A Statistical Framework to Enlarge the Potential of Digital TV Broadcasting Maria Teresa Andrade, Artur Pimenta Alves INESC Porto/FEUP Porto, Portugal 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Aims of the work • use statistical multiplexing for multi-channel TV systems with the ability of anticipating bit rate behaviour of individual channels to obtain : – Efficient use of bandwidth • anticipate amount of unused bandwidth and re-allocate to other existing services • include additional datacasting or video services using the same resources • Reduce costs – Higher picture quality – Increased programming/services choice 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
The context • DTV scenario – moving to all digital world with seamless integration with the Internet – interactivity (local and remote) – possibility of datacasting additional services – demand for higher quality and more choice – demand for HDTV programmes • Still remaining problem – bandwidth is still an expensive resource – high-quality still requires high-bandwidth – CBR encoding not efficient in the trade-off quality/bandwidth – transmission channels usually of fixed bit rate – broadband connections introduced rather slowly – existing stat mux not very efficient 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Statistical multiplexing – present situation versus advanced solution • Encoders co-located to the • Remote encoder operation multiplexer • True VBR operation • Restricted VBR mode with • Know in advance expected bit feedback loop rate requirements • No guarantees of seamless • Define a-priori maximum and constant quality minimum expected bandwidth • Released bandwidth gains redistributed within the • Include on-the-fly new services existing services in the within the multiplex multiplex 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Possible approaches regarding bit rate • constant bit rate with number of bits spent in each GOP controlled to a mean value - varying picture quality or distortion • variable bit rate controlling the distortion - constant quality sequences • constant bit rate using always the highest bit rate needed to satisfy at all times a minimum level of distortion 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
The probabilistic framework • Statistical framework using bayesian inference to describe occurrence of valleys in the bit rate – likelihood of valleys • Statistical framework using bayesian Weibull survival model to analyse duration of valleys – probability that the duration of valleys exceeds a certain time t • Numerical sampling methods (MCMC) to obtain posteriori distributions – predict occurrence and duration of valleys 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Statistical framework • Basis – Video sources with almost-constant and high picture quality – VBR operation – Sources analysed on a GOP and scene-basis – Analysis of a comprehensive number of sources – Build data base with characteristics extracted from sources: • Degree of criticality (difficulty to encode) and variability • Type of content • Parameters of a family of probabilistic models – Assign and use posteriori pdfs for real sources in a statistical mux; anticipate released bandwidth to include extra services 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Core of the work • build classification matrix (genre, profile, quality) • build statistical framework with Bayesian inference techniques – obtain statistical characterisation of VBR video sources – infer family of probabilistic models capable of adequately describing the video sources, incorporating prior knowledge obtained from sets of training data – predict the amount of unused bandwidth in respect to a specified mean value using the posteriori probabilities (predict occurrence and duration of “valleys”) 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Classifying sources • Cover whole spectrum of TV programming – Use DVB category classification for genres • Encode with two different quantisation step sizes obtaining two different quality levels – Fair and Good • Obtain statistics (mean and variance) per quality level – mouvement + detail (activity) and criticality 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Characterising the traffic • Granularity limited to GOPs (0,5 s) and to scenes: – Human eye can’t perceive variations in quality with durations less than 1 s – Mechanisms that (re) allocate bandwidth are not able to react faster – Inside a scene the type of content remains essentially the same, therefore little variation in bit rate – New scenes always start with a new GOP 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Influence of content • bit rate follows a pdf (best fit Weibull, Gamma or Beta) – at instante t i there is a given probability θ that the GOP bit rate be above or bellow a certain threshold. θ above Encoder Video source (generation Same type of of bits) content bellow 1- θ • generation of bits per GOP varies with content – probability of ocurrence of valleys will also differ θ i above Encoder Video sources (generation Different type of bits) of content bellow 1- θ i Influence (type of content) 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Problem formulation • Knowing that bitstream X has a number of characteristics , which is the probability of expecting a given bit rate behaviour, or the occurrence of valleys, throughout its duration? • valley -> a random variable with two possible states observations -> specific characteristics -> prior knowledge as a pdf model selection (maximizing a pdf) -> posteriori pdf -> state of random variable 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Bayes analyses • Unknown parameter: GOP dev • Fix a prior on the unknown parameter: p(GOP dev ) • Collect and observe the data: D = { X 1 , X 2 , ..., X N } • Calculate the posteriori distribution p(valleys) knowing the data X 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Statistical model • an unknown parameter : – GOP dev , the deviation of the GOP bit rate in respect to the expected mean bit rate and a random variable : – Occurrence of a valley in the bit rate, with 2 possible states: ⇒ a valley has occurred (GOP bit rate less than a certain threshold) • S = 1 ⇒ a valley did not occurred • S = 0 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Bayes analyses Bellow (green light) θ Sequence of scenes stream of GOPs Above (red light) 1- θ Uncertain variable or parameter, θ = GOP dev (variability of GOP bit rate) • Prior distribution of parameter, p( θ | ξ ) • • Set of observations D = {X 1 , X 2 , ..., X N } = stream of GOPs • Having observed N GOPS, how to predict the value of occurrence N+1? Will it be a valley in the GOP bit rate (green light) or not (red light)? p(x N+1 | θ , ξ ) = ? knowing p(x N+1 | θ , ξ ) and p( θ | ξ ) Use Bayes rule, average over the possible values of θ and use the expansion probability rule. 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Bayes analysis Bayes rule to determine posteriori distribution of θ given the D set of • GOPs and background knowledge b a θ ξ = θ × − θ p ( D | , ) ( 1 ) θ ξ × θ ξ p ( | ) p ( D | , ) θ ξ = p ( | D , ) , and → → + = a number of green lights ; b number of red lights ; a b N ξ p ( D | ) ξ = ∫ θ ξ × θ ξ θ p ( D | ) p ( D | , ) p ( | ) d average over the possible values of θ , using the expansion rule: • p(x N+1 = green | D, ξ ) = ∫ p(x N+1 = green | θ , ξ ) . p( θ | D, ξ ) d θ = ∫ θ . p( θ | D, ξ ) d θ � E p( θ | D, ξ ) ( θ ) 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
Bayes analyses - remarks • prior p(GOP dev ) is only an approximation – obtained posteriori p(valleys) will also be approximation • Important to carefully analyse the data, select the priors and test/calculate the posterioris for a great number of priors • Choosing the prior: – Kolmogorov method (minimum distance) – Maximum likelihood – Bayes • Test/calculate the posterioris: – Simulation methods through Markov Chain (MC Monte Carlo) 3rd International Symposium on Image and Signal Processing and Analysis ISPA 2003 September 18-20, 2003, Rome, Italy
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