Course Objective:

To provide 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, Sydrome 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.

Other Resources

Course Curriculum

Mod-01 Lec-01 Introduction to Linear Block Codes Details 1:3:24
Mod-01 Lec-02 Properties of Linear Block Codes Details 53:5
Mod-01 Lec-03 Dual of Linear Block Codes Details 49:16
Mod-01 Lec-04 Minimum Distance of Codes Details 0:51
Mod-01 Lec-05 Operations on Codes Details 50:1
Mod-01 Lec-06 Bounds on Code Parameters Details 50:32
Mod-01 Lec-07 Optimal Decoders Details 49:21
Mod-01 Lec-08 Syndrome Decoder, Basics of Finite Fields Details 1:15:25
Mod-01 Lec-09 Construction of Finite Fields Details 1:15:21
Mod-01 Lec-10 Computations in Finite Fields Details 51:20
Mod-01 Lec-11 Codes over Finite Fields, Minimal Polynomials Details 1:15:22
Mod-01 Lec-12 BCH Codes Details 1:14:52
Mod-01 Lec-13 BCH and RS Codes I Details 1:14:29
Mod-01 Lec-14 BCH and RS Codes II Details 51:54
Mod-01 Lec-15 Decoding BCH Codes Details 1:12:45
Mod-01 Lec-16 Decoding RS Codes Details 49:28
Mod-01 Lec-17 Coded Modulation and Soft Decision Decoding Details 1:12:34
Mod-01 Lec-18 Optimal Decoders for BPSK over AWGN Details 49:40
Mod-01 Lec-19 Bitwise MAP Decoder for BPSK over AWGN Details 1:14:32
Mod-01 Lec-20 Bitwise MAP Decoder from the Dual Code Details 1:14:2
Mod-01 Lec-21 Simulating Coded Modulation Details 49:40
Mod-01 Lec-22 Union Bound, Introduction to LDPC Codes Details 1:15
Mod-01 Lec-23 LDPC Codes Details 1:13:12
Mod-01 Lec-24 Message Passing, Density Evolution Analysis Details 51:23
Mod-01 Lec-25 Thresholds of LDPC Codes Details 1:14:29
Mod-01 Lec-26 Irregular LDPC Codes Details 52:26
Mod-01 Lec-27 Optimized Irregular LDPC Codes, Soft Message Passing Decoders Details 50:10
Mod-01 Lec-28 Density Evolution for Soft Message Passing Decoding of LDPC Codes Details 52:24
Mod-01 Lec-29 LDPC Codes in Practice Details 50:40
Mod-01 Lec-30 Introduction to Convolutional Codes Details 50:59
Mod-01 Lec-31 Viterbi Decoding of Convolutional Codes Details 50:9
Mod-01 Lec-32 Union Bound, Recursive Convolutional Encoders Details 51:52
Mod-01 Lec-33 Convolutional Codes in Practice Details 51:27
Mod-01 Lec-34 BCJR Decoder Details 49:36
Mod-01 Lec-35 BCJR and Max-Log-MAP Decoder, Introduction to Turbo Codes Details 50:15
Mod-01 Lec-36 Turbo Decoder Details 48:52
Mod-01 Lec-37 Turbo Codes in Practice Details 52:20
Mod-01 Lec-38 Modern Codes Details 49:33

This course is part of NPTEL online courses, delivered by IIT Madras.

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