Optical Communication Theory and Techniques (eBook)

Contents 5
Preface 8
Acknowledgments 10
INFORMATION AND COMMUNICATION THEORY FOR OPTICAL COMMUNICATIONS 11
SOLVING THE NONLINEAR SCHRÖDINGER EQUATION 12
1. INTRODUCTION 12
2. AN INTEGRAL EXPRESSION OF THE NLSE 13
3. A FIRST RECURRENCE RELATION CORRESPONDING TO A REGULAR PERTURBATION METHOD 14
4. AN IMPROVED RECURRENCE RELATION CORRESPONDING TO A LOGARITHMIC PERTURBATION METHOD 15
5. COMPUTATIONAL ISSUES 17
6. SOME RESULTS 18
7. CONCLUSIONS 19
REFERENCES 19
MODULATION AND DETECTION TECHNIQUES FOR DWDM SYSTEMS 21
1. INTRODUCTION 21
2. DIRECT DETECTION OF PAM 23
3. INTERFEROMETRIC DETECTION OF DPSK 24
4. COHERENT DETECTION OF PSK AND QAM 25
5. DISCUSSION 26
REFERENCES 28
BEST OPTICAL FILTERING FOR DUOBINARY TRANSMISSION 29
1. INTRODUCTION 29
2. QUANTUM LIMIT FOR DUOBINARY 30
3. PULSE SHAPE DEPENDENCE OF BER 32
4. CONCLUSIONS 35
REFERENCES 35
THEORETICAL LIMITS FOR THE DISPERSION LIMITED OPTICAL CHANNEL 37
1. INTRODUCTION 37
2. MATHEMATICAL ASSESSMENT OF THE PROBLEM 38
2.1 The fundamental parameters and equations 40
2.2 The closed form solution 41
3. OPTIMAL CHIRP AND CHANNEL EQUIVALENT BANDWIDTH 42
4. CONCLUSION 44
REFERENCES 44
CAPACITY BOUNDS FOR MIMO POISSON CHANNELS WITH INTER-SYMBOL INTERFERENCE 45
1. INTRODUCTION 45
2. UNCONSTRAINED MIMO POISSON CHANNEL 46
3. CONSTRAINED MIMO POISSON CHANNELS 47
APPENDIX 48
APPENDIX B 51
APPENDIX C 52
REFERENCES 52
QSPACE PROJECT: QUANTUM CRYPTOGRAPHY IN SPACE 53
1. INTRODUCTION 53
2. THE Q-SPACE PROJECT 55
2.1 Description of the experimental setup 55
3. CATCHING THE PHOTON 57
3.1 Orbital fit and the link budget equation 57
3.2 Atmospheric seeing problems 58
3.3 Acquisition from ground targets 59
4. CONCLUSIONS 59
REFERENCES 60
QUANTUM-AIDED CLASSICAL CRYPTOGRAPHY WITH A MOVING TARGET 61
1. INTRODUCTION 61
2. QKD TO UPDATE A “MOTHER KEY” 62
3. TOY-APPLICATION IN F1 RACING 63
4. CONCLUSIONS 65
ACKNOWLEDGMENTS 65
REFERENCES 66
CODING THEORY AND TECHNIQUES 68
CHANNEL CODING FOR OPTICAL COMMUNICATIONS 69
1. INTRODUCTION 69
2. THE “STANDARD” CODING SCHEME AND ITS AVATARS 71
3. THE IMPACT OF SOFT ITERATIVE DECODING 74
4. TURBO PRODUCT CODES 76
5. LOW-DENSITY PARITY-CHECK CODES 78
6. HIGH-SPEED PARALLEL DECODER ARCHITECTURES 80
7. ANNOTATED BIBLIOGRAPHY 81
REFERENCES 81
SOFT DECODING IN OPTICAL SYSTEMS: TURBO PRODUCT CODES VS. LDPC CODES 85
1. INTRODUCTION 85
2. THE OPTICAL SYSTEM MODEL 86
3. CONCATENATED BLOCK CODES 87
4. LOW-DENSITY PARITY-CHECK CODES 88
5. APPLICATIONS AND SIMULATION RESULTS 88
5.1 Optical system description 88
5.2 Simulation results 88
6. CONCLUSIONS 92
REFERENCES 92
ITERATIVE DECODING AND ERROR CODE CORRECTION METHOD IN HOLOGRAPHIC DATA STORAGE 93
1. INTRODUCTION 93
2. CHANNEL MODEL 94
3. SOURCE ENCODING AND DECODING 96
4. SIMULATION RESULTS 98
5. EXPERIMENTAL RESULTS 99
6. CONCLUSION 100
REFERENCES 100
PERFORMANCE OF OPTICAL TIME-SPREAD CDMA/ PPM WITH MULTIPLE ACCESS AND MULTIPATH INTERFERENCE 101
1. SYSTEM DESCRIPTION 102
2. CHANNEL MODEL 103
2.1 Quantization of and system synchronization 103
3. INTENSITY SAMPLES 104
3.1 Total error probability 107
4. CONCLUSIONS 108
REFERENCES 108
