ELE 486 Digital Communications and Networks

Spring 2007

Professor Sergio Verdú

1. INTRODUCTION

Information Theory. Data Compression. Channel Coding Theory. Physical Layer Communication System Design

2. ERROR CORRECTING CODES

Block, repetition, Hamming codes; Linear Codes: Parity Check matrices; Maximum Likelihood Decoding; Minimum Distance; Perfect Codes; Nonbinary codes; Reed-Solomon Codes; LDPC Codes; Sum-Product Algorithm; Convolutional Codes; Turbo Codes; Repeat-Accumulate Codes

3. DATA COMPRESSION: FUNDAMENTAL LIMITS

Entropy; Binary Data Compression; Uniquely Decodable Codes; Prefix Codes; Huffman Code; Kraft Inequality; Entropy and Minimum Average Length; Arithmetic Coding; Lempel-Ziv Compression (LZ77,LZ78,LZW); Fixed-length almost lossless compression; Shannon's theorem for discrete memoryless sources; Asymptotic Equipartition Property and Typical Sequences

4. CHANNEL CAPACITY

Mutual Information; Conditional Entropy; Entropy Chain Rule; Conditional Mutual Information; Data Processing Lemma; Joint vs Individual Mutual Informations; Discrete memoryless channels; Channel Capacity and Coding Theorem; Source-Channel Separation Principle; Capacity of Gaussian Channels (Discrete and Continuous Time);

5. LOSSY DATA COMPRESSION

Quantization; PCM and Delta Modulation; Rate-Distortion Theory; Binary sources and Bit Error Rate; Gaussian sources and Mean-Square Error; Lossy Source/Channel Coding Separation Principle;

6. MODULATION/DEMODULATION OF DIGITAL DATA

Carrier Modulated Signals; BPSK, QPSK, m-QAM, m-PSK, PAM; Demodulation in the Presence of Noise; Matched Filter: Maximal SNR Solution; Matched Filter: Minimum Probability of Error solution; The Q-function; Hypothesis Testing; Continuous-time signals in white Gaussian noise;

7. NETWORK COMMUNICATIONS

Multiaccess Communications; The Multiaccess Channel; Random Multiaccess; TDMA, FDMA; Orthogonal and Nonorthogonal CDMA; Spread Spectrum; Cellular Systems; Demodulation of CDMA; GSM; OFDM; Fading;