Korreksjonskoder

Korreksjonskoder, also known as error-correcting codes, are methods used to detect and correct errors that may occur during data transmission or storage. These errors can arise from various sources, such as noise in communication channels or physical defects in storage media. The fundamental principle behind correction codes is the deliberate addition of redundancy to the original data. This redundancy is structured in such a way that if some bits of the transmitted or stored data are corrupted, the original information can still be reconstructed.

There are two main categories of error correction codes: forward error correction (FEC) and automatic repeat request (ARQ). FEC codes add redundant information to the data before transmission. The receiver can then use this redundancy to detect and correct errors without needing to retransmit the data. ARQ systems, on the other hand, rely on feedback from the receiver to the sender. If the receiver detects an error, it requests the sender to retransmit the corrupted data.

Common examples of error correction codes include Hamming codes, Reed-Solomon codes, and Low-Density Parity-Check (LDPC) codes. Hamming codes are relatively simple and are often used for detecting and correcting single-bit errors. Reed-Solomon codes are more powerful and are widely used in applications like CD/DVDs and digital television broadcasting to handle burst errors, where multiple consecutive bits are corrupted. LDPC codes are known for their excellent performance, approaching the theoretical limits of data transmission, and are used in modern communication systems like Wi-Fi and 5G. The design of an effective correction code involves a trade-off between the amount of redundancy added and the code's ability to correct errors.