February 2000 1

School of Computing ScienceSchool of Computing ScienceSimon Fraser University, CanadaSimon Fraser University, Canada

Rate-Distortion Optimized Streaming of Fine-Grained Scalable Video Sequences

Mohamed Hefeeda & ChengHsin Hsu

MMCN 2007

31 January 2007

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MotivationsMotivations

Multimedia streaming over the Internet is becoming very popular

- More multimedia content is continually created- Users have higher network bandwidth and more

powerful computers

Users request more multimedia content And they look for the best quality that their

resources can support

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Motivations (cont’d)Motivations (cont’d)

Users have quite heterogeneous resources (bandwidth)

- Dialup, DSL, cable, wireless, …, high-speed LANs To accommodate heterogeneity scalable video

coding: Layered coded stream

- Few accumulative layers- Partial layers are not decodable

Fine-Grained Scalable (FGS) coded stream- Stream can be truncated at bit level

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Motivations (cont’d)Motivations (cont’d)

Goal: Optimize quality for heterogeneous receivers

In general setting- FGS-coded streams - Multiple senders with heterogeneous bandwidth and

store different portions of the stream

Why multiple senders?- Required in P2P streaming:

• Limited peer capacity and Peer unreliability

- Desired in distributed streaming environment:• Disjoint network path Better streaming quality

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Our Optimization ProblemOur Optimization Problem

Assign to each sender a rate and bit range to transmit such that the best quality is achieved at the receiver.

Consider a simple example to illustrate the importance of this problem

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Example: Different Streaming SchemesExample: Different Streaming Schemes

Non-scalable Layered

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Example: Different Streaming SchemesExample: Different Streaming Schemes

Optimal FGS ScalableFGS Scalable

1. FGS enables us to get the best quality from senders

2. However, there too many allocation options, and we need to carefully choose the optimal one

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Problem FormulationProblem Formulation

First: single-frame case- Optimize quality for individual frames

Then: multiple-frame case- Optimize quality for a block of frames- More room for optimization

- Details are presented in the extended version of the paper

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Input ParametersInput Parameters

T : fixed frame period n : number of senders bi : outgoing bandwidth of sender i

bI : incoming bandwidth of receiver

si : length of (contiguous) bits held by sender i

Assume w.l.g. s1 <= s2 <= …… <= sn

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Allocation: A = {(Δi , ri) | i = 1, 2, …, n}- Δi : number of bits assigned to i

- ri : streaming rate assigned to i

Specifies:- Sender 1 sends range [0, Δ1 -1] at rate r1

- Sender 2 sends range [Δ1 , Δ1+Δ2 -1] at rate r2

- …- Sender i sends range at rate ri

OutputsOutputs

]1,[1

1

1

−ΔΔ ∑∑=

−

=

i

tt

i

tt

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Integer Programming ProblemInteger Programming Problem

Minimize distortion Subject to:

- on-time delivery- assigned range is

available- assigned rate is

feasible- Aggregate rate not

exceeds receiver’s incoming BW

minA

D( Δt)t=1

n∑s.t. Δi −riT ≤0

Δtt=1

i∑ ≤si ri ≤bi

rtt=1

n∑ ≤bI

Δi,ri ∈N; i =1,2,L ,n.

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How do we Compute Distortion?How do we Compute Distortion?

Using Rate-Distortion (R-D) models- Map bit rates to perceived quality- Optimize quality rather than number of bits

Approaches to construct R-D models- Empirical Models: Many empirical samples expensive

- Analytic Models: Quality is a non-linear function of bit rate, e.g., log model [Dai 06] and GGF model [Sun 05]

- Semi-analytic Models: A few carefully chosen samples, then interpolate, e.g., piecewise linear R-D model [Zhang 03]

Detailed analysis of R-D models in our previous work [Hsu 06]

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Within each bitplane, approximate R-D function by a line segment Line segments of different bitplanes have different slopes

The Linear R-D ModelThe Linear R-D Model

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Visual Validation of Linear R-D ModelVisual Validation of Linear R-D Model

Mother & Daughter, frame 110 Foreman, frame 100

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Rigorous Validation of Linear R-D ModelRigorous Validation of Linear R-D Model

Average error is less than 2% in most cases

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Let yi be number of bits transmitted from bitplane i

Distortion is:

- d : base layer only distortion- gi : slope of bitplane i

- z : total number of bitplanes

Using the Linear R-D ModelUsing the Linear R-D Model

d + ghyhh=1

z∑

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Integer Linear Programming (ILP) ProblemInteger Linear Programming (ILP) Problem

Linear objective function

Additional constraints- number of bits

transmitted from bit plane h does not exceed its size lh

- bits assigned to senders are divided among bitplanes

minA

D( Δt)t=1

n∑ =d + gvyvv=1

z∑s.t. Δi −riT ≤0

Δtt=1

i∑ ≤si ri ≤bi

rtt=1

n∑ ≤bI

yh ≤lh

Δtt=1

n∑ ≤ yvv=1

z∑Δi,ri, yh ∈N; i =1,2,L ,n; h=1,2,L ,z.

