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September 25, 2023

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Description

Coding Theory. Instructor: Dr. Andrew Thangaraj, Department of Electronics and Communication Engineering, IIT Madras. This course provides 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.

Part I: Basics and Algebraic Codes
Linear Block Codes: Generator and parity-check matrices, Minimum Distance, Syndrome 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. (from nptel.ac.in)

Course Curriculum

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

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