I Block Codes and Their Implementation
1. Review of Algebra for Coding; Rings: Integer Rings,
2. Polynomials over Rings, Fields: The Structure of Finite Fields, Galois Fields; Construction of GF(qm)
3. Linear Block Codes, Polynomial Description of Cyclic Codes, Quadratic Residue Codes, Golay Code, Hadamard Codes, Reed-Muller Codes
4. Shift-Register Encoders and Decoders of Cyclic Codes
5. Design of BCH Codes Based on Error Correction, Binary and Non-binary BCH Codes
6. Reed-Solomon (RS) Codes, Decoding: Berlekamp-Massey Algorithm
II. Performance of Block Codes
1. Weight Distributions
2. Probabilities of Decoding error and Decoding Failure
3. Bounds on the Minimum Distance
4. Soft Decision Decoding of Block Codes, Trellis Decoding
III. Error Control for Channels with Feedback
1. Pure ARQ Protocols: Error Detection
2. Noisy Feedback Channels
3. Type-I Hybrid - ARQ Protocols
4. Type-II Hybrid - ARQ Protocols
IV. Convolutional Codes
1. Tree Codes and Trellis Codes, State Diagram, Free Distance
2. Polynomial Description of Convolutional Codes
3. Decoding; Maximum-Likelihood Sequence Estimation (MLSE): Viterbi Algorithm, Soft decision decoding, Maximum a posteriori (MAP) decoding - BCJR Algorithm
4. Sequential Decoding Algorithms: Stack Algorithm, Fano Algorithm
5. Punctured Convolutional Codes
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V. Coded Modulation Schemes
1. Trellis Coded Modulation (TCM), Ungerboeck Codes
2. Multiple TCM, Lattices and Lattice Cosets, Trellis Codes on Lattice Cosets
3. TCM for Fading Channels; Code design Criteria, Performance Evaluation
4. Block Coded Modulation (BCM), Multilevel Block Coding
5. Coding with Diversity: Space Time Coded Modulation (STCM)
6. Decoding Algorithms and Performance Analysis
7. Equalization and Decoding: Soft Output Algorithms- SOVA, MAP
VI. Concatenated Codes and Iterative Decoding
1. Block Codes, Block and Convolutional Codes
2. Recursive Systematic Convolutional Codes
3. Turbo Codes (Parallel Concatenated Convolutional Codes - PCCC), Serial CCC
4. Iterative Decoding-MAP Algorithms based on BCJR, Turbo Coded Modulation
5. Turbo Equalization
6. Performance Bounds in AWGN and Fading Channels
VII. Advanced Coding Schemes
1. Turbo-TCM
2. Space Time Coding
3. Hybrid Coding Schemes
4. Adaptive Coding
5. Unequal Error Protection
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