IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, FEBRUARY 2009
Dong Nguyen, Tuan Tran, Thinh Nguyen, and Bella Bose, Fellow, IEEE
Speaker: Yu-Jen Lai
Cheng-Chih Chao
Advisor: Hung-Yu Wei
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Introduction – Network Coding
Broadcast Schemes
Performance Analysis
Simulation Result
Conclusion
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How to transmit data reliably?
Traditional approaches:
1.Automatic repeat-request (ARQ)
2.Forward error correction (FEC)
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R1 can recover b as a+(a+b)
 R2 can recover a as b+(a+b)
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We can use Network Coding for both
increase reliability and throughput
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Scheme A (Memoryless Receiver)
 The sender has to resend a packet until all the
receivers receive this packet correctly and
simultaneously
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Scheme B (Typical ARQ Scheme)
 Receiver immediately sends a NAK only if there is a
packet loss in the current time slot
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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
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Scheme D
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Transmission bandwidth
 The average number of transmissions required to
successfully transmit a packet
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Calculate BW of schemes A, B, C, D.
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Let pi denote the packet loss probability of
receiver i.
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Scheme A and B (2 receivers)
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M receivers
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Proof (2 receivers)
 Let X1 and X2 be the numbers of attempts to
deliver a packet to R1 and R2
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Proof (M receivers)
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Scheme C (2 receivers)
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Proof
 N: buffer size, assume p1<p2
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Scheme C (M receivers)
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Proof
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Scheme D (M receivers)
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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
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Calculate network coding gain
 Compare the BW of C and D with B
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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)
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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.
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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
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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)
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Network coding gain V.S. packet loss probability in a 5receiver 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.
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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.
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Categories B: Correlate packet loss
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Correlate packet loss (conditional prob.)
 More correlated, less loss pair to code
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Categories C: Two-state Markov chain
 Two channel state: “bad” and “good”
 α=pgood→bad ; β=pbad→good
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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).
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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
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Hamming (7,4) code:
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