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