605 research outputs found
A New Converse Bound for Coded Caching
An information-theoretic lower bound is developed for the caching system studied by Maddah-Ali and Niesen. By comparing the proposed lower bound with the decentralized coded caching scheme of Maddah-Ali and Niesen, the optimal memory--rate tradeoff is characterized to within a multiplicative gap of 4.7 for the worst case, improving the previous analytical gap of 12. Furthermore, for the case when users' requests follow the uniform distribution, the multiplicative gap is tightened to 4.7, improving the previous analytical gap of 72. As an independent result of interest, for the single-user average case in which the user requests multiple files, it is proved that caching the most requested files is optimal
The Optimal Memory-Rate Trade-off for the Non-uniform Centralized Caching Problem with Two Files under Uncoded Placement
A new scheme for the problem of centralized coded caching with non-uniform
demands is proposed. The distinguishing feature of the proposed placement
strategy is that it admits equal sub-packetization for all files while allowing
the users to allocate more cache to the files which are more popular. This
creates natural broadcasting opportunities in the delivery phase which are
simultaneously helpful for the users who have requested files of different
popularities. For the case of two files, we propose a new delivery strategy
based on interference alignment which enables each user to decode his desired
file following a two-layer peeling decoder. Furthermore, we extend the existing
converse bounds for uniform demands under uncoded placement to the nonuniform
case. To accomplish this, we construct auxiliary users, corresponding to
all permutations of the files, each caching carefully selected sub-packets
of the files. Each auxiliary user provides a different converse bound. The
overall converse bound is the maximum of all these bounds. We prove that
our achievable delivery rate for the case of two files meets this converse,
thereby establishing the optimal expected memory-rate trade-off for the case of
users and two files with arbitrary popularities under uncoded placement
Generalized Degrees of Freedom of the Symmetric Cache-Aided MISO Broadcast Channel with Partial CSIT
We consider the cache-aided MISO broadcast channel (BC) in which a
multi-antenna transmitter serves single-antenna receivers, each equipped
with a cache memory. The transmitter has access to partial knowledge of the
channel state information. For a symmetric setting, in terms of channel
strength levels, partial channel knowledge levels and cache sizes, we
characterize the generalized degrees of freedom (GDoF) up to a constant
multiplicative factor. The achievability scheme exploits the interplay between
spatial multiplexing gains and coded-multicasting gain. On the other hand, a
cut-set-based argument in conjunction with a GDoF outer bound for a parallel
MISO BC under channel uncertainty are used for the converse. We further show
that the characterized order-optimal GDoF is also attained in a decentralized
setting, where no coordination is required for content placement in the caches.Comment: first revisio
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 requests. The obvious naive scheme consists
of applying times the order-optimal scheme for a single request, obtaining
a linear in 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) .Comment: 5 pages, 1 figure, to appear in GlobalSIP14, Dec. 201
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
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