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Error Detection and Correction

* Errors can be categorized as a single-bit error or a burst error. A single-bit error has one bit error per data unit. A burst error has two or more bit errors per data unit.
* Redundancy is the concept of sending extra bits for use in error detection.
* Three common redundancy methods are parity check, cyclic redundancy check (CRC), and checksum.
* An extra bit (parity bit) is added to the data unit in the parity check.
* The parity check can detect only an odd number of errors; it cannot detect an even number of errors.
* In the two-dimensional parity check, a redundant data unit follows n data units.
* CRC, a powerful redundancy checking technique, appends a sequence of redundant bits derived from binary division to the data unit.
* The divisor in the CRC generator is often represented as an algebraic poly-nomial.
* Errors are corrected through retransmission and by forward error correction.
* The Hamming code is an error correction method using redundant bits. The number of bits is a function of the length of the data bits.
* In the Hamming code, for a data unit of m bits, use the formula 2 r >= m +r +1 to determine r, the number of redundant bits needed.
* By rearranging the order of bit transmission of the data units, the Hamming code can correct burst errors.