery scheme (i.e., a mapping for the library files and user demands into a common multicast codeword) such that, after the codeword transmission, all users can retrieve their requested file. The rate of the scheme is defined as the {\em average} codeword length normalized with respect to the length of one file, where expectation is taken over the random user demands. For the same shared link network, in the case of deterministic demands, the optimal min-max rate has been characterized within a uniform bound, independent of the network parameters. In particular, fractional caching (i.e., storing file segments) and using linear network coding has been shown to provide a min-max rate reduction proportional to 1/M with respect to standard schemes such as unicasting or "naive" uncoded multicasting. The case of random demands was previously considered by applying the same order-optimal min-max scheme separately within groups of files requested with similar probability. However, no order-optimal guarantee was provided for random demands under the average rate performance criterion. In this paper, we consider the random demand setting and provide general achievability and converse results. In particular, we consider a family of schemes that combine random fractional caching according to a probability distribution $\pv$ that depends on the demand distribution $\qv$, with a linear coded delivery scheme based on ...

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arXiv2014

Caching and Coded Multicasting: Multiple Groupcast Index Coding

The capacity of caching networks has received considerable attention in the past few years. A particularly studied setting is the case of a single server (e.g., a base station) and multiple users, each of which caches segments of files in a finite library. Each user requests one (whole) file in the library and the server sends a common coded multicast message to satisfy all users at once. The problem consists of finding the smallest possible codeword length to satisfy such requests. In this paper we consider the generalization to the case where each user places $L \geq 1$ requests. The obvious naive scheme consists of applying $L$ times the order-optimal scheme for a single request, obtaining a linear in $L$ scaling of the multicast codeword length. We propose a new achievable scheme based on multiple groupcast index coding that achieves a significant gain over the naive scheme. Furthermore, through an information theoretic converse we find that the proposed scheme is approximately optimal within a constant factor of (at most) $18$.

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arXiv2014

On the Average Performance of Caching and Coded Multicasting with Random Demands

For a network with one sender, $n$ receivers (users) and $m$ possible messages (files), caching side information at the users allows to satisfy arbitrary simultaneous demands by sending a common (multicast) coded message. In the worst-case demand setting, explicit deterministic and random caching strategies and explicit linear coding schemes have been shown to be order optimal. In this work, we consider the same scenario where the user demands are random i.i.d., according to a Zipf popularity distribution. In this case, we pose the problem in terms of the minimum average number of equivalent message transmissions. We present a novel decentralized random caching placement and a coded delivery scheme which are shown to achieve order-optimal performance. As a matter of fact, this is the first order-optimal result for the caching and coded multicasting problem in the case of random demands.

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