User:Rogério Brito/Books/Topics in Error Correcting Codes

Topics in Error Correcting Codes

 * Introduction
 * Forward error correction
 * Hamming bound


 * A Small Amount of Information Theory
 * Binary symmetric channel
 * Channel capacity
 * Noisy-channel coding theorem
 * Shannon's source coding theorem
 * Shannon–Hartley theorem
 * Mutual information


 * Preliminary Concepts
 * Block code
 * Repetition code
 * Linear code
 * Parity bit
 * Parity-check matrix
 * Generator matrix
 * Dual code
 * Hamming(7,4)
 * Decoding methods


 * List of Important Codes
 * Hamming code
 * Binary Golay code
 * Ternary Golay code
 * Cyclic code
 * BCH code
 * Polynomial code
 * Hadamard code
 * Quadratic residue code
 * Goppa code
 * Space–time code
 * Bar product (coding theory)
 * Reed–Muller code
 * Reed–Solomon error correction
 * Convolutional code
 * Turbo code
 * Low-density parity-check code


 * Important Bounds on Codes
 * Hamming bound
 * Singleton bound
 * Gilbert-Varshamov bound
 * Plotkin bound
 * Griesmer bound
 * Johnson bound


 * Applications and Related Concepts
 * Linear feedback shift register
 * RAID
 * Standard RAID levels
 * Berlekamp's algorithm
 * Berlekamp–Massey algorithm
 * Vandermonde matrix
 * Finite field
 * Finite field arithmetic