# InfoCoBuild

## 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)

 Course Overview and Basics

 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

 References Error Correcting Codes Instructor: Prof. P. Vijay Kumar, Department of Electrical Communication Engineering, IISc Bangalore. This course will cover classical error-correcting codes and the more modern class of iteratively decodable codes.