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Error Correcting Codes

Error Correcting Codes. Instructor: Prof. P. Vijay Kumar, Department of Electrical Communication Engineering, IISc Bangalore. Error-correcting codes are in widespread use for data storage as well as most forms of communication where reliability is of importance. Examples range from compact discs to deep-space communication. This course will cover both classical error-correcting codes such as BCH, Reed-Solomon and convolutional codes as well as the more modern class of iteratively decodable codes, low-density parity-check codes in particular. (from nptel.ac.in)

Lecture 22 - The MPF (Marginalize the Product Function) Problem


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Basics of Block Codes
Lecture 01 - Course Overview and Basics
Lecture 02 - Example Codes and their Parameters
Mathematical Preliminaries: Groups, Rings and Fields
Lecture 03 - Mathematical Preliminaries: Groups
Lecture 04 - Subgroups and Equivalence Relations
Lecture 05 - Cosets, Rings and Fields
Vector Spaces
Lecture 06 - Vector Spaces, Linear Independence and Basis
Lecture 07 - Linear codes and Linear Independence
Lecture 08 - Spanning and Basis
Linear Codes
Lecture 09 - The Dual Code
Lecture 10 - Systematic Generator Matrix
Lecture 11 - Minimum Distance of Linear Code
Bounds on the Size of a Code
Lecture 12 - Bounds on the Size of a Code
Lecture 13 - Asymptotic Bounds
Standard Array Decoding
Lecture 14 - Standard Array Decoding
Lecture 15 - Performance Analyses of the Standard Array Decoding
Convolution Codes
Lecture 16 - State and Trellis
Lecture 17 - The Viterbi Decoder
Lecture 18 - Catastrophic Error Propagation
Lecture 19 - Path Enumeration
Lecture 20 - Viterbi Decoder over the AWGN Channel
The Generalized Distributive Law
Lecture 21 - The Generalized Distributive Law
Lecture 22 - The MPF (Marginalize the Product Function) Problem
Lecture 23 - Further Examples of the MPF Problem
Lecture 24 - Junction Trees Recap
Lecture 25 - Example of Junction Tree Construction
Lecture 26 - Message Passing on the Junction Tree
Lecture 27 - GDL Approach to Decoding Convolutional Codes
Lecture 28 - ML-Code Symbol Decoding of the Convolutional Code
Low-Density Parity-Check (LDPC) Codes
Lecture 29 - LDPC Codes
Lecture 30 - LDPC Code Terminology
Lecture 31 - Gallagher Decoding Algorithm A
Lecture 32 - Gallagher Decoding Algorithm A (cont.)
Lecture 33 - Belief-Propagation (BP) Decoding of LDPC Codes
Lecture 34 - Density Evolution under BP Decoding
Lecture 35 - Convergence and Concentration Theorem - LDPC Codes
Finite Fields
Lecture 36 - A Construction for Finite Fields
Lecture 37 - Finite Fields: A Deductive Approach
Lecture 38 - Deductive Approach to Finite Fields
Lecture 39 - Subfields of a Finite Field
Cyclic Codes
Lecture 40 - Transform Approach to Cyclic Codes
Lecture 41 - Estimating the Parameters of a Cyclic Code
Lecture 42 - Decoding Cyclic codes