Download - Farid Molazem Cmpt 820 Fall 2010
Mohamed Hefeeda
Cross-Layer Mac-Application Layer for Adaptive Retransmission and Packetization
Using Langrangian Optimization
Farid MolazemCmpt 820
Fall 2010
Mohamed Hefeeda
Introduction
We have seen that optimizing performance metrics separately in different layers might not result in the optimal solution for multimedia streaming applications
In this section, we design application-MAC layer optimization solution to minimize received video distortion
In order to do this, we find the optimal packet size and number of retransmissions necessary for the packets
We formulate the problem as an optimization function with constraint and solve it through lagrangian multipliers
Mohamed Hefeeda
Modulation
Modulation:- Varying a property of a highFrequency signal (carrier signal)to convey another signal
Digital Modulation- Carries bit data in the form of symbols
www.wikipedia.com
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Mohamed Hefeeda
Motivation for cross-layer optimization
Current packetization algorithm used in MAC layer- Does not consider time constraints- Does not consider distortion
• How does MAC layer do packetization?- : Header overhead from OSI layers- b: number of bits per symbol- : Probability of symbol error
Mohamed Hefeeda
Optimizing packetization in MAC layer does not consider characteristics of video streams
Multimedia over IP and wireless networks – M. Van Der Schaar
Mohamed Hefeeda
Formalizing Joint Cross-Layer Optimization
Organize video stream into layers according to delay deadlines of video frames- Data from different deadline layers are not jointly packetized
Hint track for packetization 1 -
Hint track for packetization 1 -
Hint track for packetization 1 - ⋮
Scalable Video Bitstream
Multi-track hinting
Mohamed Hefeeda
Formalizing Joint Cross-Layer Optimization
Multi-track hinting- Real time adaptation of packet sizes when encoding is
performed- Real time prioritization of packets based on their distortion
impacts- Real time optimization of scheduling based on the deadline
Goal of our cross-layer optimization- Minimize video distortion under a delay constraint
• The optimal packet size • Maximum number of times packet j is transmitted
Mohamed Hefeeda
Formalizing Joint Cross-Layer Optimization
Video distortion:- Packet j received: - Packet j lost:
• Whenever packet j is received successfully, total distortion is reduced:
- Represents the utility of receiving packet j- We want to maximize the expected utility in group of pictures
(GOP)
- : number of packets in a GOP- : Probability of successfully receiving packet j with respect to bit
error probability of - Delay constraint:
Mohamed Hefeeda
Formalizing Joint Cross-Layer Optimization
- : number of packets in a GOP- : Probability of successfully receiving packet j with respect to
bit error probability of - Delay constraint:
How to compute - Packet loss probability
Mohamed Hefeeda
Packetizing and transmitting data with common deadlines
We solve the problem for video layers with common deadline
We show that the problem of delay constrained transmission can be mapped to rate constrained transmission- There are Q layers with common decoding deadline- The layers are partitioned into packets and the optimal
retransmission strategy is computed for these packets- : number of packets- : size of packet j- number of times packet j is retransmitted- Time to transmit packet j:
Mohamed Hefeeda
Packetizing and transmitting data with common deadlines
The delay constrained could be rewritten as:
Optimization problemMax [ ] subject to
Mohamed Hefeeda
Lagrangian formulation
We do not know how many time each packet is retransmitted (
Optimization function using Lagrangian formulation:
Could be decomposed to optimization functions
Mohamed Hefeeda
Lagrangian formulation
A strategy to find maximum and minimum of a function subject to a constraint- Max f(x, y) subject to g(x,y)=c
Introduce variable Lagrange multiplier)
Maximum and minimum happens when f and g are tangent
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Mohamed Hefeeda
Lagrangian formulation
Solving the optimization function:
• Optimization function grows as grows
• Optimization function will be less than or equal to 0optimal value:
Actual retransmission limit
Mohamed Hefeeda
Real time cross layer algorithm for video streaming
Compute the decoding deadline for each coded block and assume there are k separate deadlines
Organize the bitstream in deadline layers and sort the deadlines in ascending order
For k=1:K- Gather all deadline layers with deadline ()- Determine - Solve rate constrained optimization problem for this deadline- Sort the packets in descending order of )/- For n=1:
• Tune the actual transmission limit • Transmit the packets and update the current time• Break if current time is larger than
Mohamed Hefeeda
Conclusions
Optimizing packet size and retransmission parameter based on MAC layer alone will be sub-optimal for video streaming applications
We can find and analytical optimal solution for packet size and retransmission parameter to minimize video distortion in the special case of all packets having the same decoding deadline
We can use this solution to design a greedy algorithm for the case we have different data with different decoding deadlines. This greedy algorithm is fast and real time and can use MAC layer feedback to determine the number of times current packets can be transmitted
Mohamed Hefeeda
Thanks