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Error Correcting Codes

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Lecture 37: Mod-10 Lec-37 Finite Fields: A Deductive Approach

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Lecture Details :

Deducing the structure of a finite field; Subfields and cyclotomic cosets.

Course Description :

Error-correcting codes are in widespread use for data storage as well as most forms of communication where reliability is of importance. Examples range from compact discs to deep-space communication.
This course will cover both classical error-correcting codes such as BCH, Reed-Solomon and convolutional codes as well as the more modern class of iteratively decodable codes, low-density, parity-check codes in particular.

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  1. Mod-01 Lec-01 Course Overview & Basics
  2. Mod-01 Lec-02 Example Codes and their Parameters
  3. Mod-02 Lec-03 Mathematical Preliminaries: Groups
  4. Mod-02 Lec-04 Subgroups and Equivalence Relations
  5. Mod-02 Lec-05 Cosets, Rings & Fields
  6. Mod-03 Lec-06 Vector Spaces, Linear
  7. Mod-03 Lec-07 Linear Codes, & Linear independence
  8. Mod-03 Lec-08 Spanning & Basis
  9. Mod-04 Lec-09 The Dual Code
  10. Mod-04 Lec-10 Systematic Generator Matrix
  11. Mod-04 Lec-11 Minimum Distance of a Linear Code
  12. Mod-05 Lec-12 Bounds on the size of a Code
  13. Mod-05 Lec-13 Asymptotic Bounds
  14. Mod-06 Lec-14 Standard Array Decoding
  15. Mod-06 Lec-15 Performance Analysis of the SAD
  16. Mod-07 Lec-16 State and Trellis
  17. Mod-07 Lec-17 The Viterbi Decoder
  18. Mod-07 Lec-18 Catastrophic Error Propagation
  19. Mod-07 Lec-19 Path Enumeration
  20. Mod-07 Lec-20 Viterbi Decoder over the AWGN Channel
  21. Mod-08 Lec-21 Generalized Distributive Law
  22. Mod-08 Lec-22 The MPF Problem
  23. Mod-08 Lec-23 Further Examples of the MPF Problem
  24. Mod-08 Lec-24 Junction Trees recap
  25. Mod-08 Lec-25 Example of Junction Tree Construction
  26. Mod-08 Lec-26 Message passing on the Junction tree
  27. Mod-08 Lec-27 GDL Approach to Decoding Convolutional Codes
  28. Mod-08 Lec-28 ML Code-Symbol Decoding of the Convolutional Code
  29. Mod-09 Lec-29 LDPC Codes
  30. Mod-09 Lec-30 LDPC Code Terminology
  31. Mod-09 Lec-31 Gallager Decoding Algorithm A
  32. Mod-09 Lec-32 BP Decoding of LDPC Codes
  33. Mod-09 Lec-33 BP Decoding (Continued)
  34. Mod-09 Lec-34 Density Evolution under BP decoding
  35. Mod-09 Lec-35 Convergence & Concentration Theorem -- LDPC Codes
  36. Mod-10 Lec-36 A Construction for Finite Fields
  37. Mod-10 Lec-37 Finite Fields: A Deductive Approach
  38. Mod-10 Lec-38 Deductive Approach to Finite Fields
  39. Mod-10 Lec-39 Subfields of a Finite field
  40. Mod-11 Lec-40 Transform Approach to Cyclic Codes
  41. Mod-11 Lec-41 Estimating the Parameters of a Cyclic Code
  42. Mod-11 Lec-42 Decoding Cyclic Codes