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Solution of ILP is a Valid FGS StreamSolution of ILP is a Valid FGS Stream

Lemma 1: - An optimal solution for the integer linear program produces a

contiguous FGS-encoded bit stream with no bit gaps

Proof sketch- minimizing

- Since g1 < g2 < … <gn<0 (line segment slopes),

- the ILP will never assign bits to yi+1 if yi is not full

d + ghyhh=1

z∑

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Solving ILP problem is expensive Solution: Transform it to Linear Programming (LP)

problem - Relax variables to take on real values

Objective function and constraints remain the same

Linear Programming RelaxationLinear Programming Relaxation

Δ i ,ri , yh ∈R+ U{0}; i = 1,2,L ,n; h = 1,2,L , z.

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Solve LP - Result is real values

Then, use the following rounding scheme for solution of the ILP

Efficient Rounding SchemeEfficient Rounding Scheme

A ={(Δi, ri)|i =1,2,L ,n}

ri = ri⎢⎣ ⎥⎦,

Δi =Δi

ri −1ri

⎢⎣⎢

⎥⎦⎥, r >1

0, 0 ≤r≤1

⎧⎨⎪

⎩⎪

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Correctness/Efficiency of Proposed RoundingCorrectness/Efficiency of Proposed Rounding

Lemma 2 (Correctness) - Rounding of the optimal solution of the relaxed

problem produces a feasible solution for the original problem

Lemma 3 (Efficiency: Size of Rounding Gap) - The rounding gap is at most nT + n, where n is the

number of senders and T is the frame period

- (Extreme) Example: n = 30 senders, T = 30 fps ==> gap is 32 bits

- Indeed negligible (frame sizes are in order of KBs)

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FGSAssign: Optimal Allocation AlgorithmFGSAssign: Optimal Allocation Algorithm

Solving LP (using Simplex method for example) may still be too much

- Need to run in real-time on PCs (not servers)

Our solution: FGSAssign- Simple, yet optimal, allocation algorithm- Greedy: Iteratively allocate bits to sender with

smallest si (stored segment) first

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Pseudo Code of FGSAssignPseudo Code of FGSAssign

1. Sort senders based on si, s1 ≤ s2 ≤ …… ≤ sn;2. x0 = …… = xn = 0; Δ1 = …… = Δn = 0; ragg = 0;3. for i = 1 to n do4. xi = min(xi−1 + biT, si);5. ri = (xi − xi−1)/T ;6. if (ragg + ri < bI ) then7. ragg = ragg + ri;8. Δi = xi − xi−1;9. else10. ri = bI − ragg;11. Δi = T × ri;12. return13. endfor

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Optimality of FGSAssignOptimality of FGSAssign

Theorem 1- The FGSAssign algorithm produces an optimal

solution in O(n log n) steps, where n is the number of senders.

Proof: see paper

Experimentally validated as well.

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Multiple-Frame OptimizationMultiple-Frame Optimization

Solve the allocation problem for blocks of m frames each

Objective: minimize total distortion in block

Why consider multiple-frame optimization?- More room for optimization- Solve the problem less often

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Multiple-Frame Optimization: Why?Multiple-Frame Optimization: Why?

More room for optimization: higher quality and less quality fluctuation

Bit rate

Dis

torti

on

(MS

E)

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Multiple-Frame OptimizationMultiple-Frame Optimization

Formulation (in extended version of the paper): - Straightforward extension to single-frame with lager number

of variables and constraints- Computationally expensive to solve

Our Solution: mFGSAssign algorithm - Heuristic (close to optimal results) - Achieves two goals:

• Minimize total distortion in a block of frames• Reduce quality fluctuations among successive frames

- Pseudo code and analysis: see extended version of the paper

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Experimental SetupExperimental Setup

Software used - MPEG-4 Reference Software ver 2.5

• Augmented to extract R-D model parameters

Algorithms implemented (in Matlab)- LP solutions using Simplex for the single-frame and

multiple-frame problems- FGSAssign algorithm- mFGSAssign algorithm- Nonscalable algorithm for baseline comparisons

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Experimental Setup (cont’d)Experimental Setup (cont’d)

Streaming scenarios- Four typical scenarios for Internet and corporate

environments

Testing video sequences - Akiyo, Mother, Foreman, Mobile (CIF)- Sample results shown for Foreman and Mobile

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Single Frame: Quality (PSNR)Single Frame: Quality (PSNR)

Foreman, Scenario I Mobile, Scenario III

Quality Improvement: 1--8 dB FGSAssign is optimal

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Multiple Frame: Quality (PSNR)Multiple Frame: Quality (PSNR)

Foreman, Scenario II Mobile, Scenario III

Scalable: higher improvement than single frame mFGSAssign: almost optimal (< 1% gap)

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Fluctuation ReductionFluctuation Reduction

Foreman, Scenario II Mobile, Scenario III

Small quality fluctuations in successive frames

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ConclusionsConclusions

Formulated and solved the bit allocation problem to optimize quality for receivers in general settings

- Multiple heterogeneous senders

Considered single and multiple frame cases Approach

- Nonlinear problem integer linear program• Using linear R-D model

- Integer linear program linear program • Using simple rounding scheme

Proposed efficient algorithms - FGSAssign: optimal and efficient- mFGSAssign: close to optimal in terms of average distortion, reduces

quality fluctuations, runs in real time

Significant quality improvements shown by our experiments

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Thank You!Thank You!

Questions??

All programs/scripts/videos are available:

http://www.cs.sfu.ca/~mhefeeda