1. Presented by Yung-Cheng Tu 2010/12/24
Introduction to Network Coding in Wireless Networks - The Random Linear Network Coding for Time Division Duplexing
Presented by Yung-Cheng Tu
2010/12/24

2. Reference papers Daniel E. Lucani, Muriel Médard and Milica Stojanovic
1. “Random Linear Network Coding for Time Division Duplexing: When to Stop Talking and Start Listening”, in INFOCOM 2009, April 2009.
2. “Random Linear Network Coding For Time Division Duplexing: Energy Analysis”,  in ICC Communication Theory Workshop, June 2009.
3. “Random Linear Network Coding for Time-Division Duplexing: Queueing Analysis”,  in IEEE International Symposium on Information Theory (ISIT), July 2009.
4. “Broadcasting in Time-Division Duplexing: A Random Linear Network Coding Approach,” in Workshop on Network Coding (Netcod), June 2009.
5. “Random Linear Network Coding for Time-Division Duplexing: Field Size Considerations”, in IEEE Globecom 2009 Communication Theory Symposium, November-December 2009.

3. About Muriel Médard
A professor in the Department of Electrical Engineering and and Research Laboratory of Electronics , MIT. Homepage:
She has about 20 network coding papers published per year from 2002 to 2010.
2009 Communication Society and Information Theory Society Joint Paper Award
Tracey Ho , Muriel Medard, Rolf Kotter, David Karger, Michelle Effros Jun Shi, Ben Leong,  "A Random Linear Network Coding Approach to Multicast", in IEEE Transactions on Information Theory, vol. 52, no. 10, pp , October 2006.
2009 William R. Bennett Prize in the Field of Communications Networking
Sachin Katti , Hariharan Rahul, Wenjun Hu, Dina Katabi, Muriel Medard, Jon Crowcroft, "XORs in the Air: Practical Wireless Network Coding", in IEEE/ACM Transactions on Networking, vol. 16, Issue 3, pp ,June 2008,.

4. Outline Brief of Network Coding
XORs (COPE)
Random Linear Network Coding
Random Linear Network Coding for Time Division Duplexing
Analysis on coding block size
Analysis on energy consumption
Analysis on queueing
Broadcasting
Analysis on field size
Comments

5. Brief of Network Coding (1)
The concept of network coding was proposed by Rudolf Ahlswede et al. in 2000.
A router doesn’t just hand off the packets it receives; it mathematically combines them into new, hybrid packets.
Traditional Network
Network Coding x1 x2 x3
x1=D1(Y)
x2=D2(Y)
x3=D3(Y) R1 R1 x1 x3 x2 x1 x3 x2 x1 Y S x2 R2 S R2 y1 y2 y3
Y=F(X) x3 R3 R3
[1] Rudolf Ahlswede, Ning Cai, Shuo-Yen Robert Li and Raymond W. Yeung, “Network Information Flow,” in IEEE Transactions on Information Theory, Vol. 46, No. 4, July 2000.

6. Brief of Network Coding (2)
If the combination is done cleverly enough, this makes the whole network more efficient.
But how that combination should be done, and what kinds of efficiency gains were possible, were unclear.
Without Network Coding
With Network Coding

7. Brief of COPE (1) Main idea
Use the XOR to forward multiple packets in a single transmission in wireless mesh network.
Packet a A S B
Packet b
Without Network Coding
With Network Coding a a a a b A S B A S B b b
ab
A sends a to S
S sends a to B
B sends b to S
S sends b to A
A sends a to S and keeps a
B sends b to S and keeps b
S sends ab to A and B.

8. Brief of COPE (2)
COPE provides a general scheme for inter-session wireless network coding.
They analyzed the throughput gains of XORs in single-hop wireless network.
The first deployment of network coding in a wireless network.
COPE can provide several-fold (3-4x) increase in the throughput of wireless ad hoc networks.

9. Random Linear Network Coding (1)
Coded packets are the linear combinations of original packs
Linear Network Coding can achieve the upper bound of network throughput obtained by Max-flow Min-cut theorem.
Coded packet Y1
Coded packet Y2
Coded packet Y3

10. Random Linear Network Coding (2)
Linear Network Coding (cont’d)
Recv 1 and Recv 2 can decode X1 and X2 only if and is nonsingular.
The structure of coded packets
A receiver must get M packets with independent coefficient vectors to decode packets.
Coefficient vector
Coefficient vector

