PRINCIPLES OF DIGITAL COMMUNICATION
CONTENTS INTRODUCTION TO DIGITAL COMMUNICATION STANDARDIZED INTERFACES AND LAYERING COMMUNICATION SOURCES SOURCE CODING COMMUNICATION CHANNELS CHANNEL ENCODING (MODULATION) ERROR CORRECTION DIGITAL INTERFACE NETWORK ASPECTS OF THE DIGITAL INTERFACE CODING FOR DISCRETE SOURCES INTRODUCTION FIXED-LENGTH CODES FOR DISCRETE SOURCES VARIABLE-LENGTH CODES FOR DISCRETE SOURCES UNIQUE DECODABILITY PRE?X-FREE CODES FOR DISCRETE SOURCES THE KRAFT INEQUALITY FOR PRE?X-FREE CODES PROBABILITY MODELS FOR DISCRETE SOURCES DISCRETE MEMORYLESS SOURCES MINIMUM L FOR PRE?X-FREE CODES LAGRANGE MULTIPLIER SOLUTION FOR THE MINIMUM L ENTROPY BOUNDS ON L HU?MAN’S ALGORITHM FOR OPTIMAL SOURCE CODES ENTROPY AND ?XED-TO-VARIABLE-LENGTH CODES FIXED-TO-VARIABLE-LENGTH CODES THE AEP AND THE SOURCE CODING THEOREMS THE WEAK LAW OF LARGE NUMBERS THE ASYMPTOTIC EQUIPARTITION PROPERTY SOURCE CODING THEOREMS THE ENTROPY BOUND FOR GENERAL CLASSES OF CODES MARKOV SOURCES CODING FOR MARKOV SOURCES CONDITIONAL ENTROPY LEMPEL-ZIV UNIVERSAL DATA COMPRESSION THE LZ77 ALGORITHM WHY LZ77 WORKS DISCUSSION 2 10 SUMMARY OF DISCRETE SOURCE CODING 2 E EXERCISES QUANTIZATION INTRODUCTION TO QUANTIZATION SCALAR QUANTIZATION CHOICE OF INTERVALS FOR GIVEN REPRESENTATION POINTS CHOICE OF REPRESENTATION POINTS FOR GIVEN INTERVALS THE LLOYD-MAX ALGORITHM VECTOR QUANTIZATION ENTROPY-CODED QUANTIZATION HIGH-RATE ENTROPY-CODED QUANTIZATION DI?ERENTIAL ENTROPY PERFORMANCE OF UNIFORM HIGH-RATE SCALAR QUANTIZERS HIGH-RATE TWO-DIMENSIONAL QUANTIZERS SUMMARY OF QUANTIZATION 3A APPENDIX A: NONUNIFORM SCALAR QUANTIZERS 3B APPENDIX B: NONUNIFORM 2D QUANTIZERS 3 E EXERCISES SOURCE AND CHANNEL WAVEFORMS ANALOG SOURCES FOURIER SERIES FINITE-ENERGY WAVEFORMS L2 FUNCTIONS AND LEBESGUE INTEGRATION OVER [?T/2, T/2] LEBESGUE MEASURE FOR A UNION OF INTERVALS MEASURE FOR MORE GENERAL SETS MEASURABLE FUNCTIONS AND INTEGRATION OVER [?T/2, T/2] MEASURABILITY OF FUNCTIONS DE?NED BY OTHER FUNCTIONS L1 AND L2 FUNCTIONS OVER [?T/2, T/2] THE FOURIER SERIES FOR L2 WAVEFORMS THE T-SPACED TRUNCATED SINUSOID EXPANSION FOURIER TRANSFORMS AND L2 WAVEFORMS MEASURE AND INTEGRATION OVER R FOURIER TRANSFORMS OF L2 FUNCTIONS THE DTFT AND THE SAMPLING THEOREM THE DISCRETE-TIME FOURIER TRANSFORM THE SAMPLING THEOREM SOURCE CODING USING SAMPLED WAVEFORMS THE SAMPLING THEOREM FOR [??W, ?