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| Preface | |
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| Acknowledgements | |
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| Introduction to digital communication | |
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| Standardized interfaces and layering | |
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| Communication sources | |
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| Source coding | |
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| Communication channels | |
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| Channel encoding (modulation) | |
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| Error correction | |
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| Digital interface | |
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| Network aspects of the digital interface | |
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| Supplementary reading | |
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| Coding for discrete sources | |
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| Introduction | |
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| Fixed-length codes for discrete sources | |
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| Variable-length codes for discrete sources | |
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| Unique decodability | |
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| Prefix-free codes for discrete sources | |
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| The Kraft inequality for prefix-free codes | |
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| Probability models for discrete sources | |
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| Discrete memoryless sources | |
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| Minimum L for prefix-free codes | |
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| Lagrange multiplier solution for the minimum L | |
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| Entropy bounds on L | |
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| Huffman's algorithm for optimal source codes | |
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| Entropy and fixed-to-variable-length codes | |
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| Fixed-to-variable-length codes | |
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| The AEP and the source coding theorems | |
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| The weak law of large numbers | |
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| The asymptotic equipartition property | |
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| Source coding theorems | |
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| The entropy bound for general classes of codes | |
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| Markov sources | |
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| Coding for Markov sources | |
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| Conditional entropy | |
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| Lempel-Ziv universal data compression | |
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| The LZ77 algorithm | |
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| Why LZ77 works | |
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| Discussion | |
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| Summary of discrete source coding | |
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| Exercises | |
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| Quantization | |
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| Introduction to quantization | |
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| Scalar quantization | |
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| Choice of intervals for given representation points | |
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| Choice of representation points for given intervals | |
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| The Lloyd-Max algorithm | |
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| Vector quantization | |
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| Entropy-coded quantization | |
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| High-rate entropy-coded quantization | |
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| Differential entropy | |
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| Performance of uniform high-rate scalar quantizers | |
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| High-rate two-dimensional quantizers | |
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| Summary of quantization | |
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| Appendixes | |
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| Nonuniform scalar quantizers | |
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| Nonuniform 2D quantizers | |
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| Exercises | |
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| Source and channel waveforms | |
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| Introduction | |
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| Analog sources | |
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| Communication channels | |
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| Fourier series | |
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| Finite-energy waveforms | |
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| L[subscript 2] functions and Lebesgue integration over [-T/2, T/2] | |
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| Lebesgue measure for a union of intervals | |
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| Measure for more general sets | |
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| Measurable functions and integration over [-T/2, T/2] | |
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| Measurability of functions defined by other functions | |
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| L[subscript 1] and L[subscript 2] functions over [-T/2, T/2] | |
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| Fourier series for L[subscript 2] waveforms | |
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| The T-spaced truncated sinusoid expansion | |
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| Fourier transforms and L[subscript 2] waveforms | |
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| Measure and integration over R | |
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| Fourier transforms of L[subscript 2] functions | |
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| The DTFT and the sampling theorem | |
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| The discrete-time Fourier transform | |
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| The sampling theorem | |
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| Source coding using sampled waveforms | |
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| The sampling theorem for [Delta - W, Delta + W] | |
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| Aliasing and the sinc-weighted sinusoid expansion | |
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| The T-spaced winc-weighted sinusoid expansion | |
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| Degrees of freedom | |
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| Aliasing - a time-domain approach | |
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| Aliasing - a frequency-domain approach | |
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| Summary | |
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| Appendix: Supplementary material and proofs | |
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| Countable sets | |
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| Finite unions of intervals over [-T/2, T/2] | |
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| Countable unions and outer measure over [-T/2, T/2] | |
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| Arbitrary measurable sets over [-T/2, T/2] | |
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| Exercises | |
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| Vector spaces and signal space | |
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| Axioms and basic properties of vector spaces | |
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| Finite-dimensional vector spaces | |
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| Inner product spaces | |
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| The inner product spaces R[superscript n] and C[superscript n] | |
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| One-dimensional projections | |
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| The inner product space of L[subscript 2] functions | |
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| Subspaces of inner product spaces | |
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| Orthonormal bases and the projection theorem | |
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| Finite-dimensional projections | |
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| Corollaries of the projection theorem | |
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| Gram-Schmidt orthonormalization | |
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| Orthonormal expansions in L[subscript 2] | |
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| Summary | |
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| Appendix: Supplementary material and proofs | |
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| The Plancherel theorem | |
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| The sampling and aliasing theorems | |
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| Prolate spheroidal waveforms | |
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| Exercises | |
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| Channels, modulation, and demodulation | |
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| Introduction | |
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| Pulse amplitude modulation (PAM) | |
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| Signal constellations | |
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| Channel imperfections: a preliminary view | |
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| Choice of the modulation pulse | |
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| PAM demodulation | |
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| The Nyquist criterion | |
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| Band-edge symmetry | |
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| Choosing {p(t - kT); k [set membership] Z} as an orthonormal set | |
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| Relation between PAM and analog source coding | |
