Topical Outline:
Introduction to Linear Block Codes
-Linear Vector spaces
-Generator and parity check matrices
-Syndrome decoding, standard arrays
Finite field fundamentals
-Groups, fields, rings, elementary Galois fields
-Irreducible, minimal and primitive polynomials
-Extension fields
-Conjugacy classes, minimal polynomials, factorization of
-Ideals and generator polynomials
General Cyclic codes
-General theory of linear cyclic codes
-Shift register encoders and decoders
BCH and Reed-Solomon codes
-Generator polynomial approach to encoding BCH codes
-The BCH bound
-Basic properties of Reed Solomon Codes
-Decoding BCH codes: Peterson's algorithm
-Decoding BCH codes: Berlekamp's algorithm
-Decoding RS codes: Berlekamp-Massey algorithm
-Decoding RS codes: Euclid's algorithm
Convolutional Codes
-Shift register encoding
-Viterbi decoding
Serial Concatenated Codes
Parallel Concatenated Codes
-Parallel Concatenation Encoder
-Interleaving
-MAP Decoding, SOVA
-Turbo Decoding
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