+ W] ALIASING AND THE SINC-WEIGHTED SINUSOID EXPANSION THE T-SPACED SINC-WEIGHTED SINUSOID EXPANSION DEGREES OF FREEDOM ALIASING — A TIME-DOMAIN APPROACH ALIASING — A FREQUENCY-DOMAIN APPROACH SUMMARY 4A APPENDIX: SUPPLEMENTARY MATERIAL AND PROOFS COUNTABLE SETS FINITE UNIONS OF INTERVALS OVER [?T/2, T/2] COUNTABLE UNIONS AND OUTER MEASURE OVER [?T/2, T/2] ARBITRARY MEASURABLE SETS OVER [?T/2, T/2] 4 E EXERCISES VECTOR SPACES AND SIGNAL SPACE THE AXIOMS AND BASIC PROPERTIES OF VECTOR SPACES FINITE-DIMENSIONAL VECTOR SPACES INNER PRODUCT SPACES THE INNER PRODUCT SPACES RN AND CN ONE-DIMENSIONAL PROJECTIONS THE INNER PRODUCT SPACE OF L2 FUNCTIONS SUBSPACES OF INNER PRODUCT SPACES ORTHONORMAL BASES AND THE PROJECTION THEOREM FINITE-DIMENSIONAL PROJECTIONS COROLLARIES OF THE PROJECTION THEOREM GRAM-SCHMIDT ORTHONORMALIZATION 5A APPENDIX: SUPPLEMENTARY MATERIAL AND PROOFS THE PLANCHEREL THEOREM THE SAMPLING AND ALIASING THEOREMS PROLATE SPHEROIDAL WAVEFORMS 5 E EXERCISES CHANNELS, MODULATION, AND DEMODULATION PULSE AMPLITUDE MODULATION (PAM) SIGNAL CONSTELLATIONS CHANNEL IMPERFECTIONS: A PRELIMINARY VIEW CHOICE OF THE MODULATION PULSE PAM DEMODULATION THE NYQUIST CRITERION BAND-EDGE SYMMETRY CHOOSING {P(T?KT); K ?Z} AS AN ORTHONORMAL SET RELATION BETWEEN PAM AND ANALOG SOURCE CODING MODULATION: BASEBAND TO PASSBAND AND BACK DOUBLE-SIDEBAND AMPLITUDE MODULATION QUADRATURE AMPLITUDE MODULATION (QAM) QAM SIGNAL SET QAM BASEBAND MODULATION AND DEMODULATION QAM: BASEBAND TO PASSBAND AND BACK IMPLEMENTATION OF QAM SIGNAL SPACE AND DEGREES OF FREEDOM DISTANCE AND ORTHOGONALITY CARRIER AND PHASE RECOVERY IN QAM SYSTEMS TRACKING PHASE IN THE PRESENCE OF NOISE LARGE PHASE ERRORS SUMMARY OF MODULATION AND DEMODULATION 6 E EXERCISES RANDOM PROCESSES AND NOISE RANDOM PROCESSES EXAMPLES OF RANDOM PROCESSES THE MEAN AND COVARIANCE OF A RANDOM PROCESS ADDITIVE NOISE CHANNELS GAUSSIAN RANDOM VARIABLES, VECTORS, AND PROCESSES THE COVARIANCE MATRIX OF A JOINTLY GAUSSIAN RANDOM VECTOR THE PROBABILITY DENSITY OF A JOINTLY GAUSSIAN RANDOM VECTOR SPECIAL CASE OF A 2-DIMENSIONAL ZERO-MEAN GAUSSIAN RANDOM VECTOR Z = AW WHERE A IS ORTHOGONAL PROBABILITY DENSITY FOR GAUSSIAN VECTORS IN TERMS OF PRINCIPAL AXES FOURIER TRANSFORMS FOR JOINT DENSITIES LINEAR FUNCTIONALS AND ?LTERS FOR RANDOM PROCESSES GAUSSIAN PROCESSES DE?NED OVER ORTHONORMAL EXPANSIONS LINEAR ?LTERING OF GAUSSIAN PROCESSES COVARIANCE FOR LINEAR FUNCTIONALS AND ?LTERS STATIONARITY AND RELATED CONCEPTS WIDE-SENSE STATIONARY (WSS) RANDOM PROCESSES E?ECTIVELY STATIONARY AND E?ECTIVELY WSS RANDOM PROCESSES LINEAR FUNCTIONALS FOR E?ECTIVELY WSS RANDOM PROCESSES LINEAR ?LTERS FOR E?ECTIVELY WSS RANDOM PROCESSES STATIONARY AND WSS PROCESSES IN THE FREQUENCY DOMAIN WHITE