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  • 1. Bitrate allocation for multiple video streams at competitive equilibria Mayank Tiwari 1 ,Theodore Groves 2 ,Pamela Cosman 1 1 Department of Electrical and Computer Engineering 2 Department of Economics University of California, San Diego La Jolla, CA - 92093 Asilomar Conference on Signals, Systems, and Computers
  • 2. Rate allocation for multiple video streams Encoder 1 Encoder 2 Encoder N MULTIPLEXER user 2 user 1 user N Encoder output buffer Constant Bitrate (CBR) channel Decoder input buffer DEMULTIPLEXER Decoder 1 Controller … . . . . . . . . . Decoder 2 Decoder N . . . 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 x c O 1 O 2 Two users (i = 1,2) and Two goods (j = 1,2) model Initial endowment Any allocation in the box 20 apples 15 5 7 13 25 oranges 15 10 19 6
  • 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 O 1 O 2 c The Budget Line Slope = - P 1 / P 2 B 1 (p) B 2 (p) In general equilibrium theory, the wealth of a user is defined as the value of the user’s initial endowment at the current prices Affordable region for user 2 at p Affordable region for user 1 at p
  • 10. Offer curve for user 1 (OC 1 ) c = x a O 1 O 2 OC 1 Indifference curves for user 1 p a p b p c The offer curve is the locus of the user’s optimal choice given current price (which defines current wealth) x b x c
  • 11. The Pareto set and contract curve in Edgeworth box OC 1 OC 2 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: Utility for User i: , for user i at TS j
  • 13. Competitive equilibrium for multiple video streams Normalize p 1 = 1 without loss of generality Solve the above equation numerically for p 2
  • 14. Example rate distortion distortion distortion distortion rate rate rate R R R R TS 1 TS 2 User 1 User 2 : initial endowment :allocation at competitive equilibrium
  • 15. Problems with adjacent TS rate distortion distortion distortion distortion rate rate rate R R R R TS 1 TS 2 User 1 User 2
    • 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
    : initial endowment :allocation at competitive equilibrium
  • 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) user 1 user 2 EQL_TS FUL_TS PRE_TS REM_TS EQL_TS FUL_TS PRE_TS REM_TS
  • 20. Results (multiplexing 4 videos) user 3 user 4
  • 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