Learn · Error Correcting Codes
Lecture 10 of 42Linear Codes
Systematic Generator Matrix
Prof. P. Vijay Kumar · IISc Bangalore
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- Error Correcting Codes, IISc Bangalore (at NPTEL)
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All the lectures
- Course Overview & Basics
- Example Codes and their Parameters
- Mathematical Preliminaries: Groups
- Subgroups and Equivalence Relations
- Cosets, Rings & Fields
- Vector Spaces, Linear Independence and Basis
- 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
- 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 (Continued)
- 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