To provide an introduction to traditional and modern coding theory. Topics covered include linear block codes, cyclic codes (BCH and RS codes), convolutional codes, turbo codes and low-density parity-check (LDPC) codes.
Part I: Basics and Algebraic Codes.
Linear Block Codes: Generator and parity-check matrices, Minimum Distance, Sydrome decoding, Bounds on minimum distance.
Cyclic Codes: Finite fields, Binary BCH codes, RS codes.
Part II: Coding in digital communications.
AWGN channel: BPSK modulation, Capacity, Coding gain, ML and MAP decoders, Soft-versus hard-decision decoding.
Convolutional Codes: Encoders, Trellis, Viterbi decoding.
Part III: Modern iterative coding.
Turbo codes: Encoders, interleavers, turbo decoder.
Low-density Parity-check Codes: Ensembles of LDPC codes, Message-passing decoders, Threshold phenomenon and density evolution.
Linear Block Codes
Introduction to Coding Theory, Linear Block Codes, Generator Matrices.
Linear Block Codes, Parity check matrices, Vector space view of codes, Dual codes.
Dual Codes, Self-orthogonal and Self-Dual codes, Examples of dual codes, Relation between parity-check matrix and dual code.
Minimum Distance Decoder, Hamming Distance, Error Correcting Capability of codes, Geometric View of Decoding.
Syndrome Decoder, Relationship between Minimum distance and Parity-Check Matrix.
Construction of Codes with d=3, Hamming Codes, Extending codes, Puncturing Codes.