Bitrate allocation for multiple video streams at competitive equilibria

1. Asilomar Conference on Signals, Systems, and Computers Bitrate allocation for multiple video streams at competitive equilibria Mayank Tiwari1,Theodore Groves2,Pamela Cosman1 1Department of Electrical and Computer Engineering 2Department of Economics University of California, San Diego La Jolla, CA - 92093

2. Rate allocation for multiple video streams user 1 Encoder 1 Decoder 1 Constant Bitrate (CBR) channel user 2 Encoder output buffer Decoder input buffer Encoder 2 Decoder 2 DEMULTIPLEXER MULTIPLEXER . . . . . . . . . . . . user N Encoder N Decoder N … Controller Objective: To improve the quality* of multiple video streams by joint encoding using competitive equilibrium approach * MSE reduction was the quality criterion used in this research

3. Multiplexing video streams: Applications • Video surveillance • Cognitive radio • Many video source providers sharing a transmission channel • Controller: Channel provider • Same source provider • Controller: Source provider • Controller: Autonomous users

4. Motivation • Existing methods for video multiplexing rely on relative complexity of the video • The overall quality is improved but not all the videos may experience improvement in quality • High complexity videos gain at the expense of the low complexity videos • We propose a competitive equilibrium approach to simultaneously improve the quality of all the videos

5. Definitions • An outcome is said to be Pareto optimal (or Pareto efficient) if it is impossible to make some individuals better off without making some other individuals worse off • A pure exchange economy is an economy in which no production is possible and the commodities that are ultimately consumed are those that individuals possess as an initial endowments • A market clearing price is a price at which the aggregate supply of each commodity equals the aggregate demand for it

6. Competitive equilibrium • A competitive equilibrium consists of a vector of prices and an allocation such that given the prices, each user maximizes his utility function subject to his resource constraints and market clearing • An allocation at competitive equilibrium is Pareto optimal • The price at competitive equilibrium is market clearing price • An Edgeworth Box is a graphical tool for exhibiting Pareto optimal allocations and illustrating a competitive equilibrium in pure exchange economy

7. An Edgeworth box 5 O2 13 6 x 15 Any allocation in the box 25 oranges 19 c 10 Initial endowment 7 O1 15 20 apples Two users (i = 1,2) and Two goods (j = 1,2) model

8. Preferences in the EW box : initial endowment for user i at TS j : an allocation for user i at TS j

9. Budget set O2 In general equilibrium theory, the wealth of a user is defined as the value of the user’s initial endowment at the current prices B2(p) Affordable region for user 2 at p c Affordable region for user 1 at p B1(p) The Budget Line Slope = - P1 / P2 O1

10. Offer curve for user 1 (OC1) Indifference curves for user 1 OC1 O2 The offer curve is the locus of the user’s optimal choice given current price (which defines current wealth) xc xb c = xa pa pb O1 pc

11. The Pareto set and contract curve in Edgeworth box OC1 OC2 Competitive equilibrium The competitive equilibrium budget line

12. Competitive equilibrium for multiple video streams • users -> Video users • goods -> Time-slots (TS) • 1 TS = Size of a GOP • A user can employ any type of encoding within GOP Curve Fitting: , for user i at TS j Utility for User i:

13. Competitive equilibrium for multiple video streams Normalize p1 = 1 without loss of generality Solve the above equation numerically for p2

14. Example : initial endowment :allocation at competitive equilibrium User 1 distortion distortion rate R rate R User 2 distortion distortion rate rate R R TS 1 TS 2

15. Problems with adjacent TS • Adjacent TS are similar in nature • A user would want to trade across distant TS to get more improvement • Two TS do not represent entire video stream User 1 distortion distortion rate R rate R User 2 distortion distortion : initial endowment rate rate R R :allocation at competitive equilibrium TS 1 TS 2

16. Methods for multiplexing video streams - 1 • REM_TS: ex-ante approximation model • Finding the competitive equilibrium sequentially for current TS and average of remaining TS • PRE_TS: ex-post approximation model • Finding the competitive equilibrium sequentially for current TS and average of previous TS • Assumption: Previous TS are good prediction of future TS

17. Methods for multiplexing video streams - 2 • EQL_TS: Each video in every TS receives equal number of bits • FUL_TS: Full information about R-D curves in all the TS • Divide bits according to the relative complexity (Equal slope) of TS • Normalize the number of bits among the users in each TS

18. Simulation setup • H.264/AVC reference software JM 11.0 • Baseline profile of H.264/AVC • 30-second test videos, taken from a 72 minute travel documentary • Resolution: 176 X 120 pixels • 30 frames per second • GOP size = 15 frames (I-P-P-P) • Considered problem of multiplexing up to 12 video streams

19. Results (multiplexing 4 videos) FUL_TS FUL_TS REM_TS PRE_TS PRE_TS REM_TS EQL_TS EQL_TS user 1 user 2

20. Results (multiplexing 4 videos) user 4 user 3

21. PSNR fluctuation (user 2)

22. Conclusions • Proposed two competitive equilibrium approach for joint encoding to improve the video quality • All the videos experience improvement in quality, irrespective of their complexity • PSNR gain is greater for videos with higher motion fluctuation across TS • Further improvement is possible by using multiple reference frames or hierarchical B-frames within GOP • Classification of videos to better predict the future frames