Course Overview & Basics – Example Codes and their Parameters – Mathematical Preliminaries: Groups – Subgroups and Equivalence Relations – Cosets, Rings & Fields – Vector Spaces, Linear – Linear Codes, & Linear independence – Spanning & Basis – The Dual Code – Systematic Generator Matrix – Minimum Distance of a Linear Code – Bounds on the size of a Code – Asymptotic Bounds – Standard Array Decoding – Performance Analysis of the SAD – State and Trellis – The Viterbi Decoder – Catastrophic Error Propagation – Path Enumeration – Viterbi Decoder over the AWGN Channel – Generalized Distributive Law – The MPF Problem – Further Examples of the MPF Problem – Junction Trees recap – Example of Junction Tree Construction

Message passing on the Junction tree – GDL Approach to Decoding Convolutional Codes – ML Code-Symbol Decoding of the Convolutional Code – LDPC Codes – LDPC Code Terminology – Gallager Decoding Algorithm A – BP Decoding of LDPC Codes – BP Decoding – Density Evolution under BP decoding – Convergence & Concentration Theorem — LDPC Codes – A Construction for Finite Fields – Finite Fields: A Deductive Approach – Deductive Approach to Finite Fields – Subfields of a Finite field – Transform Approach to Cyclic Codes – Estimating the Parameters of a Cyclic Code – Decoding Cyclic Codes

Other Resources

Course Curriculum

Course Overview & Basics Details 53:26
Example Codes and their Parameters Details 57:39
Mathematical Preliminaries: Groups Details 55:19
Subgroups and Equivalence Relations Details 59:24
Cosets, Rings & Fields Details 58:50
Vector Spaces, Linear Details 57:19
Linear Codes, & Linear independence Details 55:29
Spanning & Basis Details 56:17
The Dual Code Details 0:57
Systematic Generator Matrix Details 59:56
Minimum Distance of a Linear Code Details 55:23
Bounds on the size of a Code Details 55:59
Asymptotic Bounds Details 54:53
Standard Array Decoding Details 55:29
Performance Analysis of the SAD Details 57:6
State and Trellis Details 56:15
The Viterbi Decoder Details 57:2
Catastrophic Error Propagation Details 56:48
Path Enumeration Details 57:31
Viterbi Decoder over the AWGN Channel Details 56:41
Generalized Distributive Law Details 57:5
The MPF Problem Details 58:14
Further Examples of the MPF Problem Details 57:43
Junction Trees recap Details 58:11
Example of Junction Tree Construction Details 56:14
Message passing on the Junction tree Details 54:36
GDL Approach to Decoding Convolutional Codes Details 56:34
ML Code-Symbol Decoding of the Convolutional Code Details 56:4
LDPC Codes Details 56:11
LDPC Code Terminology I Details 56:10
Gallager Decoding Algorithm A Details 57:21
BP Decoding of LDPC Codes Details 54:58
BP Decoding I Details 56:34
Density Evolution under BP decoding Details 57:4
Convergence & Concentration Theorem — LDPC Codes Details 56:54
A Construction for Finite Fields Details 57:1
Finite Fields: A Deductive Approach Details 56:33
Deductive Approach to Finite Fields Details 56:47
Subfields of a Finite field Details 57:28
Transform Approach to Cyclic Codes Details 56:56
Estimating the Parameters of a Cyclic Code Details 57:56
Decoding Cyclic Codes Details 53:56

This Course is provided by IISc Bangalore as part of NPTEL online courses.

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