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| Modulation: baseband to passband and back | |
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| Double-sideband amplitude modulation | |
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| Quadrature amplitude modulation (QAM) | |
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| QAM signal set | |
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| QAM baseband modulation and demodulation | |
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| QAM: baseband to passband and back | |
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| Implementation of QAM | |
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| Signal space and degrees of freedom | |
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| Distance and orthogonality | |
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| Carrier and phase recovery in QAM systems | |
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| Tracking phase in the presence of noise | |
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| Large phase errors | |
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| Summary of modulation and demodulation | |
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| Exercises | |
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| Random processes and noise | |
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| Introduction | |
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| Random processes | |
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| Examples of random processes | |
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| The mean and covariance of a random process | |
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| Additive noise channels | |
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| Gaussian random variables, vectors, and processes | |
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| The covariance matrix of a jointly Gaussian random vector | |
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| The probability density of a jointly Gaussian random vector | |
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| Special case of a 2D zero-mean Gaussian random vector | |
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| Z = AW, where A is orthogonal | |
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| Probability density for Gaussian vectors in terms of principal axes | |
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| Fourier transforms for joint densities | |
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| Linear functionals and filters for random processes | |
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| Gaussian processes defined over orthonormal expansions | |
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| Linear filtering of Gaussian processes | |
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| Covariance for linear functionals and filters | |
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| Stationarity and related concepts | |
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| Wide-sense stationary (WSS) random processes | |
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| Effectively stationary and effectively WSS random processes | |
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| Linear functionals for effectively WSS random processes | |
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| Linear filters for effectively WSS random processes | |
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| Stationarity in the frequency domain | |
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| White Gaussian noise | |
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| The sinc expansion as an approximation to WGN | |
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| Poisson process noise | |
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| Adding noise to modulated communication | |
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| Complex Gaussian random variables and vectors | |
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| Signal-to-noise ratio | |
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| Summary of random processes | |
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| Appendix: Supplementary topics | |
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| Properties of covariance matrices | |
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| The Fourier series expansion of a truncated random process | |
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| Uncorrelated coefficients in a Fourier series | |
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| The Karhunen-Loeve expansion | |
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| Exercises | |
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| Detection, coding, and decoding | |
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| Introduction | |
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| Binary detection | |
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| Binary signals in white Gaussian noise | |
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| Detection for PAM antipodal signals | |
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| Detection for binary nonantipodal signals | |
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| Detection for binary real vectors in WGN | |
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| Detection for binary complex vectors in WGN | |
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| Detection of binary antipodal waveforms in WGN | |
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| M-ary detection and sequence detection | |
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| M-ary detection | |
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| Successive transmissions of QAM signals in WGN | |
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| Detection with arbitrary modulation schemes | |
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| Orthogonal signal sets and simple channel coding | |
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| Simplex signal sets | |
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| Biorthogonal signal sets | |
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| Error probability for orthogonal signal sets | |
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| Block coding | |
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| Binary orthogonal codes and Hadamard matrices | |
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| Reed-Muller codes | |
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| Noisy-channel coding theorem | |
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| Discrete memoryless channels | |
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| Capacity | |
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| Converse to the noisy-channel coding theorem | |
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| Noisy-channel coding theorem, forward part | |
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| The noisy-channel coding theorem for WGN | |
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| Convolutional codes | |
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| Decoding of convolutional codes | |
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| The Viterbi algorithm | |
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| Summary of detection, coding, and decoding | |
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| Appendix: Neyman-Pearson threshold tests | |
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| Exercises | |
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| Wireless digital communication | |
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| Introduction | |
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| Physical modeling for wireless channels | |
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| Free-space, fixed transmitting and receiving antennas | |
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| Free-space, moving antenna | |
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| Moving antenna, reflecting wall | |
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| Reflection from a ground plane | |
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| Shadowing | |
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| Moving antenna, multiple reflectors | |
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| Input/output models of wireless channels | |
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| The system function and impulse response for LTV systems | |
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| Doppler spread and coherence time | |
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| Delay spread and coherence frequency | |
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| Baseband system functions and impulse responses | |
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| A discrete-time baseband model | |
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| Statistical channel models | |
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| Passband and baseband noise | |
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| Data detection | |
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| Binary detection in flat Rayleigh fading | |
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| Noncoherent detection with known channel magnitude | |
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| Noncoherent detection in flat Rician fading | |
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| Channel measurement | |
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| The use of probing signals to estimate the channel | |
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| Rake receivers | |
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| Diversity | |
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| CDMA: the IS95 standard | |
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| Voice compression | |
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| Channel coding and decoding | |
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| Viterbi decoding for fading channels | |
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| Modulation and demodulation | |
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| Multiaccess interference in IS95 | |
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| Summary of wireless communication | |
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| Appendix: Error probability for noncoherent detection | |
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| Exercises | |
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| References | |
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| Index | |