MTEC-109A	Statistical Information Processing
Lecture	Tutorial	Practical	Credit	Major Test	Minor Test	Total	Time
3	0	0	3	60	40	100	3 Hrs.
Course Outcomes (CO)
CO1	Characterize and apply probabilistic techniques in modern decision systems, such as information systems, receivers, filtering and statistical operations.
CO2	Demonstrate mathematical modelling and problem solving using such models.
CO3	Comparatively evolve key results developed in this course for applications to signal processing, communications systems.
CO4	Develop frameworks based in probabilistic and stochastic themes for modelling and analysis of various systems involving functionalities in decision making, statistical inference, estimation and detection.

## Unit 1

Review of random variables: Probability Concepts, distribution and density functions, moments, independent, uncorrelated and orthogonal random variables; Vector-space representation of Random variables, Vector quantization, Tchebaychef inequality theorem, Central Limit theorem, Discrete &Continuous Random Variables. Random process: Expectations, Moments,Ergodicity, Discrete-Time Random Processes Stationary process, autocorrelation and auto covariance functions, Spectral representation of random signals, Properties of power spectral density, Gaussian Process and White noise process.

## Unit 2

Random signal modelling: MA(q), AR(p), ARMA(p,q) models, Hidden Markov Model &its applications ,Linear System with random input , Forward and Backward Predictions, Levinson Durbin Algorithm.Statistical Decision Theory: Bayes' Criterion, Binary Hypothesis Testing, M -aryHypothesis Testing, Minimax Criterion, Neyman- Pearson Criterion, Composite Hypothesis Testing.Parameter Estimation Theory: Maximum Likelihood Estimation, Generalized Likelihood Ratio Test ,Some Criteria for Good Estimators, Bayes' Estimation Minimum Mean -Square Error Estimate, Minimum, Mean Absolute Value of Error Estimate Maximum A Posteriori Estimate , Multiple Parameter Estimation Best Linear Unbiased Estimator ,Least-Square Estimation Recursive Least-Square Estimator.

## Unit 3

Spectral analysis: Estimated autocorrelation function, Periodogram, Averaging theperiodogram (Bartlett Method), Welch modification, Parametric method, AR(p) spectral estimation and detection of Harmonic signals. Information Theory and Source Coding: Introduction, Uncertainty, Information andEntropy, Source coding theorem, Huffman, Shanon Fano , Arithmetic , Adaptive coding , RLE , LZW Data compaction, , LZ-77, LZ-78. Discrete Memory less channels, Mutual information, channel capacity, Channel coding theorem, Differential entropy and mutual information for continuous ensembles.

## Unit 4

Application of Information Theory: Group, Ring & Field, Vector, GF addition,multiplication rules. Introduction to BCH codes, Primitive elements ,Minimal polynomials, Generator polynomials in terms of Minimal polynomials, Some examples of BCH codes,& Decoder, Reed- Solomon codes & Decoder, Implementation of Reed Solomon encoders and decoders.

## References:

- 1) Papoulis and S.U. Pillai, 'Probability, Random Variables and Stochastic Processes',4th Edition, McGraw-Hill, 2002.
- 2) D.G. Manolakis, V.K. Ingle and S.M. Kogon, 'Statistical and Adaptive Signal Processing', McGraw Hill, 2000.
- 3) Mourad Barkat , 'Signal Detection and Estimation', Artech House, 2nd Edition, 2005.
- 4) 4) R G. Gallager, 'Information theory and reliable communication', Wiley, 1 edition, 1968. . J. MacWilliams and N. J. A. Sloane, 'The Theory of Error - Correcting Codes', New
- 5) York, North-Holland, 1977.
- 6) 6) Rosen K.H, 'Elementary Number Theory', Addison -Wesley, 6 edition, 2010.