PERFORMANCE ANALYSIS AND COMPARISON OF TRELLIS-CODED AND TURBO-CODED OPTICAL CDMA SYSTEMS 109
1. INTRODUCTION 110
2. SYSTEM MODEL 111
3. SIMULATION DETAILS 112
4. SIMULATION RESULTS 114
5. CONCLUSION 116
CHARACTERIZING, MEASURING, AND CALCULATING PERFORMANCE IN OPTICAL FIBER COMMUNICATION SYSTEMS 117
A METHODOLOGY FOR CALCULATING PERFORMANCE IN AN OPTICAL FIBER COMMUNICATIONS SYSTEM 118
ACKNOWLEDGMENTS 123
REFERENCES 124
MARKOV CHAIN MONTE CARLO TECHNIQUE FOR OUTAGE PROBABILITY EVALUATION IN PMD- COMPENSATED SYSTEMS 125
1. INTRODUCTION 125
2. MARKOV CHAIN MONTE CARLO METHOD 126
3. ACCURACY 129
4. RESULTS 131
5. CONCLUSIONS 132
REFERENCES 132
A PARAMETRIC GAIN APPROACH TO PERFORMANCE EVALUATION OF DPSK/DQPSK SYSTEMS WITH NONLINEAR PHASE NOISE 133
1. INTRODUCTION 133
2. SYSTEM SET-UP 134
3. ASE STATISTICS 135
4. MODEL FOR NOISE PROPAGATION 136
5. RESULTS AND DISCUSSION 137
6. CONCLUSIONS 139
ACKNOWLEDGMENTS 140
REFERENCES 140
CHARACTERIZATION OF INTRACHANNEL NONLINEAR DISTORTION IN ULTRA-HIGH BIT-RATE TRANSMISSION SYSTEMS 141
1. INTRODUCTION 141
2. CHARACTERIZING INTRACHANNEL NONLINEAR DISTORTION 142
2.1 Signal waveform distortion 142
2.2 Characterizing nonlinear distortion using BER measurements 149
3. CONCLUSIONS 151
ACKNOWLEDGMENTS 152
REFERENCES 152
MATHEMATICAL AND EXPERIMENTAL ANALYSIS OF INTERFEROMETRIC CROSSTALK NOISE INCORPORATING CHIRP EFFECT IN DIRECTLY MODULATED SYSTEMS 155
1. INTRODUCTION 155
2. CROSSTALK PDF CALCULATION 156
3. THEORETICAL AND EXPERIMENTAL RESULTS 157
REFERENCES 159
ON THE IMPACT OF MPI IN ALL-RAMAN DISPERSION-COMPENSATED IMDD AND DPSK LINKS 160
1. INTRODUCTION 160
2. THEORETICAL APPROACH 161
3. PENALTY RESULTS 163
4. ACCOUNTING FOR FIBER NONLINEARITIES 165
5. CONCLUSIONS 167
REFERENCES 167
MODULATION FORMATS AND DETECTION 168
MODULATION FORMATS FOR OPTICAL FIBER TRANSMISSION 169
1. INTRODUCTION 169
2. CLASSIFICATION OF MODULATION FORMATS 169
3. EXAMPLES 171
4. SUMMARY AND CONCLUSIONS 172
REFERENCES 173
DISPERSION LIMITATIONS IN OPTICAL SYSTEMS USING OFFSET DPSK MODULATION 175
1. INTRODUCTION 175
2. SYSTEM MODEL AND BER CALCULATION 176
3. CD AND PMD PENALTIES FOR AND 179
4. CONCLUSIONS 181
ACKNOWLEDGMENT 181
REFERENCES 181
INTEGRATED OPTICAL FIR-FILTERS FOR ADAPTIVE EQUALIZATION OF FIBER CHANNEL IMPAIRMENTS AT 40 GBIT/ S 182
1. INTRODUCTION 182
2. ADAPTIVE COMPENSATION OF CD AND PMD WITH ELECTRICAL SPECTRUM MONITORING AS FEEDBACK SIGNAL 184
3. CONCLUSION 187
REFERENCES 188
PERFORMANCE OF ELECTRONIC EQUALIZATION APPLIED TO INNOVATIVE TRANSMISSION TECHNIQUES 189
1. INTRODUCTION 189
1.1 System setup 190
2. SIMULATION AND RESULTS 192
3. CONCLUSIONS 195
ACKNOWLEDGMENT 196
REFERENCES 196
PERFORMANCE BOUNDS OF MLSE IN INTENSITY MODULATED FIBER OPTIC LINKS 197
1. INTRODUCTION 197
2. MLSE IN FIBER OPTIC LINKS 198
2.1 Error probability and performance 199
ACKNOWLEDGMENTS 202
REFERENCES 202
ON MLSE RECEPTION OF CHROMATIC DISPERSION TOLERANT MODULATION SCHEMES 204
1. INTRODUCTION 204
2. MLSE FOR NONLINEAR CHANNELS 205
3. TRANSMISSION SCENARIO AND RESULTS 206
3.1 Static sampling phase sensitivity 207
3.2 Chirped NRZ modulation 208
3.3 Optical duobinary modulation 209
4. CONCLUSIONS 210
REFERENCES 210
Author Index 212
Index 213

