Reliability Gain of Network Coding
- INFOCOM 08
University of Massachusetts
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
Contribution
• Define the expected number of transmissions
per packet
Network Topology
• Topology: Tree based reliable multicast network
• s: source
• p: probability of pkt
loss
• k: each node has k
children
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
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.
Analysis…
• Quantifies..
– Probability distribution of the number of
transmissions
– Expected number of transmissions
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
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..
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
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
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
1) Link-by-Link ARQ
2) NC
Link-by-Link Error Control
• Expected # of transmissions at root
• 1) Link-by-Link ARQ
• 2) NC
Link-by-Link Error Control
• Total # of transmissions in the entire tree
• # of nodes at height r
– Each node has K children
Numerical Results
• Expected # of transmissions at root w/ different p
– B: 16, h=2
Numerical Results
• Expected # of transmissions in tree w/ different p
– B: 16, h=2
Numerical Results
• Effect of Block size
Conclusion
• Quantified the reliability benefit of NC for tree
based multicasting
• Analyzed the expected number of
transmissions at source and within tree