1. Block-based coded transmission: HISO channel, Gaussian memoryless channel, HIHO channel, discrete memoryless channel, binary symmetric channel, optimum soft-input and hard-input block decoding (MAP, ML), optimum block decoding for the Gaussian memoryless channel and the discrete memoryless channel, problems
2. Fundamentals of block codes: Galois fields, repetition code, single parity check code, elementary modifications of block codes, minimum distance and bounded minimum distance decoding, error detection, erasure filling, burst errors, performance bounds (Singleton bound, Hamming bound, asymptotic performance bounds, capacity of the binary symmetric channel), problems
3. Linear block codes: Linearity, minimal distance, weight distribution and weight enumerator, error probability of the ML decoder, matrix description, dual code, syndrome, syndrome decoding, repetition code, single parity check code, Hamming codes, modifications and compositions of linear block codes (permutation, length and rate modifications, subfield-subcodes, product codes, interleaved codes, serially concatenated codes, turbo codes), problems
4. Cyclic block codes: Polynomial description, dual code, syndrome decoding, matrix description, shift-register circuits for encoding and decoding, primitive cyclic codes, defining set, cyclic redundancy check (CRC) codes, frequency-domain description, Reed-Solomon codes, BCH codes, problems
5. Convolutional codes: Elementary encoders, distance profile and free distance, weight distribution and weight enumerator, error probability of the ML decoder, truncation and termination, matrix description, syndrome, syndrome decoding, polynomial description, noncatastrophic encoders, trellis description, graph-searching decoders, Viterbi algorithm for hard-input and soft-input ML decoding, sequential decoding, trellis-coded modulation, problems
6. Turbo codes: Encoder, elementary parameters, BER performance, weight distribution and spectral thinning, interleaver, L-values, iterative turbo decoding algorithm, BCJR algorithm, max-log-MAP algorithm, EXIT chart, problems
Appendix – Mathematical fundamentals: Galois fields, Hamming weight and Hamming distance, Hamming spheres, standard array, polynomials over GF(q), primitive elements and exponential representation, extension fields and splitting fields, primitive polynomials, DFT over GF(q), problems
