Introduction to Error Correcting Codes
Michael Purser · Medical Entomology and Zoology · 1994
Part 1 Introduction: bit strings and codes codes and error correction erasures and soft decision decoding hamming distance and sphere-packing Shannon's theorem. Part 2 Linear codes: matrix representation the standard array the null-matrix or parity-check matrix the syndrome the columns of the null matrix perfect codes further bounds on linear codes the Varsharmov-Gilbert bound the Plorkin bound bounds in practice nonbinary linear codes nonbinary codes with characteristic 2. Part 3 Cyclic codes: the generating polynomial systematic cyclic codes the roots of g(x) and the null-matrix error detection with cycle codes weight distribution shortened cyclic codes and feedback shift registers error correction with cyclic codes nonbinary cyclic codes. Part 4 BCH codes: minimum polynomials the roots of BCH codes some examples of BCH codes error correction of binary BCH codes practical procedures for solving the equations an example of BCH error correction error correction of nonbinary BCH codes Reed Solomon (RS) codes a worked RS example an example of practical use of RS codes other aspects of RS codes. Part 5 Convolutional codes: tree and trellis codes the Viterbi algorithm linear convolutional codes control of decoding errors.