Farid Molazem Cmpt 820 Fall 2010

1. Cross-Layer Mac-Application Layer for Adaptive Retransmission and Packetization Using Langrangian Optimization FaridMolazem Cmpt 820 Fall 2010

2. 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

3. Modulation • Modulation: • Varying a property of a high Frequency signal (carrier signal) to convey another signal • Digital Modulation • Carries bit data in the form of symbols www.wikipedia.com www.wikipedia.com

4. 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

5. Optimizing packetization in MAC layer does not consider characteristics of video streams Multimedia over IP and wireless networks – M. Van Der Schaar

6. 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 Scalable Video Bitstream Hint track for packetization 1 - Hint track for packetization 1 - Hint track for packetization 1 - Multi-track hinting

7. 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

8. 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:

9. 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

10. 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:

11. Packetizing and transmitting data with common deadlines • The delay constrained could be rewritten as: • Optimization problem Max [ ] subject to

12. Lagrangian formulation • We do not know how many time each packet is retransmitted ( • Optimization function using Lagrangian formulation: • Could be decomposed to optimization functions

13. 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 www.wikipedia.com

14. Lagrangian formulation • Solving the optimization function: • Optimization function grows as grows • Optimization function will be less than or equal to 0 • optimal value: • Actual retransmission limit

15. 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

16. 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

17. Thanks