11. Random Linear Network Coding (3)
How to select the coefficients ξ ?
Randomly Select
Coefficients are chosen uniformly at random from a finite field Fq (Fq is the set of integers from 0 to q-1, where q=2g )
If q is large, then the probability of that two coefficient vectors are dependent is small.
In the simple case of only one source and destination.
M original packets are coded to N packets. (N ≥ M)
The expected number of successfully received packets before having M linearly independent combinations, is xM x2 x1 S R yN y2 y1
Encode

12. Random Linear Network Coding for Time Division Duplexing (1)
The original network coding research considers a channel with no erasures and, therefore, no need for feedback.
For networks with packet erasures, two approaches have been used.
Transmitting coded data packets until the receiver sends an ACK. (In TDD mode, senders must stop and wait for ACK per-packet.)
Codes data packets in a block-by-block fashion using ACKs to indicate successful transmission of each block.

13. Random Linear Network Coding for Time Division Duplexing (2)
Why the network coding is better?
In unicast, the sender can reduce the retransmissions by sending more coded packets. y1 y2 y4 y3 y5 x1 x2 x4 x3
decode x4 x3 x2 x1 S R y1 y2 y4
encode y3 y5

14. Random Linear Network Coding for Time Division Duplexing (3)
Why the network coding is better? (cont’d)
In multicast, the sender only needs to know the number of packets that its receivers requires to decode packets, rather than which packets are required by the receivers.
Traditional Network
Network Coding x1 x2 x3 x4
R1 and R2 may loss different packets y1 y2 y3 y4 R1 R1 x4 x3 x2 x1 y4 y3 y2 y1 S S x1 x2 x3 x4
Retransmit 4 packets
Continue to transmit the other 2 coded packets y5 y6 R2 R2

15. Random Linear Network Coding for Time Division Duplexing (4)
The work focus on the problem of transmitting M data packets through a link using random linear network coding.
The system transmits Ni coded packets (CP), and waits to receive an ACK packet that updates the value of i to j, at which point it will transmit Nj coded packets.
The system will keep transmitting and stopping to update i, until i = 0.
i: the number of coded packets that the receiver requires to decoded.
Ni: the number of packets that the sender will send

16. Random Linear Network Coding for Time Division Duplexing (5)
Every time the system stops to wait for an ACK, it incurs in an additional delay.
We want to minimize the number of stops required to complete transmission of the M packets.
There is a natural trade off in the choice of the Ni’s.
if the Ni’s are too small given the channel conditions, the system will have to transmit more ACK packets.
if the Ni’s are too large, the receiver will have decoded the M packets before the transmitter stops.
The communication process

17. When To Stop Talking And Start Listening? [Infocom 2009]
How to estimated the Ni?
This paper uses a Markov chain to estimate the expected the completing time given the Ni.

18. When To Stop Talking And Start Listening? (cont’d)
The expected completing time:
, where
The objective is to minimize the value of TM.
Find the N1,N2,…NM
to solve the minimization problem.

19. When To Stop Talking And Start Listening? (cont’d)
Instead of using the previous approach, we perform a search for the optimal values Ni using integer values.
In particular, the search method for the optimal value can be made much simpler by exploiting the recursive characteristic of the problem.

20. When To Stop Talking And Start Listening? (cont’d)
Compare the utilization with other schemes
Optimal TDD (n=the bits of data in a coded packets)
Go-back-N (GBN) [15]
Selective Repeat (SR) [15]
[15] Ozugur, T., Naghshineh, M., Kermani, P., Copeland, J. A.,“On the performance of ARQ protocols in infrared networks”, Int. Jour. Commun. Syst., vol. 13, pp , 2000

21. Parameters: g=20 bits, nack=100 bits, n=10000 bits, h=80 bits, Trt=0
Parameters: g=20 bits, nack=100 bits, n=10000 bits, h=80 bits, Trt=0.25 ms
The utilization of network coding
is much better for high packet error probability.
*This is numerical results, not simulations or experiments.

22. The expected completing time of transmitting 10 packets with different Ni.
Full Duplex Optimal:
The sender transmits coded packets back-to-back until an ACK packet
Once the M packets have been decoded. The receiver transmits ACK packets each of duration Tack.
The TDD optimal scheme and the network coding full duplex optimal scheme have similar performance over a wide
range of block error probabilities.
*This is numerical results, not simulations or experiments.

23. Energy Analysis [ICC 2009]
Let Ep be the transmission energy of a coded packet, and Eack be the transmission energy of an ACK packet.
Using the same Markov chain state diagram in [Infocom 2009]
The expected energy for completing the transmission given that the Markov chain is in state i:
Objective: Find the N1,N2…,NM, to minimize EM.

