Fundamental Limits of Caching in Wireless D2D Networks

We consider a wireless Device-to-Device (D2D) network where communication is restricted to be single-hop. Users make arbitrary requests from a finite library of files and have pre-cached information on their devices, subject to a per-node storage capacity constraint. A similar problem has already been considered in an ``infrastructure'' setting, where all users receive a common multicast (coded) message from a single omniscient server (e.g., a base station having all the files in the library) through a shared bottleneck link. In this work, we consider a D2D ``infrastructure-less'' version of the problem. We propose a caching strategy based on deterministic assignment of subpackets of the library files, and a coded delivery strategy where the users send linearly coded messages to each other in order to collectively satisfy their demands. We also consider a random caching strategy, which is more suitable to a fully decentralized implementation. Under certain conditions, both approaches can achieve the information theoretic outer bound within a constant multiplicative factor. In our previous work, we showed that a caching D2D wireless network with one-hop communication, random caching, and uncoded delivery, achieves the same throughput scaling law of the infrastructure-based coded multicasting scheme, in the regime of large number of users and files in the library. This shows that the spatial reuse gain of the D2D network is order-equivalent to the coded multicasting gain of single base station transmission. It is therefore natural to ask whether these two gains are cumulative, i.e.,if a D2D network with both local communication (spatial reuse) and coded multicasting can provide an improved scaling law. Somewhat counterintuitively, we show that these gains do not cumulate (in terms of throughput scaling law).Comment: 45 pages, 5 figures, Submitted to IEEE Transactions on Information Theory, This is the extended version of the conference (ITW) paper arXiv:1304.585

An Efficient Coded Multicasting Scheme Preserving the Multiplicative Caching Gain

Coded multicasting has been shown to be a promis- ing approach to significantly improve the caching performance of content delivery networks with multiple caches downstream of a common multicast link. However, achievable schemes proposed to date have been shown to achieve the proved order-optimal performance only in the asymptotic regime in which the number of packets per requested item goes to infinity. In this paper, we first extend the asymptotic analysis of the achievable scheme in [1], [2] to the case of heterogeneous cache sizes and demand distributions, providing the best known upper bound on the fundamental limiting performance when the number of packets goes to infinity. We then show that the scheme achieving this upper bound quickly loses its multiplicative caching gain for finite content packetization. To overcome this limitation, we design a novel polynomial-time algorithm based on random greedy graph- coloring that, while keeping the same finite content packetization, recovers a significant part of the multiplicative caching gain. Our results show that the order-optimal coded multicasting schemes proposed to date, while useful in quantifying the fundamental limiting performance, must be properly designed for practical regimes of finite packetization.Comment: 6 pages, 7 figures, Published in Infocom CNTCV 201

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) $18$.Comment: 5 pages, 1 figure, to appear in GlobalSIP14, Dec. 201

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.Comment: 5 pages, 3 figure, to appear in ISWCS 201