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Coding Theory

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Lecture 1: Mod-01 Lec-01 Introduction to Linear Block Codes

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Lecture Details :

Coding Theory by Dr. Andrew Thangaraj, Department of Electronics & Communication Engineering, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

Course Objective:

To provide an introduction to traditional and modern coding theory. Topics covered include linear block codes, cyclic codes (BCH and RS codes), convolutional codes, turbo codes and low-density parity-check (LDPC) codes.
Outline:

Part I: Basics and Algebraic Codes.
Linear Block Codes: Generator and parity-check matrices, Minimum Distance, Sydrome decoding, Bounds on minimum distance.
Cyclic Codes: Finite fields, Binary BCH codes, RS codes.

Part II: Coding in digital communications.
AWGN channel: BPSK modulation, Capacity, Coding gain, ML and MAP decoders, Soft-versus hard-decision decoding.
Convolutional Codes: Encoders, Trellis, Viterbi decoding.

Part III: Modern iterative coding.
Turbo codes: Encoders, interleavers, turbo decoder.
Low-density Parity-check Codes: Ensembles of LDPC codes, Message-passing decoders, Threshold phenomenon and density evolution.

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  1. Mod-01 Lec-01 Introduction to Linear Block Codes
  2. Mod-01 Lec-02 Properties of Linear Block Codes
  3. Mod-01 Lec-03 Dual of Linear Block Codes
  4. Mod-01 Lec-04 Minimum Distance of Codes
  5. Mod-01 Lec-05 Operations on Codes
  6. Mod-01 Lec-06 Bounds on Code Parameters
  7. Mod-01 Lec-07 Optimal Decoders
  8. Mod-01 Lec-08 Syndrome Decoder, Basics of Finite Fields
  9. Mod-01 Lec-09 Construction of Finite Fields
  10. Mod-01 Lec-10 Computations in Finite Fields
  11. Mod-01 Lec-11 Codes over Finite Fields, Minimal Polynomials
  12. Mod-01 Lec-12 BCH Codes
  13. Mod-01 Lec-13 BCH and RS Codes I
  14. Mod-01 Lec-14 BCH and RS Codes II
  15. Mod-01 Lec-15 Decoding BCH Codes
  16. Mod-01 Lec-16 Decoding RS Codes
  17. Mod-01 Lec-17 Coded Modulation and Soft Decision Decoding
  18. Mod-01 Lec-18 Optimal Decoders for BPSK over AWGN
  19. Mod-01 Lec-19 Bitwise MAP Decoder for BPSK over AWGN
  20. Mod-01 Lec-20 Bitwise MAP Decoder from the Dual Code
  21. Mod-01 Lec-21 Simulating Coded Modulation
  22. Mod-01 Lec-22 Union Bound, Introduction to LDPC Codes
  23. Mod-01 Lec-23 LDPC Codes
  24. Mod-01 Lec-24 Message Passing, Density Evolution Analysis
  25. Mod-01 Lec-25 Thresholds of LDPC Codes
  26. Mod-01 Lec-26 Irregular LDPC Codes
  27. Mod-01 Lec-27 Optimized Irregular LDPC Codes, Soft Message Passing Decoders
  28. Mod-01 Lec-28 Density Evolution for Soft Message Passing Decoding of LDPC Codes
  29. Mod-01 Lec-29 LDPC Codes in Practice
  30. Mod-01 Lec-30 Introduction to Convolutional Codes
  31. Mod-01 Lec-31 Viterbi Decoding of Convolutional Codes
  32. Mod-01 Lec-32 Union Bound, Recursive Convolutional Encoders
  33. Mod-01 Lec-33 Convolutional Codes in Practice
  34. Mod-01 Lec-34 BCJR Decoder
  35. Mod-01 Lec-35 BCJR and Max-Log-MAP Decoder, Introduction to Turbo Codes
  36. Mod-01 Lec-36 Turbo Decoder
  37. Mod-01 Lec-37 Turbo Codes in Practice
  38. Mod-01 Lec-38 Modern Codes