1. Reliability Gain of Network Coding - INFOCOM 08
University of Massachusetts

2. Motivation
NC improves Network Reliability by reducing the # of retransmission in lossy network
Capacity gain of NC extensively studied
Exact reliability gain of NC is not well known
Goal: Quantify the reliability gain of NC

3. Contribution
Define the expected number of transmissions per packet

4. Network Topology Topology: Tree based reliable multicast network
s: source
p: probability of pkt loss
k: each node has k children

5. Four error control techniques
End-to-End ARQ:
Source: Root of the tree retransmits each pkt until it is correctly received by all the receivers.
Others: only forward pkts
End-to-End FEC: rateless coding
Same as End-to-End ARQ
Src: Block coding mechanism is used to create coded pkts

6. Four error control techniques
Link-by-Link ARQ
Each node is responsible for each pkt to its children
Parents retransmit pkts until they are delivered to its children
Link-by-Link FEC – NC
Each node performs encoding and forwards pkts.

7. Analysis…
Quantifies..
Probability distribution of the number of transmissions
Expected number of transmissions

8. End-to-End Error Control
Probability distribution of the number of transmissions
Nr: the total # of transmissions of a pkt from the root of a subtree of height r
- P of j pkts transmitted out of i
- Fr(i) = P{ Nr <= i }: probability of Nr <= i, r: height

9. End-to-End Error Control
Fo(i) : r=0, leaf node
1) End-to-End ARQ
2) End-to-End FEC: need at least B pkt for decoding..

10. End-to-End Error Control
Expected # of transmissions
At root, height h:
1) End-to-End ARQ
Sending a pkt again because the pkt is not delivered, so (1 – F(h))
2) End-to-End FEC
Need 1 retransmission for B pkts

11. End-to-End Error Control
Xr : # of transmissions in a subtree per each pkt at the root
The expected # of transmissions per pkt in the entire tree
: the expected # of transmissions at root
: the total # of transmission for the pkt

12. Link-by-Link Error Control
Link-by-Link: relationship only between a parent and its children
Fr(i) = P{ Nr <= i }: probability of Nr <= I
Link-by-Link ARQ NC

13. Link-by-Link Error Control
Expected # of transmissions at root
1) Link-by-Link ARQ
2) NC

14. Link-by-Link Error Control
Total # of transmissions in the entire tree
# of nodes at height r
Each node has K children

15. Numerical Results Expected # of transmissions at root w/ different p
B: 16, h=2

16. Numerical Results Expected # of transmissions in tree w/ different p
B: 16, h=2

17. Numerical Results
Effect of Block size

18. Conclusion
Quantified the reliability benefit of NC for tree based multicasting
Analyzed the expected number of transmissions at source and within tree