Error correction code

Forward error correction (FEC) is a technique used to control errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code (ECC), which allows the receiver to detect and correct a limited number of errors without needing a reverse channel for re-transmission. This method is particularly useful in situations where re-transmissions are costly or impossible, such as one-way communication links or when transmitting to multiple receivers in multicast.

The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code. FEC can be applied in situations where re-transmissions are costly or impossible, such as one-way communication links or when transmitting to multiple receivers in multicast. Long-latency connections also benefit; in the case of satellites orbiting distant planets, retransmission due to errors would create a delay of several hours. FEC is also widely used in modems and in cellular networks.

Turbo codes are a type of FEC that achieves near-Shannon-limit error correction with iterative decoding. This means that turbo codes can correct errors very close to the theoretical maximum limit for error correction, as defined by Shannon's theorem. The iterative decoding process used by turbo codes allows for continuous improvement in error correction, making them highly effective for reliable data transmission in various communication scenarios.