Error Correcting Codes
IISc Bangalore, , Prof. P. Vijay Kumar
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Updated On 02 Feb, 19
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
4.1 ( 11 )
Deducing the structure of a finite field; Subfields and cyclotomic cosets.
Sep 12, 2018
Excellent course helped me understand topic that i couldn't while attendinfg my college.
March 29, 2019
Great course. Thank you very much.