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Long-Range Prediction for Real-Time MPEG Video Traffic: An H  Filter Approach

Long-Range Prediction for Real-Time MPEG Video Traffic: An H  Filter Approach

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Long-Range Prediction for Real-Time MPEG Video Traffic: An H  Filter Approach

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  1. Long-Range Prediction for Real-Time MPEG Video Traffic: An H Filter Approach Chih-Hu Wang (王志湖), Bor-Sen Chen (陳博現), Bore-Kuen Lee(李柏坤), Tsu-Tian Lee(李祖添), Chien-Nan Jimmy Liu (劉建男), and Chauchin Su (蘇朝琴) CSVT, Dec. 2008

  2. Outline • Introduction • Time Series • Time Series Model of MPEG Video Stream • State-Space Model • H Estimation • Neural Networks • Performance Comparisons • References

  3. Introduction • Video traffic • Example of CBR (H.264) and VBR (MPEG-1) • Goal: Predict the size n-th frame using time series

  4. Time Series • A time series is a set of observation xt, each one being recorded at a specified time t. [13] • Examples of time series model • Random walk model with zero mean • St = X1 + X2 + … + Xt, where {Xt} is iid noise. • Model with trend and seasonality • Xt = mt + Yt. (Trend component + Zero mean value) LSE Residual Seasonal model

  5. Time Series Model of MPEG Video Stream (1/4) • Video stream • Traffic prediction • y(n+td) = a(n+td) + c(n+td) + d(n+td) + w(n+td) • y(n+td): the number of bits of the (n+td)-th frame. • a(n+td): the local linear trend component. • c(n+td): the long-term periodical component. • d(n+td): the short-term periodical component. • w(n+td): the residual modeling error or noise. I B … B P B … B P B … B P … B I K N = +

  6. Time Series Model of MPEG Video Stream (2/4) • Local linear trend • a(n+td) = a(n) +b(n)td + v(n) • b(n): slop of the linear trend • b(n) can be modeled by the random walk model in practical video sequences. • b(n+1) = b(n) + u(n) • u(n) is an iid process with zero mean • c(n+td) = c(n+td-N), t=1toNc(t+n+td) = 0 • d(n+td) = d(n+td-K), t=1toKd(t+n+td) = 0

  7. Time Series Model of MPEG Video Stream (3/4) • Start from td = 1 • y(n+1) = a(n+1) + c(n+1) + d(n+1) + w(n+1) y(n) = GX(n) + w(n) a(n) b(n) c(n) c(n-1) … c(n-N+2) d(n) d(n-1) … d(n-K+2) y(n) = (1 0 1 0 … 0 1 0 … 0) + w(n) N-2 K-2 G X(n)

  8. Time Series Model of MPEG Video Stream (4/4) • X(n+1) = FX(n) + BV(n) X(n+1) F X(n) B V(n) 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 … 0 0 0 0 0 0 0 1 0 0 0 0 … 0 0 0 0 a(n+1) b(n+1) c(n+1) c(n) … c(n-N+3) d(n+1) d(n) … d(n-K+3) a(n) b(n) c(n) c(n-1) … c(n-N+2) d(n) d(n-1) … d(n-K+2) -1 … -1 -1 1 0 … 0 0 0 1 … 0 … 1 0 0 0 … 0 1 0 v(n) u(n) r(n) m(n) N-2 N-2 N-2 = + -1 … -1 -1 1 0 … 0 0 0 1 … 0 … 1 0 0 0 … 0 1 0 N-2 K-2 K-2 K-2 K-2 ps. t=1toNc(t+n+td) = 0  c(n+1+td) = -c(n+2+td) - … - c(n+N+td)

  9. State-Space Model (1/2) • State-space model • X(n+1) = FX(n) + BV(n) y(n) = GX(n) + w(n) • Goal: • Estimate • Obtain • Obtain and • Finally,

  10. State-Space Model (2/2) • State-space model [13] • Observation equation: express the observation Yt as a linear function of a state variable Xt plus noise. • Yt = GtXt + Wt, t = 1, 2, … • State equation: determine the state Xt+1 at time t+1 in terms of the Xt and noise. • Xt+1 = FtXt + Vt, t = 1, 2, …

  11. H Estimation (1/4) • Definition: H norm of a transform operator T[12] • ||T|| = sup ||T(x)||/||x|| • The maximum energy gain from the input x to the output T(x) T x T(x)

  12. H Estimation (2/4) • State-space model • y(n) = GX(n) + w(n) • X(n+1) = FX(n) + BV(n) • Transfer matrix from disturbances to filtered errors [12] • Optimal H problem [12] • Find optimal that minimize ||T|| T

  13. H Estimation (3/4) • Sub-optimal H problem [12] • Find sub-optimal that achieves ||T||< r

  14. H Estimation (4/4) • Solution of the sub-optimal H problem • P(n) needs to satisfy • 2 is a free designed parameter

  15. Neural Networks (1/4) • Neuron model [15] p1 w1,1 w1,2 n a p2  f … b w1,R pR a = f(Wp+b) 1 a a a 1 1 1 n n n -1 -1 -1 linear transfer function tangent sigmoid transfer function log sigmoid transfer function

  16. Neural Networks (2/4) • Focused time-delay neural network (FTDNN) • # of parameters: 312 weights and 48 bias constants N1 b D1 N2 b D2 N25 … … … b D12 w’1,1w’1,2 … w’1,24 w1,1w1,2 … w1,12 w2,1w2,2 … w2.12 … w24,1w24.2 … w24.12 N24 Tapped delay line b

  17. Neural Networks (3/4) • Nonlinear autoregressive network with exogenous inputs (NARX) • # of parameters: 600 weights and 48 bias constants TDL N1 b … N2 12 b N25 TDL … w1,1 … w1,24 … w24,1 … w24,24 w’1,1w’1,2 … w’1,24 b … N24 12 b

  18. Neural Networks (4/4) • Elman network • # of parameters: 888 weights and 48 bias constants D N1 b … 24 N2 b N25 … b w1,1 … w1,36 … w24,1 … w24,36 … 12 N24 b

  19. Performance Comparisons (1/4) • Time comparison

  20. Performance Comparisons (2/4) • MPEG-1 dino star ‘x’ FTDNN ‘*’ Elman ‘+’ NARX ‘o’ H mr.bean soccer atp race

  21. Performance Comparisons (3/4)

  22. Performance Comparisons (4/4) • MPEG-4 aladdin dusk contact Jurassic soccer star4

  23. References • [13] P. J. Brockwell and R. A. Davis, Introduction to Time Series and Forecasting. New York: Springer, 1996. • [12] B. Hassibi, A. H. Sayed, and T. Kailath, “Linear estimation in Krein spaces-Part II: Application,” IEEE Trans. Automat. Contr., 1996. • [15] H. Demuth, M. Beale, and M. Hagan, Neural Network Toolbox 5: User’s Guide. Natick, MA: The MathWorks, 2007.