Speaker: Yu-Jen Lai Cheng-Chih Chao Advisor: Hung-Yu Wei 2009/06/08 1 Dong Nguyen, Tuan Tran, Thinh Nguyen, and Bella Bose, Fellow, IEEE IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, FEBRUARY 2009

Introduction – Network Coding Broadcast Schemes Performance Analysis Simulation Result Conclusion 2009/06/082

How to transmit data reliably? Traditional approaches: 1.Automatic repeat-request (ARQ) 2.Forward error correction (FEC) 2009/06/083

R 1 can recover b as a+(a+b) R 2 can recover a as b+(a+b) 2009/06/084

We can use Network Coding for both increase reliability and throughput 2009/06/085

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 2009/06/086

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 2009/06/087 Scheme CScheme D

Transmission bandwidth  The average number of transmissions required to successfully transmit a packet Calculate BW of schemes A, B, C, D. Let p i denote the packet loss probability of receiver i. 2009/06/088

Scheme A and B (2 receivers) M receivers

Proof (2 receivers)  Let X1 and X2 be the numbers of attempts to deliver a packet to R1 and R2

Proof (M receivers)

Scheme C (2 receivers) Proof  N: buffer size, assume p1<p2

Scheme C (M receivers) Proof

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

Calculate network coding gain  Compare the BW of C and D with B

Simulation categories A.Packet losses independent, uncorrelated across the receivers B.Packet losses independent, correlated across the receivers C.Burst losses (using two-state Markov chain)

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.

Network coding gain V.S. different p 1  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

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)

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.

Transmission bandwidth of finite buffer size  For infinite buffer size simulation, N = 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.

Categories B: Correlate packet loss

Correlate packet loss (conditional prob.)  More correlated, less loss pair to code

Categories C: Two-state Markov chain  Two channel state: “bad” and “good”  α=p good→bad ; β=p bad→good

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 2009/06/0825

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Hamming (7,4) code: 2009/06/0827