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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 06 - Vector Spaces, Linear Independence and Basis

Go to the Course Home or watch other lectures:

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