Nonlinear Digital Encoders for Data Communications

Preface ix

Introduction xi

Chapter 1. Applications of Nonlinear Digital Encoders 1

1.1. Secure communications using nonlinear digital encoders 1

1.1.1. The general nonlinear digital encoder scheme 3

1.1.2. Quasi-chaotic sequence properties 5

1.1.3. An example of simple nonlinear digital encoder: the Frey chaotic encoder 7

1.1.4. Simulation results revealing the quasi-chaotic properties for the sequences generated using the Frey encoder 9

1.2. Chaotic spreading sequences for direct-sequence code division multiple access 15

1.3. Sequence synchronization in discrete-time nonlinear systems 19

1.3.1. An example of sequence synchronization using the inverse system 19

1.3.2. The dead-beat synchronization method 23

1.3.3. A communication scheme using the dead-beat synchronization 25

Chapter 2. Presentation of the Frey Nonlinear Encoder as a Digital Filter 29

2.1. The mathematical analysis of the Frey encoder 29

2.2. The definitions and properties of the unsigned and 2's complement signed sample operators 30

2.3. The properties of the LCIRC nonlinear function used in the Frey encoder scheme 38

2.4. The simulation of the Frey sequence generator block in Simulink: some practical considerations 41

2.4.1. The transmitter chaotic sequence generator 41

2.4.2. The receiver chaotic sequence generator and the dead-beat synchronization with the transmitter block 43

2.4.3. The Simulink implementations for the blocks used in the Frey chaotic codec 45

Chapter 3. Trellis-Coded Modulation Schemes Using Nonlinear Digital Encoders 49

3.1. The presentation of the Frey nonlinear encoder as a convolutional encoder 49

3.2. Frey encoder trellis design optimization methods for pulse amplitude - trellis-coded modulation (TCM) schemes 54

3.2.1. Increasing the coding gain by reducing the representation code word length in the input 56

3.2.2. Equivalence between a nonlinear and a linear encoder in a particular case 66

3.2.3. Generalized optimum encoder for a PAM-TCM transmission 69

3.2.4. Increasing the coding gain by increasing the number of outputs 75

3.3. Optimum nonlinear encoders for phase shift keying - TCM schemes 84

3.3.1. Rate-1/2 optimum encoder for a QPSK-TCM transmission 84

3.3.2. Generalized optimum encoder for a PSK-TCM transmission 85

3.4. Optimum nonlinear encoders for quadrature amplitude modulation - TCM schemes 89

3.5. Performance analysis of TCM data communications using modified nonlinear digital encoders: simulation results 91

Chapter 4. Parallel Turbo Trellis-Coded Modulation Schemes Using Nonlinear Digital Encoders 97

4.1. Recursive convolutional-left circulate (RC-LCIRC) encoder in a turbo trellis-coded modulation (TTCM) scheme 97

4.2. New recursive and systematic convolutional nonlinear encoders for parallel TTCM schemes 100

4.3. Punctured TTCM transmissions using recursive systematic convolutional nonlinear encoders 108

4.4. Extrinsic information transfer (EXIT) charts analysis for TTCM schemes using nonlinear RSC encoders 114

4.5. Performance analysis of TTCM data communications using nonlinear digital encoders: simulation results 115

Appendix 133

Bibliography 145

Index 151