Spring 2007

Professor Sergio Verdú

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

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

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

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);

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;

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;

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