878 research outputs found
Users Caching Two Files: An Improved Achievable Rate
Caching is an approach to smoothen the variability of traffic over time.
Recently it has been proved that the local memories at the users can be
exploited for reducing the peak traffic in a much more efficient way than
previously believed. In this work we improve upon the existing results and
introduce a novel caching strategy that takes advantage of simultaneous coded
placement and coded delivery in order to decrease the worst case achievable
rate with files and users. We will show that for any cache size
our scheme outperforms the state of the art
Reliable Physical Layer Network Coding
When two or more users in a wireless network transmit simultaneously, their
electromagnetic signals are linearly superimposed on the channel. As a result,
a receiver that is interested in one of these signals sees the others as
unwanted interference. This property of the wireless medium is typically viewed
as a hindrance to reliable communication over a network. However, using a
recently developed coding strategy, interference can in fact be harnessed for
network coding. In a wired network, (linear) network coding refers to each
intermediate node taking its received packets, computing a linear combination
over a finite field, and forwarding the outcome towards the destinations. Then,
given an appropriate set of linear combinations, a destination can solve for
its desired packets. For certain topologies, this strategy can attain
significantly higher throughputs over routing-based strategies. Reliable
physical layer network coding takes this idea one step further: using
judiciously chosen linear error-correcting codes, intermediate nodes in a
wireless network can directly recover linear combinations of the packets from
the observed noisy superpositions of transmitted signals. Starting with some
simple examples, this survey explores the core ideas behind this new technique
and the possibilities it offers for communication over interference-limited
wireless networks.Comment: 19 pages, 14 figures, survey paper to appear in Proceedings of the
IEE
Increasing Availability in Distributed Storage Systems via Clustering
We introduce the Fixed Cluster Repair System (FCRS) as a novel architecture
for Distributed Storage Systems (DSS), achieving a small repair bandwidth while
guaranteeing a high availability. Specifically we partition the set of servers
in a DSS into clusters and allow a failed server to choose any cluster
other than its own as its repair group. Thereby, we guarantee an availability
of . We characterize the repair bandwidth vs. storage trade-off for the
FCRS under functional repair and show that the minimum repair bandwidth can be
improved by an asymptotic multiplicative factor of compared to the state
of the art coding techniques that guarantee the same availability. We further
introduce Cubic Codes designed to minimize the repair bandwidth of the FCRS
under the exact repair model. We prove an asymptotic multiplicative improvement
of in the minimum repair bandwidth compared to the existing exact repair
coding techniques that achieve the same availability. We show that Cubic Codes
are information-theoretically optimal for the FCRS with and complete
clusters. Furthermore, under the repair-by-transfer model, Cubic Codes are
optimal irrespective of the number of clusters
Single-Server Multi-Message Private Information Retrieval with Side Information
We study the problem of single-server multi-message private information
retrieval with side information. One user wants to recover out of
independent messages which are stored at a single server. The user initially
possesses a subset of messages as side information. The goal of the user is
to download the demand messages while not leaking any information about the
indices of these messages to the server. In this paper, we characterize the
minimum number of required transmissions. We also present the optimal linear
coding scheme which enables the user to download the demand messages and
preserves the privacy of their indices. Moreover, we show that the trivial MDS
coding scheme with transmissions is optimal if or .
This means if one wishes to privately download more than the square-root of the
number of files in the database, then one must effectively download the full
database (minus the side information), irrespective of the amount of side
information one has available.Comment: 12 pages, submitted to the 56th Allerton conferenc
Compute-and-Forward: Harnessing Interference through Structured Codes
Interference is usually viewed as an obstacle to communication in wireless
networks. This paper proposes a new strategy, compute-and-forward, that
exploits interference to obtain significantly higher rates between users in a
network. The key idea is that relays should decode linear functions of
transmitted messages according to their observed channel coefficients rather
than ignoring the interference as noise. After decoding these linear equations,
the relays simply send them towards the destinations, which given enough
equations, can recover their desired messages. The underlying codes are based
on nested lattices whose algebraic structure ensures that integer combinations
of codewords can be decoded reliably. Encoders map messages from a finite field
to a lattice and decoders recover equations of lattice points which are then
mapped back to equations over the finite field. This scheme is applicable even
if the transmitters lack channel state information.Comment: IEEE Trans. Info Theory, to appear. 23 pages, 13 figure
Cooperative Data Exchange based on MDS Codes
The cooperative data exchange problem is studied for the fully connected
network. In this problem, each node initially only possesses a subset of the
packets making up the file. Nodes make broadcast transmissions that are
received by all other nodes. The goal is for each node to recover the full
file. In this paper, we present a polynomial-time deterministic algorithm to
compute the optimal (i.e., minimal) number of required broadcast transmissions
and to determine the precise transmissions to be made by the nodes. A
particular feature of our approach is that {\it each} of the
transmissions is a linear combination of {\it exactly} packets, and we
show how to optimally choose the value of We also show how the
coefficients of these linear combinations can be chosen by leveraging a
connection to Maximum Distance Separable (MDS) codes. Moreover, we show that
our method can be used to solve cooperative data exchange problems with
weighted cost as well as the so-called successive local omniscience problem.Comment: 21 pages, 1 figur
Compute-and-Forward: Finding the Best Equation
Compute-and-Forward is an emerging technique to deal with interference. It
allows the receiver to decode a suitably chosen integer linear combination of
the transmitted messages. The integer coefficients should be adapted to the
channel fading state. Optimizing these coefficients is a Shortest Lattice
Vector (SLV) problem. In general, the SLV problem is known to be prohibitively
complex. In this paper, we show that the particular SLV instance resulting from
the Compute-and-Forward problem can be solved in low polynomial complexity and
give an explicit deterministic algorithm that is guaranteed to find the optimal
solution.Comment: Paper presented at 52nd Allerton Conference, October 201
The Sampling Rate-Distortion Tradeoff for Sparsity Pattern Recovery in Compressed Sensing
Recovery of the sparsity pattern (or support) of an unknown sparse vector
from a limited number of noisy linear measurements is an important problem in
compressed sensing. In the high-dimensional setting, it is known that recovery
with a vanishing fraction of errors is impossible if the measurement rate and
the per-sample signal-to-noise ratio (SNR) are finite constants, independent of
the vector length. In this paper, it is shown that recovery with an arbitrarily
small but constant fraction of errors is, however, possible, and that in some
cases computationally simple estimators are near-optimal. Bounds on the
measurement rate needed to attain a desired fraction of errors are given in
terms of the SNR and various key parameters of the unknown vector for several
different recovery algorithms. The tightness of the bounds, in a scaling sense,
as a function of the SNR and the fraction of errors, is established by
comparison with existing information-theoretic necessary bounds. Near
optimality is shown for a wide variety of practically motivated signal models
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