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Electronics & Communication Engineering

Electronics & Communication

Error Correcting Codes

Error Correcting Codes

01 Course Overview & Basics

02 Example Codes and their Parameters

03 Mathematical Preliminaries Groups

04 Subgroups and Equivalence Relations

05 Cosets, Rings & Fields

06 Vector Spaces, Linear Independence and Basis

07 Linear Codes, & Linear independence

08 Spanning & Basis

09 The Dual Code

10 Systematic Generator Matrix

11 Minimum Distance of a Linear Code

12 Bounds on the size of a Code

13 Asymptotic Bounds

14 Standard Array Decoding

15 Performance Analysis of the SAD

16 State and Trellis

17 The Viterbi Decoder

18 Catastrophic Error Propagation

19 Path Enumeration

20 Viterbi Decoder over the AWGN Channel

21 Generalized Distributive Law

22 The MPF Problem

23 Further Examples of the MPF Problem

24 Junction Trees

25 Example of Junction Tree Construction

26 Message passing on the Junction tree

27 GDL Approach to Decoding Convolutional Codes

28 ML Code-Symbol Decoding of the Convolutional Code

30 LDPC Code Terminology

31 Gallager Decoding Algorithm A

32 BP Decoding of LDPC Codes

33 BP Decoding (Continued)

34 Density Evolution under BP decoding

35 Convergence & Concentration Theorem � LDPC Codes

36 A Construction for Finite Fields

37 Finite Fields A Deductive Approach

38 Deductive Approach to Finite Fields

39 Subfields of a Finite field

40 Transform Approach to Cyclic Codes

41 Estimating the Parameters of a Cyclic Code

42 Decoding Cyclic Codes

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