1 School of Computing Science Simon Fraser University, Canada Rate-Distortion Optimized Streaming of Fine-Grained Scalable Video Sequences Mohamed Hefeeda & ChengHsin Hsu MMCN January 2007

2 Motivations  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

3 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

4 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

5 Our 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

6 Example: Different Streaming Schemes Non-scalableLayered

7 Example: Different Streaming Schemes Optimal FGS Scalable FGS 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

8 Problem 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

9 Input Parameters  T : fixed frame period  n : number of senders  b i : outgoing bandwidth of sender i  b I : incoming bandwidth of receiver  s i : length of (contiguous) bits held by sender i  Assume w.l.g. s 1 <= s 2 <= …… <= s n

10  Allocation: A = {(Δ i, r i ) | i = 1, 2, …, n} -Δ i : number of bits assigned to i -r i : streaming rate assigned to i  Specifies: -Sender 1 sends range [0, Δ 1 -1] at rate r 1 -Sender 2 sends range [Δ 1, Δ 1 +Δ 2 -1] at rate r 2 -… -Sender i sends range at rate r i Outputs

11 Integer 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

12 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]

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

14 Visual Validation of Linear R-D Model Mother & Daughter, frame 110 Foreman, frame 100

15 Rigorous Validation of Linear R-D Model  Average error is less than 2% in most cases

16  Let y i be number of bits transmitted from bitplane i  Distortion is: -d : base layer only distortion -g i : slope of bitplane i -z : total number of bitplanes Using the Linear R-D Model

17 Integer Linear Programming (ILP) Problem  Linear objective function  Additional constraints -number of bits transmitted from bit plane h does not exceed its size l h -bits assigned to senders are divided among bitplanes

18 Solution 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 g 1 < g 2 < … <g n <0 (line segment slopes), -the ILP will never assign bits to y i+1 if y i is not full

19  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 Relaxation

20  Solve LP  -Result is real values  Then, use the following rounding scheme for solution of the ILP Efficient Rounding Scheme

21 Correctness/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)

22 FGSAssign: 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 s i (stored segment) first

23 Pseudo Code of FGSAssign 1.Sort senders based on s i, s 1 ≤ s 2 ≤ …… ≤ s n ; 2.x 0 = …… = x n = 0; Δ 1 = …… = Δ n = 0; r agg = 0; 3.for i = 1 to n do 4. x i = min(x i−1 + b i T, s i ); 5. r i = (x i − x i−1 )/T ; 6. if (r agg + r i < b I ) then 7. r agg = r agg + r i ; 8. Δ i = x i − x i−1 ; 9. else 10. r i = b I − r agg ; 11. Δ i = T × r i ; 12. return 13.endfor

24 Optimality 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.

25 Multiple-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

26 Multiple-Frame Optimization: Why?  More room for optimization: higher quality and less quality fluctuation Bit rate Distortion (MSE)

27 Multiple-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

28 Experimental 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

29 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

30 Single Frame: Quality (PSNR) Foreman, Scenario I Mobile, Scenario III  Quality Improvement: 1--8 dB  FGSAssign is optimal

31 Multiple Frame: Quality (PSNR) Foreman, Scenario II Mobile, Scenario III  Scalable: higher improvement than single frame  mFGSAssign: almost optimal (< 1% gap)

32 Fluctuation Reduction Foreman, Scenario II Mobile, Scenario III  Small quality fluctuations in successive frames

33 Conclusions  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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