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