63,237 research outputs found
Optimal Index Codes via a Duality between Index Coding and Network Coding
In Index Coding, the goal is to use a broadcast channel as efficiently as
possible to communicate information from a source to multiple receivers which
can possess some of the information symbols at the source as side-information.
In this work, we present a duality relationship between index coding (IC) and
multiple-unicast network coding (NC). It is known that the IC problem can be
represented using a side-information graph (with number of vertices
equal to the number of source symbols). The size of the maximum acyclic induced
subgraph, denoted by is a lower bound on the \textit{broadcast rate}.
For IC problems with and , prior work has shown that
binary (over ) linear index codes achieve the lower bound
for the broadcast rate and thus are optimal. In this work, we use the the
duality relationship between NC and IC to show that for a class of IC problems
with , binary linear index codes achieve the lower bound on
the broadcast rate. In contrast, it is known that there exists IC problems with
and optimal broadcast rate strictly greater than
Communication Algorithms with Advice
We study the amount of knowledge about a communication network that must be given to its nodes in order to efficiently disseminate information. Our approach is quantitative: we investigate the minimum total number of bits of information (minimum size of advice) that has to be available to nodes, regardless of the type of information provided. We compare the size of advice needed to perform broadcast and wakeup (the latter is a broadcast in which nodes can transmit only after getting the source information), both using a linear number of messages (which is optimal). We show that the minimum size of advice permitting the wakeup with a linear number of messages in a n-node network, is Θ(nlog n), while the broadcast with a linear number of messages can be achieved with advice of size O(n). We also show that the latter size of advice is almost optimal: no advice of size o(n) can permit to broadcast with a linear number of messages. Thus a
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