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Coding Theory

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)

Lecture 01 - Introduction to Linear Block Codes

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Lecture 01 - Introduction to Linear Block Codes

Lecture 02 - Properties of Linear Block Codes

Lecture 03 - Dual of Linear Block Codes

Lecture 04 - Minimum Distance of Codes

Lecture 05 - Operations on Codes

Lecture 06 - Bounds on Code Parameters

Lecture 07 - Optimal Decoders

Lecture 08 - Syndrome Decoder, Basics of Finite Fields

Lecture 09 - Constructions of Finite Fields

Lecture 10 - Constructions of Finite Fields (cont.)

Lecture 11 - Codes over Finite Fields, Minimal Polynomials

Lecture 12 - BCH Codes

Lecture 13 - BCH and RS Codes I

Lecture 14 - BCH and RS Codes II

Lecture 15 - Decoding BCH Codes

Lecture 16 - Decoding RS Codes

Lecture 17 - Coded Modulation and Soft Decision Decoding

Lecture 18 - Optimal Decoders for BPSK over AWGN

Lecture 19 - Bitwise Map Decoder for BPSK over AWGN

Lecture 20 - Bitwise Map Decoder from the Dual Code

Lecture 21 - Simulating Coded Modulation

Lecture 22 - Union Bound, Introduction to LDPC Codes

Lecture 23 - LDPC Codes

Lecture 24 - Message Passing, Density Evolution Analysis

Lecture 25 - Thresholds of LDPC Codes

Lecture 26 - Irregular LDPC Codes

Lecture 27 - Optimized Irregular LDPC Codes, Soft Message Passing Decoders

Lecture 28 - Density Evolution for Soft Message Passing Decoding of LDPC Codes

Lecture 29 - LDPC Codes in Practice

Lecture 30 - Introduction to Convolutional Codes

Lecture 31 - Viterbi Decoding of Convolutional Codes

Lecture 32 - Union Bound, Recursive Convolutional Encoders

Lecture 33 - Convolutional Codes in Practice

Lecture 34 - BCJR Decoder

Lecture 35 - BCJR and Max-Log-MAP Decoder, Introduction to Turbo Codes

Lecture 36 - Turbo Decoder

Lecture 37 - Turbo Codes in Practice

Lecture 38 - Modern Codes