Algebraic Coding Theory
Classical:
- Motivation, brief history of coding and modulation, channel models (BEC, BSC and AWGN), information theory: entropy, mutual information, capacity; algebra: groups, rings, fields, vector spaces
- Linear block codes: orthogonality, parity-check matrices, duality, examples Linear block codes II: distance spectrum, Varshamov's bound, DFTs in finite fields
- Linear block codes III: Reed Solomon codes, linear complexity, decoding of RS codes
- Convolutional codes I: state machines, trellises, the Viterbi Algorithm , transfer functions
- Convolutional codes II: the Forward-Backward (BCJR) Algorithm
Modern (Iterative Decoding):
- History, Bayesian networks, belief propagation, graphical models of codes, log-likelihood ratios, extrinsic information transfer (EXIT) model
- Parallel concatenated (turbo) codes, interleaver designs, distance spectrum
- Serially concatenated codes
- Low-density parity-check codes, regular and irregular, BEC and AWGN
- Irregular turbo codes, BEC and AWGN
- Applications of iterative decoding: Turbo equalization, iterative channel estimation, fixed point implementation aspects
- Current research I: Multi-antenna communication, capacity, LDPC code design, irregular Turbo code design
- Current research II: Multi-user transmission, multi-access channels, broadcast channels