QUANTUM-AIDED CLASSICAL CRYPTOGRAPHY WITH A MOVING TARGET (p. 53-54)

Fabrizio Tamburini1,3, Sante Andreoli2, and Tommaso Occhipinti1,

1 Dept. of Astronomy, University of Padova, vicolo dell’Osservatorio 2,I-35122 Padova, Italy.
2 Magneti Marelli Holding S.p.A., Motorsport.
3 Department of Information Engineering, University of Padova, via Gradenigo 6/B, I-35131, Padova, Italy.


Abstract: We propose an encryption method obtained combining low-light optical communication, in the limit of quantum key distribution (QKD) techniques, and classical cryptography with pre-shared key. We present a toy-application to the telemetric data transmission Formula 1 racing. Key words: optical communication; secure communication; cryptography; quantum cryptography.

1. INTRODUCTION

The recent method proposed to create and distribute securely a quantum encryption key to send secure messages takes its vital inspiration from the basic laws of quantum mechanics. Quantum cryptography started with the studies by Bennett and Brassard in 1980s and by Bennett in 1992 [1,2] as a new method for generating and distributing secure cryptographic keys using the properties of Quantum Mechanics. In contrast to existing methods of classical key distribution (CKD), quantum key distribution, QKD bases its security on the laws of nature. The impossibility of cloning or measuring a quantum state without inducing an irreversible collapse of its wavefunction ensures the build-up of a secure encryptographic key distribution between two parties. For a review see e.g. [3]. Similar experiments [4, 5] illustrated the feasibility of quantum encryption in practical situations.

Free-space QKD was first realized [6,7] over a small distance of 32 cm only with a point-to-point table top optical path, and recently improved in atmospheric transmission distances of 75 m [8] in daylight and 1 km [9] in nighttime over outdoor folded paths, where the quanta of light were sent to a mirror and back to the detector. A daylight quantum key distribution had been realized over a distance of 1.6 km by Buttler et al. [5]. Recently Aspelmeyer et al. realized a quantum key distribution over the Danube using entangled photons [10]. Several groups have also demonstrated QKD over multi-kilometer distances of optical fiber [11–17] and recently realized a version of the experiment "in the real world", in which Alice and Bob were connected with 1.45 km of optical fiber sharing entangled photons.

The average raw key bit rate was found to be about 80 bits/s after error correction and privacy amplification. idQuantique, MagiQ technologies and NEC realized commercial applications of secure quantum key distribution [18–20]. MagiQ technologies guarantee, for example, a fast-generating quantum key rate of 10 keys per second. The field is now sufficiently mature to be commercially implemented and to be a tool in fundamental research beyond the foundations of quantum mechanics and basic physics [21,22].

2. QKD TO UPDATE A "MOTHER KEY"

In this paper we suggest a simple procedure to aid the classical cryptographic methods with Quantum Cryptography, when the environmental conditions and/or the requirements of obtaining a long key in a short time strongly play against QKD. This procedure will increase, time-by-time, with the onetime- pad methods of Quantum Cryptography, the global security of the scheme. This method was studied to improve the security of bi-directional telemetry of race cars in view of possible, future, quantum computer attacks.

A classical cryptographic scheme can be reduced to three main quantities:

m the message, k the key and c the code, with the corresponding random variables M, K and C that describe their statistical behaviours. The encoding C = Code(M,K) and the decoding M = Dec(C,K) are suitable deterministic processes which are described by a set of instructions that require a computational effort that depends both on the length of the cryptographic key and on the chosen protocol. Even if modern classical encryption protocols, based on the computational complexity of their encoding algorithms, still resist to the attacks made with nowadays technology, they will become vulnerable in the next future to the attacks of quantum computers, e.g. with Shor’s algorithm (for a review, see [23]).

This problem will be avoided with a fast-generating QKD scheme that will change the key with a rate much faster than the computational time needed to break the code, without giving enough time to the cracker to get the encoded information. In environmental conditions with high bit error rate the application of this procedure will become more and more difficult giving more chances to the cracker to break the code.