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Efficient Operation of Wireless
Packet Networks Using Network
Coding
Desmond S. Lun, Muriel M´edard, and Ralf Koetter
指導老師:許子衡 老師
學生:羅英辰
學號:M97G0216
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Introduction
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Lossless Networks
There is a significant effect on many network
problems, particularly multicast, where it has
been given the name, the “wireless multicast
advantage”.
Minimum-energy broadcast problem
Wireline:Various
minimum-weight spanning tree
algorithm.<NP-complete>
Multicast Incremental Power(MIP)
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Random multicast connections.
Random wireless networks of varying size.
Reductions ranging from 13% to 49% .
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A.Model
A directed hypergraph H=(N,A)
A is the set of hyperarcs.
N is the set of nodes.
A hyperarc is a pair (i,J).
i
are start nodes, which are included N.
J
are end nodes, which are non-empty subset of N.
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(i,J) represents a lossless broadcast link from i
to nodes in the non-empty set J.
zi,J is the average rate at which packets are
injected and received on hyperarc (i,J).
The rate vector z is called the coding subgraph
and can be varied within a constraint set Z
dictated to us by lower layers.
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B.Single multicast connections
A multicast of rate arbitrarily close to R is
achievable with coding from source node s to
t T
sink nodes in the set T.
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From such a coding subgraph, the connection
can be straightforwardly achieved using the
decentralized, random coding schemes or by
modifying the deterministic coding schemes.
To establish a minimum-cost multicast
connection in a lossless wireless packet
network.
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These two problems:
Subgraph
selection program
Coding program
Subgraph selection program:
f is a cost function.
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We have Z 0.1 A
And f z (i , J )A ai , J zi , J
•ai,J is the cost per unit rate.
We have flows x(1)
and x(2) of unit size from
t1 to t2.
. zi , J max
(1)
( 2)
x
,
x
jJ iJj jJ iJj
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It achieves the optimal cost of 5/2.
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The constraint set not only necessarily induces a
degree of coupling among separate links because of
contention for the wireless medium, it is also usually
difficult to describe.
Heuristic approach is to find a set of feasible
constraint sets {Z1, Z2, . . . , ZN} (for example, each
Zn could correspond to the links established by some
set of noninterfering transmitters)
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N
N
n 1
n 1
Z n Z n , 0, n 1
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The constraint set Z poses less of a problem in
low energy systems because nodes seldom
transmit and there is less contention.
If energy is the most limiting constraint and we
wish to achieve minimum-energy multicast
without regard for throughput or bandwidth,
then Z can be dropped altogether.
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ai,J
represents the energy required to transmit
to nodes in J from node I for some fixed time
interval.
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