Course Details

Course details of EE5160
Course NoEE5160
Course TitleError Control Coding
Course Content1. Mathematical Preliminaries: Groups, rings, fields, vector spaces, linear algebra review, Finite fields: construction, structure of fields, polynomials over finite fields, minimal polynomials, factorization of polynomials 2. Linear block codes: Generator and parity check matrices, dual code, distance of a code.Decoding linear codes: MAP decoder, ML decoder, standard array and syndrome decoding, bounded distance decoder.Bounds on codes: Singleton, Hamming, Plotkin, Gilbert-Varshamov bounds and asymptotic bounds, Weight enumerators, MacWilliams relation for binary block codes, Code constructions: puncturing, extending, shortening, direct sum, product construction, interleaving, concatenation, Performance of block codes 3. Important algebraic block codes: Cyclic codes, BCH codes, Reed-Solomon codes, Reed-Muller codes and Hamming codes, Berlekamp-Massey algorithm for decoding BCH and Reed-Solomon codes 4. Convolutional codes, Various formulations of convolutional codes using shift registers, generator sequences, polynomials, and matrices, recursive and non recursive encoders, Code parameters: constraint length, memory, free distance, Structural properties of convolutional codes: state diagram, trellis diagram, non-catastrophic encoders, weight enumerators, Decoding convolutional codes: Viterbi and BCJR algorithms, hard decision and soft decision decoding, Performance of convolutional codes 5. Capacity achieving codes: LDPC codes: Tanner graphs, Low density parity check (LDPC) codes, iterative decoding, bit flipping and sum product algorithmsIntroduction to turbo codes
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