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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 03 - Dual of 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