This book is an expanded third edition of the book Performance Analysis of Digital Transmission Systems, originally published in 1990. Second edition of the book titled Digital Transmission Systems: Performance Analysis and Modeling was published in 1998. The book is intended for those who design communication systems and networks. A computer network designer is interested in selecting communication channels, error protection schemes, and link control protocols. To do this efficiently, one needs a mathematical model that accurately predicts system behavior. Two basic problems arise in mathematical modeling: the problem of identifying a system and the problem of applying a model to the system analysis. System identification consists of selecting a class of mathematical objects to describe fundamental properties of the system behavior. We use a specific class of hidden Markov models (HMMs) to model communication systems. This model was introduced by C. E. Shannon more than 50 years ago as a Noisy Discrete Channel with a finite number of states. The model is described by a finite number of matrices whose elements are estimated on the basis of experimental data. We develop several methods of model identification and show their relationship to other methods of data analysis, such as spectral methods, autoregressive moving average CARMA) approximations, and rational transfer function approximations.
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ISBN-13
978-1-4419-9070-9 (9781441990709)
DOI
10.1007/978-1-4419-9070-9
Schweitzer Klassifikation
Preface.- Notation.- 1. Error Source Models.- 1.1 Description of Error Sources by Hidden Markov Models.- 1.2 Binary Symmetric Stationary Channel.- 1.3 Error Source Description by Matrix Processes.- 1.4 Error Source Description by Semi-Markov Processes.- 1.5 Some Particular Error Source Models.- 1.6 Conclusion.- References.- 2. Matrix Probabilities.- 2.1 Matrix Probabilities and Their Properties.- 2.2 Matrix Transforms.- 2.3 Matrix Distributions.- 2.4 Markov Functions.- 2.5 Monte Carlo Method.- 2.6 Computing Scalar Probabilities.- 2.7 Conclusion.- References.- 3. Model Parameter Estimation.- 3.1 The Em Algorithm.- 3.2 Baum-Welch Algorithm.- 3.3 Markov Renewal Process.- 3.4 Matrix-Geometric Distribution Parameter Estimation.- 3.5 Matrix Process Parameter Estimation.- 3.6 Hmm Parameter Estimation.- 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.- 4.3 Maximum A Posteriori Decoding.- 4.4 Block Code Performance Characterization.- 4.5 Convolutional Code Performance.- 4.6 Computer Simulation.- 4.7 Zero-Redundancy Codes.- 4.8 Conclusion.- References.- 5. Performance Analysis of Communication Protocol.- 5.1 Basic Characteristics of Two-Way Systems.- 5.2 Return-Channel Messages.- 5.3 Synchronization.- 5.4 Arq Performance Characteristics.- 5.5 Delay-Constained Systems.- 5.6 Conclusion.- References.- 6. Continuous Time Hmm.- 6.1 Continuous and Discrete Time Hmm.- 6.2 Fitting Continuous Time Hmm.- 6.3 Conclusion.- References.- 7. Continuous State Hmm.- 7.1 Continuous and Discrete State Hmm.- 7.2 Operator Probability.- 7.3 Filtering, Prediction, and Smoothing.- 7.4 Linear Systems.- 7.5 Autoregressive Moving Average Processes.- 7.6 Parameter Estimation.- 7.7 Arma Channel Modeling.- 7.8 Conclusion.- References.- Appendix 1.- 1.1 Matrix Processes.- 1.2 Markov Lumpable Chains.- 1.3 Semi-Markov Lumpable Chains.- References.- Appendix 2.- 2.1 Asymptotic Expansion of Matrix Probabilities.- 2.2 Chernoff Bounds.- 2.3 Block Graphs.- References.- Appendix 3.- 3.1 Statistical Inference.- 3.2 Markov Chain Model Building.- 3.3 Semi-Markov Process Hypothesis Testing.- 3.4 Matrix Process Parameter Estimation.- References.- Appendix 4.- 4.1 Sums With Binomial Coefficients.- 4.2 Maximum-Distance-Separable Code Weight Generating Function.- 4.3 Union Bounds on Viterbi Algorithm Performance.- References.- Appendix 5.- 5.1 Matrices.- References.- Appendix 6.- 6.1 Markov Chains and Graphs.- References.- Appendix 7.- 7.1 Markov Processes.- 7.2 Gauss-Markov Processes.- References.
