Network Coding and Wireless Physical-layer ... - Jacobs University
Network Coding and Wireless Physical-layer ... - Jacobs University
Network Coding and Wireless Physical-layer ... - Jacobs University
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LIST OF FIGURES<br />
ix<br />
4.4 <strong>Network</strong> example with scalable data multicast . . . . . . . . . . . . . . . . 47<br />
4.5 Line graph derived from Fig. 4.4 . . . . . . . . . . . . . . . . . . . . . . . . 47<br />
4.6 The minimum subtree graph derived from Fig. 4.5 . . . . . . . . . . . . . . 48<br />
5.1 <strong>Network</strong> coding in a butterfly network . . . . . . . . . . . . . . . . . . . . 60<br />
5.2 Detailed system model including LT-encoding <strong>and</strong> decoding blocks as well<br />
as the buffer structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60<br />
5.3 Robust soliton distribution with k = 1000, c = 0.1, <strong>and</strong> δ = 0.5 . . . . . . . 63<br />
5.4 Robust soliton distribution around the first peak in comparison with distorted<br />
distribution caused by erasures at the edge BD . . . . . . . . . . . 66<br />
5.5 Robust soliton distribution around the second peak in comparison with<br />
distorted distribution caused by erasures at the edge BD . . . . . . . . . . 66<br />
5.6 Histogram of the number of LT-encoded symbols needed to be transmitted<br />
in an erasure-free case such that all original symbols are recovered . . . . . 67<br />
5.7 Comparison of histograms of the number of LT-encoded symbols needed<br />
to be transmitted such that all original symbols are recovered in two cases,<br />
a point-to-point communication with an erasure probability of 0.05 <strong>and</strong> a<br />
coded butterfly network with an erasure probability of 0.1 at BD . . . . . 67<br />
5.8 <strong>Network</strong> coding in a butterfly network when only BD is erasure-prone . . . 68<br />
5.9 Comparison of histograms of the number of LT-encoded symbols needed to<br />
be transmitted in a coded butterfly network with the erasure probability of<br />
0.1 at BD such that all original symbols are recovered in two cases, without<br />
using the proposed algorithm <strong>and</strong> with Algorithm 5.1 . . . . . . . . . . . . 73<br />
5.10 Comparison of histograms of the number of LT-encoded symbols needed to<br />
be transmitted in a coded butterfly network with the erasure probability of<br />
0.1 at BD such that all original symbols are recovered in two cases, without<br />
using the proposed algorithm <strong>and</strong> with Algorithms 5.1 <strong>and</strong> 5.2 . . . . . . . 74