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Inhaltsangabe
Preface.- Notation.- 1. Error Source Models.- 1.1 Description of Error Sources by Hidden Markov Models.- 1.1.1 Finite State Channel.- 1.1.2 Hidden Markov Models.- 1.1.3 Discrete-Time Finite State Systems.- 1.1.4 Error Source HMM.- 1.1.5 Gilbert's Model.- 1.1.6 Equivalent Models.- 1.1.7 The HMM Model Generality.- 1.1.8 Satellite Channel Model.- 1.1.9 Fading Wireless Channels.- 1.1.10 Concatenated Channel Error Sources.- 1.2 Binary Symmetric Stationary Channel.- 1.2.1 Model Description.- 1.2.2 Diagonalization of the Matrices.- 1.2.3 Models with Two Sets of States.- 1.2.4 Block Matrix Representation.- 1.3 Error Source Description by Matrix Processes.- 1.3.1 Matrix Process Definition.- 1.3.2 Block Matrix Representation.- 1.3.3 Matrix Processes and Difference Equations.- 1.3.4 Matrix Processes and Markov Functions.- 1.4 Error Source Description by Semi-Markov Processes.- 1.4.1 Semi-Markov Processes.- 1.4.2 Semi-Markov Lumping of Markov Chain.- 1.5 Some Particular Error Source Models.- 1.5.1 Single-Error-State Models.- 1.5.2 Alternating Renewal Process Models.- 1.5.3 Alternating State HMM.- 1.5.4 Fading Channel Errors.- 1.6 Conclusion.- References.- 2. Matrix Probabilities.- 2.1 Matrix Probabilities and Their Properties.- 2.1.1 Basic Definitions.- 2.1.2 Properties of Matrix Probabilities.- 2.1.3 Random Variables.- 2.2 Matrix Transforms.- 2.2.1 Matrix Generating Functions.- 2.2.2 Matrix z-Transforms.- 2.2.3 Matrix Fourier Transform.- 2.2.4 Matrix Discrete Fourier Transform.- 2.2.5 Matrix Transforms and Difference Equations.- 2.3 Matrix Distributions.- 2.3.1 Matrix Multinomial Distribution.- 2.3.2 Matrix Binomial Distribution.- 2.3.3 Matrix Pascal Distribution.- 2.4 Markov Functions.- 2.4.1 Block Matrix Probabilities.- 2.4.2 Matrix Multinomial Distribution.- 2.4.3 Interval Distributions of Markov Functions.- 2.4.4 Signal Flow Graph Applications.- 2.5 Monte Carlo Method.- 2.5.1 Error Source Simulation.- 2.5.2 Performance Characteristic Calculation.- 2.6 Computing Scalar Probabilities.- 2.6.1 The Forward and Backward Algorithms.- 2.6.2 Scalar Generating Functions.- 2.7 Conclusion.- References.- 3. Model Parameter Estimation.- 3.1 The Em Algorithm.- 3.1.1 Kullback-Leibler Divergence.- 3.1.2 Minimization Algorithms.- 3.1.3 The EM Algorithm.- 3.1.4 Maximization of a Function.- 3.1.5 EM Algorithm Acceleration.- 3.1.6 Statistical EM Algorithm.- 3.2 Baum-Welch Algorithm.- 3.2.1 Phase-Type Distribution Approximation.- 3.2.2 HMM Approximation.- 3.2.3 Fitting HMM to Experimental Data.- 3.2.4 Matrix Form of the BWA.- 3.2.5 Scaling.- 3.3 Markov Renewal Process.- 3.3.1 Fast Forward and Backward Algorithms.- 3.3.2 Fitting MRP.- 3.4 Matrix-Geometric Distribution Parameter Estimation.- 3.4.1 Distribution Simplification.- 3.4.2 ML Parameter Estimation.- 3.4.3 Sequential Least Mean Square Method.- 3.4.4 Piecewise Logarithmic Transformation.- 3.4.5 Prony's Method.- 3.4.6 Matrix Echelon Parametrization.- 3.4.7 Utilization of the Cumulative Distribution Function.- 3.4.8 Method of Moments.- 3.4.9 Transform Domain Approximation.- 3.5 Matrix Process Parameter Estimation.- 3.5.1 ML Parameter Estimation.- 3.5.2 Interval Distribution Estimation.- 3.5.3 Utilization of Two-Dimensional Distributions.- 3.5.4 Polygeometric Distributions.- 3.5.5 Error Bursts.- 3.6 Hmm Parameter Estimation.- 3.6.1 Multilayered Error Clusters.- 3.6.2 Nested Markov Chains.- 3.6.3 Single-Error-State Models.- 3.7 Monte Carlo Method of Model Building.- 3.8 Error Source Model in Several Channels.- 3.9 Conclusion.- References.- 4. Performance of Forward Error-Correction Systems.- 4.1 Basic Characteristics of One-Way Systems.- 4.2 Elements of Error-Correcting Coding.- 4.2.1 Field Galois Arithmetic.- 4.2.2 Linear Codes.- 4.2.3 Cyclic Codes.- 4.2.4 Bose-Chaudhuri-Hocquenghem Codes.- 4.2.5 Reed-Solomon Codes.- 4.2.6 Convolutional Codes.- 4.2.6 Trellis-Code Modulation.- 4.3 Maximum A Posteriori Decoding.- 4.3.1 MAP Symbol Estimation.- 4.3.2 MAP Sequence Decoding.- 4.4 Block Code Performance Char
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