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		Network Coding: Mixin' it up
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The information theoretic aspects of large networks with
many terminals presents several interesting and
non-intuitive phenomena. One such phenomenon was first
explored in a detailed manner in excellent work by Ahlswede
et al., who proved that for a large class of network
problems, allowing internal nodes to perform non-trivial
arithmetic operations on information on incoming links to
generate information on outgoing links could substantially
improve throughput, compared to the more traditional
scenario where such nodes were restricted to only copying
and forwarding incoming messages on outgoing links. Further
work by various authors showed how to design codes (called
network codes) to transmit under this new paradigm, and also
demonstrated exciting new phenomena for such coding
techniques such as robustness against network failures,
distributed design, and increased security.

We consider the low-complexity design and analysis of
network codes, with a focus on codes for multicasting
information. We examine both centralized and decentralized
design of such codes, and also randomized versus
deterministic design algorithms.  We compare different
notions of linearity and show the interplay between these
notions in the design of linear network codes. We determine
bounds on the complexity of network codes. We also consider
the problem of error-correction and secrecy for network
codes when a malicious adversary controls some subset of the
network resources.

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