Nonlinear Digital Encoders for Data Communications (eBook)

Calin Vladeanu is Associate Professor of telecommunications at the University Politehnica of Bucharest, Romania. His current research interests include turbo-coded modulations for wireless communications, applications of nonlinear sequence generators for spreading and channel coding. He is the author of three books (in Romanian) dedicated to CDMA mobile systems. Safwan El Assad is Associate Professor at the University of Nantes, France. His current research interests are in the field of chaos-based exchanged and stored information security, including chaos-based cryptography and crypto-compression systems for secure data transmission and storing, chaos-based watermarking and steganography.

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