error correction.md

Error Correction

• Repetition Code

  • Turns a 1-bit message into a 3-bit codeword.

• Hamming Codes

  • Takes 4 bits and turns it into 7 bits codeword.
  • Parity bit - 1 in 16 to detect change
  • (15, 11) Hamming code
  • Extended hamming code checks for parity bit as well
  • Get only the position of the bits containing 1, xor them, and get error index.

• Reed Solomon Codes

  • Special case of BCH codes

• Turbo Codes

Erasure Code

Galois Field

• Equation is solvable by radicals if there is a simple way of finding its root. Like equations.
• The coefficients are rational numbers. Rational numbers form a field, means arithmetic operations generate another rational number.

Reference

• Reed Solomon Code