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# Coding Theory

### Overview

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, interleaves, turbo decoder.
Low-density Parity-check Codes: Ensembles of LDPC codes, Message-passing decoders, Threshold phenomenon and density evolution.

### Syllabus

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

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