Chapter 6 Optimize The Payload Length In DRP
6.3 Numerical Result
The variation of throughput with various bit error rates in AWGN is shown in Figure 7 and Figure 8. If the successive reservation time is fixed, the throughput using the payload length L′opt would be close to the maximal throughput using the payload length Lopt at higher tramission rate RPSDU. Because the packet transmission time T2 is shorter at the higher data rate, the number of successful packets be more, and N′ approximates N very well. With the same reason, N′ approximates N at longer reservation time. In Figure 9 and Figure 10, it shows the variation of packet error rate and L′opt with different RPSDU. If the bit error rate is small, the payload length could be larger, because the packet error rate increases slowly when the payload length gets longer. The number of packets in the continuous interval would becomes more at higher RPSDU, but the packet error rate increases more slowly than it, . Figure 11 and Figure 12 show the throughput and packet error rate with different bit error rate using the optimal payload length at RPSDU = 480Mbps and RPSDU = 200Mbps. In Table IV, we set the target packet error rate must be less than 0.05. It shows its throughput is much less than that with larger packet error rates, because the proportion of overhead is too large. We must consider both the proportion of overhead and the packet error rate to reach the maximal throughput.
Figure 7 Variation of throughput with bit error rate in AWGN using Lopt and L′opt at 480 Mbps and 200Mpswith M=4
Figure 8 Variation of throughput with bit error rate in AWGN using Lopt and L′opt at 480 Mbps and 200Mpswith M=8
Figure 9 Variation of L′opt with different RPSDU
Figure 10 Variation of packet error rate with different RPSDU
Figure 11 Throughput and packet error rate with different bit error rate using the optimal payload length at RPSDU = 480Mbps
Figure 12 Throughput and packet error rate with different bit error rate using the optimal payload length at RPSDU = 200Mbps
Table IV Throughput for different payload length
Reservation MAS Number 8
Bit Error Rate 10−5
RPLCP 480 Mbps 200 Mbps
Packet Error Rate 0.27 0.05 0.23 0.05
Payload Length in bytes 4007 (Lopt) 636 3261 (Lopt) 636
Throughput in Mbps 193 75.5 107.9 61.4
CHAPTER 7
MINIMAL RESERVED TIME FOR HD H.264 VIDEO
In this section, we propose a model to evaluate the minimal reservation time for the wireless HD H.264 video transmission under the error constraint. First, we formulate an optimization problem to calculate the minimal number of packets that we must reserved to satisfy the error constraint before the decoder is empty. Second, we will show that the ratio of the minimal number of reserved packets to the packets to be transmitted approximates the reciprocal of packet success rate, when the number of transmitted packets is large enough. Third, we consider the impact of the payload length on the reservation time and find the optimal payload length to reach the minimal reservation time in AWGN. We would prove that the payload length for minimal reservation time would converge to L,opt if the number of packets to be transmitted is large enough. The condition is always satisfied because the video frame size of the HD H.264 video is large and would be fragmented into a large number of packets.
7.1 Minimal Reservation Time under fixed Packet Error Rate
For the wireless HD H.264 video transmission, the error rate of the video frame per 120-minute HD movie should be less than one [15]. The error rate of the video frame 𝑃𝑒 of this requirement must be less than 1 120 ∗ 60 ∗ f at f fps, where f is the frame rate of the transmitted video. Suppose that a video frame is fragmented into NF packets, and the packets error rate must be less than 1 − 1 − PN F e to satisfy the constraint without retransmission. If NF becomes larger, the packets error rate gets smaller. Because the size of the H.264 HD video frame is large, it could be fragmented to a great number of packets, so the packet error rate must be very small, and the complexity of PHY would be high. We could use the retransmission policy to solve this problem, but we must calculate the exact time for retransmission and reserve it before the deadline of the video frame, or the latency would happen.
Assume that we reserve the time which is enough to transmit NR packet where NR is larger than NF, the error rate of the video frame is the probability that there is less than NF-1 packets transmitting correctly. From Eq. (6), the probability of error is:
PF = NF−1Pi∗ 1 − P NR−i
Although the transmission time of the video frame may be less than the time we reserved, the remaining time would not be wasted, because it could be released in WiMedia. To find the minimal reservation time under the fixed packet error rate, we could find smallest NR and then times the T2 shown in Figure 6. We suppose that
This optimization problem is an integer programming problem. We must solve it and create a table to look up ahead of implementation. If NF and the packet error rate is small, Nmin would be several times of NF . It takes much time to retransmit the error packet. When NF big enough, the ratio Nmin to NF converges to the reciprocal of packet success rate. It is shown below:
If NF → ∞, then Nmin → ∞.
By central limit theroem, X − Nmin ∗ P L Nmin ∗ P L ∗ 1 − P L
~N 0,1 ,
where X is the number of packets receivied correctly.
P X − Nmin ∗ P L
Because the video frame size of HD H.264 video is large and we can hold some video frame in the MAC buffer, the amount of fragmented packets is large enough to make NNmin
F converges to the reciprocal of packet error rate.
