excellent video tutorials which are not available in NPTEL....... enjoy...... 1. Introduction to Coding Theory, Linear Block Codes, Generator Matrices. 2. Linear Block Codes, Parity check matrices, Vector Space view of codes, Dual codes. 3. Dual Codes, Self-orthogonal and Self-Dual codes, Examples of dual codes, Relation between parity-check matrix and dual code. 4. Minimum Distance Decoder, Hamming Distance, Error Correcting Capability of codes, Graphical View of Decoding. 5. Syndrome Decoder, Relationship between Minimum distance and Parity-Check Matrix. 6. Construction of Codes with d=3, Hamming Codes, Extending codes, Puncturing Codes. 7. Shortening codes, Hamming bound, Singleton bound, Gilbert-Varshamov bound, Introduction to finite fields. 8. Groups, Order of group elements, Fermat's Little theorem, Finite fields, Polynomials over fields, Polynomial Division. 9. Polynomial factorisation over a field, Irreducible polynomials, Existence and construction of codes of a given size. 10. Examples of finite field construction, Power notation, primitives and primitive polynomials. 11. BCH codes, Construction of BCH codes for given minimum distance, Vandermonde matrices, BCH bound. 12. Properties of BCH codes (cyclic), Their representation as polynomials, Minimum polynomials. 13. Minimum polynomials, their construction and properties, Their connection with cyclic codes, Generator polynomial of a cyclic code. 14. Dimension of BCH codes, Examples of BCH codes, Systematic encoding, Syndrome decoding for BCH codes, Error Locators. 15. Reed-Solomon(RS) Codes, Dimension, Definition of distance, weight in GF(2^m), Generator polynomial, Minimum distance and binary expansion of RS codes. 16. Reed-Solomon(RS) Codes: Decoding overview, PGZ decoder for RS codes. 17. AWGN channels, Coding gain, Encoding and decoding in AWGN channels. 18. Bitwise MAP Decoder, Likelihood ratios, LLRs. (Not Avaiable) 19. ML and Map decoding for Repetition codes, Probability of decoding error, Channel Capacity, Capacity for various schemes, Eb/No, Coding Gain.(Not Avaiable) 20. Coding gain performances of previously studied codes, Proof of capacity and random codes, Low-Density Parity check(LDPC) codes, Regular LDPC codes, Gallager construction of LDPC codes. 21. Socket construction of regular LDPC codes, Tanner Graphs, Neighbourhoods and cycles in graphs. 22. Gallager A decoding algorithm for LDPC codes and its analysis, LDPC Threshold. 23. Simulation of Gallager decoding, Neighbourhood view of Gallager A decoding algorithm. 24. Irregular LDPC codes, Node and edge perspective. 25. Gallager-A decoder on irregular LDPC codes, Degree optimisation to achieve higher thresholds. 26. Soft-decision Message Passing Decoder for AWGN channels. 27. Soft-decision Message Passing Decoder for AWGN channels--contd., Density evolution for for AWGN channels. 28. Density evolution for for AWGN channels, Summary of LDPC codes. 29. Convolutional codes- Feedforward Convolutional Encoder, Trellis Representation. 30. Viterbi Decoder for convolutional codes. 31. Viterbi Decoder Contd., Recursive convolutional encoders. 32. Recursive convolutional encoders, Puncturing, Turbo encoders.ex 33. Turbo Encoders, Turbo Decoders. 34. Free distance of convolutional codes, Trellises for block codes, Code concatenation. 35. Tutorial: Miscellaneous problem set. 36. Tutorial: Miscellaneous problem set..Contd.
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