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Last updated:

September 25, 2023

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Description

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 Curriculum

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

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