Paritycheckalgoritmer

Paritycheckalgoritmer are techniques used to detect and, in some cases, correct errors in digital data by using parity information. The core idea is to append parity bits to data words so that the total number of 1s satisfies a chosen parity (even or odd). When data are read or transmitted, the parity is recomputed and compared to the stored parity, revealing discrepancies that indicate errors.

A simple parity check adds a single parity bit per data word. It can detect any odd number of bit flips but cannot detect even numbers of errors or locate the erroneous bit, and it provides no correction.

Two-dimensional parity extends this idea by adding parity bits for both rows and columns in a block of data. This arrangement improves error localization and can identify the position of a single-bit error, while still detecting many multi-bit errors.

Hamming codes are a family of parity-based error-correcting codes that arrange parity bits at specific positions so that a single-bit error changes a unique syndrome, enabling both detection and correction of that error. An extended Hamming code adds an overall parity bit to improve detection of certain error patterns, including some double-bit errors.

In practice, parity-check matrices are used in more formal block codes. For data transmission and storage, the syndrome s = Hx^T is computed from the received word x; a nonzero syndrome indicates an error, and its value points to a likely error pattern.

Applications include memory error correction (ECC RAM), RAID implementations that use parity for recovery, and various communication protocols. Limitations include inability to correct multiple simultaneous errors reliably and the overhead required for additional parity bits, which reduces usable capacity. More advanced codes such as CRCs and Reed-Solomon offer stronger detection and correction capabilities beyond simple parity-based methods.