GAUSSIAN NOISE THE SINC EXPANSION AS AN APPROXIMATION TO WGN POISSON PROCESS NOISE ADDING NOISE TO MODULATED COMMUNICATION COMPLEX GAUSSIAN RANDOM VARIABLES AND VECTORS SIGNAL-TO-NOISE RATIO 7 10 SUMMARY OF RANDOM PROCESSES 7A APPENDIX: SUPPLEMENTARY TOPICS PROPERTIES OF COVARIANCE MATRICES THE FOURIER SERIES EXPANSION OF A TRUNCATED RANDOM PROCESS UNCORRELATED COE?CIENTS IN A FOURIER SERIES THE KARHUNEN-LOEVE EXPANSION 7 E EXERCISES DETECTION, CODING, AND DECODING BINARY DETECTION BINARY SIGNALS IN WHITE GAUSSIAN NOISE DETECTION FOR PAM ANTIPODAL SIGNALS DETECTION FOR BINARY NON-ANTIPODAL SIGNALS DETECTION FOR BINARY REAL VECTORS IN WGN DETECTION FOR BINARY COMPLEX VECTORS IN WGN DETECTION OF BINARY ANTIPODAL WAVEFORMS IN WGN M-ARY DETECTION AND SEQUENCE DETECTION M-ARY DETECTION SUCCESSIVE TRANSMISSIONS OF QAM SIGNALS IN WGN DETECTION WITH ARBITRARY MODULATION SCHEMES ORTHOGONAL SIGNAL SETS AND SIMPLE CHANNEL CODING SIMPLEX SIGNAL SETS BIORTHOGONAL SIGNAL SETS ERROR PROBABILITY FOR ORTHOGONAL SIGNAL SETS BLOCK CODING BINARY ORTHOGONAL CODES AND HADAMARD MATRICES REED-MULLER CODES THE NOISY-CHANNEL CODING THEOREM DISCRETE MEMORYLESS CHANNELS CAPACITY CONVERSE TO THE NOISY-CHANNEL CODING THEOREM NOISY-CHANNEL CODING THEOREM, FORWARD PART THE NOISY-CHANNEL CODING THEOREM FOR WGN CONVOLUTIONAL CODES DECODING OF CONVOLUTIONAL CODES THE VITERBI ALGORITHM SUMMARY OF DETECTION, CODING AND DECODING 8A APPENDIX: NEYMAN-PEARSON THRESHOLD TESTS 8 E EXERCISES WIRELESS DIGITAL COMMUNICATION PHYSICAL MODELING FOR WIRELESS CHANNELS FREE SPACE, ?XED TRANSMITTING AND RECEIVING ANTENNAS FREE SPACE, MOVING ANTENNA MOVING ANTENNA, RE?ECTING WALL RE?ECTION FROM A GROUND PLANE SHADOWING MOVING ANTENNA, MULTIPLE RE?ECTORS INPUT/OUTPUT MODELS OF WIRELESS CHANNELS THE SYSTEM FUNCTION AND IMPULSE RESPONSE FOR LTV SYSTEMS DOPPLER SPREAD AND COHERENCE TIME DELAY SPREAD, AND COHERENCE FREQUENCY BASEBAND SYSTEM FUNCTIONS AND IMPULSE RESPONSES A DISCRETE-TIME BASEBAND MODEL STATISTICAL CHANNEL MODELS PASSBAND AND BASEBAND NOISE DATA DETECTION BINARY DETECTION IN ?AT RAYLEIGH FADING NON-COHERENT DETECTION WITH KNOWN CHANNEL MAGNITUDE NON-COHERENT DETECTION IN ?AT RICIAN FADING CHANNEL MEASUREMENT THE USE OF PROBING SIGNALS TO ESTIMATE THE CHANNEL RAKE RECEIVERS DIVERSITY CDMA; THE IS95 STANDARD VOICE COMPRESSION CHANNEL CODING AND DECODING VITERBI DECODING FOR FADING CHANNELS MODULATION AND DEMODULATION MULTIACCESS INTERFERENCE IN IS95 9 10 SUMMARY OF WIRELESS COMMUNICATION 9A APPENDIX: ERROR PROBABILITY FOR NON-COHERENT DETECTION 9 E EXERCISES