Wireless Broadcast Using Network Coding

1. IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, FEBRUARY 2009 Speaker: Yu-Jen Lai Cheng-Chih Chao Advisor: Hung-Yu Wei Wireless Broadcast Using Network Coding Dong Nguyen, Tuan Tran, Thinh Nguyen, and Bella Bose, Fellow, IEEE

2. Outline • Introduction – Network Coding • Broadcast Schemes • Performance Analysis • Simulation Result • Conclusion

3. Reliable Broadcast • How to transmit data reliably? Traditional approaches: • Automatic repeat-request (ARQ) • Forward error correction (FEC)

4. NC in wireless ad hoc networks • R1 can recover b as a+(a+b) • R2 can recover a as b+(a+b)

5. NC in broadcast scheme • We can use Network Coding for both increase reliability and throughput

6. Broadcast Schemes • Scheme A (Memoryless Receiver) • The sender has to resend a packet until all the receivers receive this packet correctly and simultaneously • Scheme B (Typical ARQ Scheme) • Receiver immediately sends a NAK only if there is a packet loss in the current time slot

7. Broadcast Schemes (cont.) • Scheme C (Time-Based Retransmission) • Transmission phase and retransmission phase • The sender maintains a list of lost packets • In the retransmission phase, xoring a maximum set of the lost packet to retransmit • Scheme D (Improved Time-Based Retransmission) • Dynamically change the combined packets based on what the receivers have received Scheme C Scheme D

8. Performance analysis • Transmission bandwidth • The average number of transmissions required to successfully transmit a packet • Calculate BW of schemes A, B, C, D. • Let pi denote the packet loss probability of receiver i.

9. Performance analysis (Scheme A and B) • Scheme A and B (2 receivers) • M receivers

10. Performance analysis (Scheme A and B) • Proof (2 receivers) • Let X1 and X2 be the numbers of attempts to deliver a packet to R1 and R2

11. Performance analysis (Scheme A and B) • Proof (M receivers)

12. Performance analysis (Scheme C) • Scheme C (2 receivers) • Proof • N: buffer size, assume p1<p2

13. Performance analysis (Scheme C) • Scheme C (M receivers) • Proof

14. Performance analysis (Scheme D) • Scheme D (M receivers) • Proof • In the long run, the number of losses will be dominated by the number of losses at the receiver with the largest error probability

15. Performance analysis (cont.) • Calculate network coding gain • Compare the BW of C and D with B

16. Simulation result • Simulation categories • Packet losses independent, uncorrelated across the receivers • Packet losses independent, correlated across the receivers • Burst losses (using two-state Markov chain)

17. Simulation result (1) • Transmission bandwidths of schemes A, B, C, D, under 2 receivers and p2=0.1, p1 varies • The number of transmissions per successful packet in scheme D is the smallest, which is slightly more efficient than scheme C.

18. Simulation result (2) • Network coding gain V.S. different p1 • The gain is largest when p1 and p2 is equal. Because in this case, the maximum number of lost packet pairs is achieved. • On the other hand, when two receivers have disparate packet loss rates, the coding gain is small

19. Simulation result (3) • Transmission bandwidth versus the number of receivers • Scheme C and D significantly outperform scheme A and B when the number of receivers is large • Scheme C increases very slightly ; Scheme D is unchange (Theorem 3)

20. Simulation result (4) • Network coding gain V.S. packet loss probability in a 5-receiver scenario • The packet loss probabilities at other receivers are: p2=p3=0, p4=p1+0.3, p5=0.3 • Even if some receiver without a packet loss, network coding scheme is still better.

21. Simulation result (5) • Transmission bandwidth of finite buffer size • For infinite buffer size simulation, N = 1000. In this case, we consider finite buffer size under p1=p2. • We can see that BW is lower when buffer size increase. It is because that larger buffer size has more coding pair and more coding opportunity.

22. Simulation result (6) • Categories B: Correlate packet loss

23. Simulation result (7) • Correlate packet loss (conditional prob.) • More correlated, less loss pair to code

24. Simulation result (8) • Categories C: Two-state Markov chain • Two channel state: “bad” and “good” • α=pgood→bad ; β=pbad→good

25. Conclusion • Advantage • The idea of using network coding is good (scheme C). • (In scheme D) It also concern that retransmission packet may be loss only at part of receivers. • The analysis procedure is simple and result is concise (closed-form). • Drawback • Some condition can be improved • The full knowledge of which packet loss by which receiver • The price of using network coding is that packet need to be decoded in receiver (but this price is small compared with the network coding gain) • Simulation is too many simplification(ex. no contention, no higher layer considered) • As the buffer increase, the latency may also increase (not suitable for multimedia applications) • It will break down if there is no feedback channel • Full of ACK in this system since it assume BS knows everything; besides, there is a big problem that broadcast ACK may contention severely

26. Thanks for listening!!

27. Backup: Hamming Code • Hamming (7,4) code: