126,366 research outputs found
Network monitoring in multicast networks using network coding
In this paper we show how information contained in robust network codes can be used for passive inference of possible locations of link failures or losses in a network. For distributed randomized network coding, we bound the probability of being able to distinguish among a given set of failure events, and give some experimental results for one and two link failures in randomly generated networks. We also bound the required field size and complexity for designing a robust network code that distinguishes among a given set of failure events
Universal and Robust Distributed Network Codes
Random linear network codes can be designed and implemented in a distributed
manner, with low computational complexity. However, these codes are classically
implemented over finite fields whose size depends on some global network
parameters (size of the network, the number of sinks) that may not be known
prior to code design. Also, if new nodes join the entire network code may have
to be redesigned.
In this work, we present the first universal and robust distributed linear
network coding schemes. Our schemes are universal since they are independent of
all network parameters. They are robust since if nodes join or leave, the
remaining nodes do not need to change their coding operations and the receivers
can still decode. They are distributed since nodes need only have topological
information about the part of the network upstream of them, which can be
naturally streamed as part of the communication protocol.
We present both probabilistic and deterministic schemes that are all
asymptotically rate-optimal in the coding block-length, and have guarantees of
correctness. Our probabilistic designs are computationally efficient, with
order-optimal complexity. Our deterministic designs guarantee zero error
decoding, albeit via codes with high computational complexity in general. Our
coding schemes are based on network codes over ``scalable fields". Instead of
choosing coding coefficients from one field at every node, each node uses
linear coding operations over an ``effective field-size" that depends on the
node's distance from the source node. The analysis of our schemes requires
technical tools that may be of independent interest. In particular, we
generalize the Schwartz-Zippel lemma by proving a non-uniform version, wherein
variables are chosen from sets of possibly different sizes. We also provide a
novel robust distributed algorithm to assign unique IDs to network nodes.Comment: 12 pages, 7 figures, 1 table, under submission to INFOCOM 201
Polynomial time algorithms for multicast network code construction
The famous max-flow min-cut theorem states that a source node s can send information through a network (V, E) to a sink node t at a rate determined by the min-cut separating s and t. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to re-encode the information they receive. We demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed. We give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity. We extend these algorithms to integer capacities and to codes that are tolerant to edge failures
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Cores of Cooperative Games in Information Theory
Cores of cooperative games are ubiquitous in information theory, and arise
most frequently in the characterization of fundamental limits in various
scenarios involving multiple users. Examples include classical settings in
network information theory such as Slepian-Wolf source coding and multiple
access channels, classical settings in statistics such as robust hypothesis
testing, and new settings at the intersection of networking and statistics such
as distributed estimation problems for sensor networks. Cooperative game theory
allows one to understand aspects of all of these problems from a fresh and
unifying perspective that treats users as players in a game, sometimes leading
to new insights. At the heart of these analyses are fundamental dualities that
have been long studied in the context of cooperative games; for information
theoretic purposes, these are dualities between information inequalities on the
one hand and properties of rate, capacity or other resource allocation regions
on the other.Comment: 12 pages, published at
http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/318704 in EURASIP
Journal on Wireless Communications and Networking, Special Issue on "Theory
and Applications in Multiuser/Multiterminal Communications", April 200
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