24. Energy Analysis (cont’d)
Numerical results
Consider the transmission power is normalized, i.e., P=1. (Eo=P*Tp, Eack=P*nack/R)
Other parameters used:
M = 10, packet size n = 10; 000 bits, R = 1:5 Mbps, h = 80 bits,
g = 20 bits, nack = 100 bits.
Energy consumption and Completion time with different schemes:

25. Queueing Analysis [ISIT 2009]
We study the scenarios for random linear network coding for TDD channels when the data packets arrive randomly at the source node according to a Poisson process.
Queue model
If the buffer has fewer than m data packets, the system will wait until m packets arrive before providing service.
If the buffer contains more than K packets, the system will service exactly K packets.
If the buffer has M packets with m ≤ M ≤ K, then the system will service M packets.

26. Queueing Analysis (cont’d)
We can use the bulk queueing model M/G(m,K)/1 developed in [7] in to study the problem.
In [7], the transition probability of the number of packets in the queue is presented.
Assume that the number of coded packets to be sent back-to-back (Ni) are chosen to minimize the mean transmission time.
Expected service time of each block transmission can obtained. [Infocom 2009]
[7] Bar-Lev, S. K., Parlar, M., Perry, D., Stadje, W., Van der Duyn Schouten, F. A., “Applications of bulk queues to group testing models with incomplete identification”,
European Journal of Operational Research, no. 183, pp , 2007.

27. Queueing Analysis (cont’d)
Numerical results
The mean queue size and mean batch size for different (m,K) with λ = 30 PACKET/S, B = 30
Smaller K, longer queue
Smaller m, shorter queue
m=minimum coding group size, K=maximum coding group size.
Previous works assumed that the coding group size M is fixed.
This work tells us we should code all packets in queue together once the system idles.

28. Broadcasting in Time-Division Duplexing [Netcod 2009]
The time window allocated to the system to transmit N, coded packets in broadcasting scheme
Allocate a time period to each receiver’s ACK.

29. Broadcasting in Time-Division Duplexing (cont’d)
Transmission begins with M information packets, which are encoded into NM random linear coded packets.
Each ACK informs the transmitter how many dofs are missing, say i1, i2,…,iN for receivers 1,2, ..., N, respectively.
The transmitter then sends Ni coded packets, where i=maxj=1,2,…N ij.
If an ACK is lost, the transmitter assumes the previous state for
the corresponding receiver.
This process is repeated until all M packets have been decoded successfully by all receivers.

30. Broadcasting in Time-Division Duplexing (cont’d)
Markov chain for the case of N = 2 receivers and a block size of M = 3.
If we consider independent packet erasure channels for each of the receivers, the transition probability is
Equal to the transition probability P(s’i|Ni) in [infocom 2009]

31. Broadcasting in Time-Division Duplexing (cont’d)
Similar to the work in [infocom 2009]
Estimate the expected completing time of each state.
Find a Ni for each state to minimize expected completing time.
Comparison schemes
Worst link channel
In this heuristic we approximate the system as a link to the receiver with the worst channel, i.e. Pe = maxj Pej.
Broadcast with Round Robin in Full Duplex Channel (RR Full Duplex):
Broadcast with Round Robin in TDD (RR TDD)
the transmitter broadcasts all M packets back-to-back,
If there are nodes that have not acknowledged the block of packets, the transmitter repeats the process, i.e. sends all M packets.
Why not compare with Selective Repeat?

32. Broadcasting in Time-Division Duplexing (cont’d)
Numerical results

33. Field Size Considerations [Globecom 2009]
This work considers the broadcasting TDD scheme.
The objective is also to minimize the value of the expected transmission time TM.
The previous works assumed the field size q is given.
This work analyze the mean completing time of optimal TDD with different field size q.
q=2g

34. Field Size Considerations (cont’d)
Numerical results
Mean completion time for the TDD scheme with two receivers.
parameters R = 1.5 Mbps, h = 80 bits, nack = 100 bits.

35. Other issues of network coding
Summary
The authors proposed a network coding scheme for TDD to handle the retransmission when packets are lost.
They analyzed the one-hop performance of this scheme in terms of
Block size
Energy
Queue length
Field size
Other issues of network coding
Extension of XORs (routing, scheduling)
Load balance (Multi-path routing, bandwidth allocation)
Security and reliability

36. Comments Only numerical results.
The improvement of network coding seems slight, especially when packet error rate is low.
Prof. Muriel Médard tries to perform the network coding in underwater network in recent years.
The analyses are worth learning.
The scheme can be extended to multi-hop network. But the analyses will become much hard.
How to extend to TDMA in mesh network is a problem.