An Introduction to Coding Theory

Description

In this course you will learn :

• Week 1-

  Lecture 1: Introduction to error control coding

  Lecture 2: Introduction to linear block codes, generator matrix and parity check matrix

  Lecture 3: Properties of linear block codes: Syndrome, error detection

• Week 2

  Lecture 4: Decoding of linear block codes

  Lecture 5: Distance properties of linear block codes

• Week 3

  Lecture 6: Some simple linear block codes: Repetition codes, Single parity check codes, Hamming codes, Reed Muller codes

  Lecture 7: Bounds on size of codes: Hamming bound, Singleton bound, Plotkin bound, Gilbert-Varshamov bound

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  Week 4

  Lecture 8: Introduction to convolutional codes-I: Encoding, state diagram, trellis diagram

   

  Lecture 9: Introduction to convolutional codes-II: Classification, realization, distance properties

  Lecture 10: Decoding of convolutional codes-I: Viterbi algorithm

• Week 5-

  Lecture 11: Decoding of convolutional codes-II: BCJR algorithm

  Lecture 12: Performance bounds for convolutional codes

• Week 6-

  Lecture 13: Low density parity check codes

  Lecture 14: Decoding of low density parity check codes: Belief propagation algorithm on BSC and AWGN channels

• Week 7-

  Lecture 15: Turbo codes

  Lecture 16: Turbo decoding

• Week 8-

  Lecture 17: Distance properties of turbo codes

  Lecture 18: Convergence of turbo codes 

  Lecture 19: Automatic repeat request schemes

  Lecture 20: Applications of linear codes