7.2 Minimal Reserved Time Analysis
The minimum reservation time is to ensure the QoS of HD video transmission over the error-prone wireless environments. In home environment, the transmission rate is basically stable, in this case, the minimal reserved time is primarily affected by the payload length. To calculate the optimal payload length for achieving the minimal reservation time, following optimization problem is constructed:
Min Nmin(L) ∗ T2 L (15)
where Nmin(L) is minimal reserved number of packets fragmented by payload length L, and T2 L is the packet transmission and ACK response time using payload length L.
where NF L is the number of the fragmented packets of each video frame using payload length L.
The optimization problem (15) is equivalent to:
Max 1
Nmin(L) ∗ T2 L
⇒ Max P L ∗ L
L ∗ NF L ∗ T2 L
Because the video frame size to transmit is constant for this problem, L ∗ NF L is a constant. The optimization problem becomes:
Max P L ∗ L T2(L)
This problem is the same as equation (9) and also an optimization problem to maximize the throughput, so L′opt = Lrop. For HD H.264 video transmission, the condition is always satisfied. We can use L′opt to fragment the video frames and use the equation (15) to calculated the reservation time in AWGN. The reservation time is
TR = Nmin L′opt ∗ T2 L′opt (16)
7.3 Numerical Result
When the number of fragmented packets is getting large, the ratio of minimal reservation packet number t would converge to the reciprocal of packet success rate.
The result is shown in Figure 13. It means that average retransmission times of each packet are about PSR1 .
Figure 13 Variation of minimal reservation packet number to the number of fragmented packets with bit error rate
If we buffer NMB video frames in the MAC and send NMB video frames every NMB ∗ f second, and the decoder buffer holds the same number of video frame, the latency of video would not happen. It means that the deadline of the NMB video frames is NMB ∗ f second, it must reserve enough time including retransmission to transmit NMB video frames before the deadline. Table VI is an example of created table by solving Eq. (14), where NMB is 15 at f=30, and the bit rate of video is from 10 Mbps to 20Mbps, and the range of payload length is from 125 bytes to 4095 bytes.
If NF is not on the table, we can use the linear interpolation to calculate the value of
NMIN
NF , and it could also satisfy the error constraint, because the convexity of the curve in Figure 13. Suppose that the bit rate and the frame rate of the HD H.264 video is 10 Mbps and 30fps respectively and buffer fifteen video frames in the MAC for our following simulation. The detail of parameter of video in our simulation is shown in Table VII.
TABLE VI Table of NNmin
Number of Frames in the MAC Buffer 15
Dead Line of the Video Frames 0.5 second (≈ 7 superframes)
Data Size in the Buffer 5 Mb
In Figure 14, we find that the approximated payload length for maximal throughput L′opt and the payload length Lrop of minimal Reservation time are close, and there is a little difference at small bit error rate, because the number of fragmented packets of the video is small. Figure 15 shows that the number of reserved MAS per superframe. The maximal MAS number which we can use per superframe is 224. From Figure 15, it could also transmit the HD video when the error rate is small such as 4 ∗ 10−4. Figure 16 and Figure 17 show the reserved MAS number with different bit error rates of 480Mbps and 200 Mbps with the error constraints of P = 10−8, 10−12, and 10−14 . We would find the reservation time is almost the same
and we can reserve a little more time to reach much smaller error rate of video frame.
When the bit error is small enough, the reservation time is small, and could support several to transmit HD H.264 video. If we try to let the packet error rate get small, the payload length must be getting small, and the overhead of each packet becomes larger, so the minimal reservation time must be longer to satisfy the error criteria of video frame. A numerical example is shown in Table VIII.
Figure 14 Payload length in different bit error rate for minimal reservation time with Pe = 10−8
Figure 15 Number of reserved MAS per superframe with Pe = 10−8
Figure 16 Reserved MAS number with different bit error rate at R=480Mbps under the error constraint Pe = 10−8, 10−12, and 10−14
Figure 17 Reserved MAS number with different bit error rate at R=200Mbps under the error constraint Pe = 10−8, 10−12, and 10−14
Table VIII Minimal reservation time for different payload length
Bit Error Rate 10−5
Bit rate of video 10 Mbps
Frame Rate of video 30 fps
NMB 15
Delay Constraint 0.5 s (≈7 superframe)
Error Rate of video frame 10−7
RPLCP 480 Mbps 200 Mbps
Packet Error Rate 0.28 0.05 0.24 0.05
Payload Length in bytes 4095 (Lopt′) 636 3384 (Lopt′) 636 Total Reservation Time 31729 μs 65480μs 55127μs 81597μs
Total Reserved MAS 124 256 216 319
MAS Per Superframe ≈19 ≈37 ≈31 ≈46
CHAPTER 8 CONCLUSIION
In this work, we have proposed an control architecture to transmit the HD H.264 in WiMdeia system. We have shown that HD H.264 video transmission can meet its performance criteria even with large packet error rate. An analytical model is also established to calculate the payload length for the minimal reservation time which is enough to transmit the fragmented packets with retransmission to satisfy the error constraint of video before the encoder buffer is ran out. The reservation time is close to the transmission time of the fragmented packet without retransmission multiplying the reciprocal of packet success rate. It means that the average retransmission times of each packet are about the reciprocal of PSR. Reserving additional time for retransmission, the error rate criteria of video frame could be satisfied easily, and could reduce the complexity of PHY layer. When the bit error rate is small enough, the architecture could support several users to transmit HD H.264 video.
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