The Theory of Error Correcting Codes.

The same sort of theory can be extended to create error-correcting codes based on CRC computations.

Error correction | The Language Gym

For example, if an error occurs on a CD then the electronics corrects it in real time so that the data flow is uninterrupted. All this means that real codes have to be simple and regular.

Energy requirements of error correction codes in …

Of course this isn’t how error detecting/correcting codes are implemented in practice! It is the theory but making it work turns out to be much more difficult.

What we really want our codes to do is protect against burst errors of m bits in a row rather than m bits anywhere in the word. Such burst error correcting codes are more efficient but how to create them is a difficult problem.

Error Detecting and Correcting Codes ..

These were the first family of asymptotically good codes for which there existed a linear-time decoding algorithm that could correct a constant fraction of error.

A Commonsense Approach to the Theory of Error-Correcting Codes

In, (FCT '97/LNCS #1279), wesurvey some key developments in the complexity of error-correctingcodes and show how to construct linear-time encodable and decodableerror-correcting codes that approach the Shannon bound.

The Error Correcting Codes (ECC) Page - CNR

Error correction codes are a way to represent a set of symbols sothat if any 1 bit of the representation is accidentally flipped, youcan still tell which symbol it was.

The Error Correcting Codes (ECC) Page ..

Systems capable of requesting the retransmission of bad messages in response to error detection include an automatic request for retransmission, or automatic repeat request (ARQ) processing, in their communication software package. They use acknowledgments, negative acknowledgment messages and timeouts to achieve better data transmission.

ARQ is an error control (error correction) method that uses error-detection codes and positive and negative acknowledgments. When the transmitter either receives a negative acknowledgment or a timeout happens before acknowledgment is received, the ARQ makes the transmitter resend the message.

Error-correcting code (ECC) or forward error correction (FEC) is a method that involves adding parity data bits to the message. These parity bits will be read by the receiver to determine whether an error happened during transmission or storage. In this case, the receiver checks and corrects errors when they occur. It does not ask the transmitter to resend the frame or message.

A hybrid method that combines both ARQ and FEC functionality is also used for error correction. In this case, the receiver asks for retransmission only if the parity data bits are not enough for successful error detection and correction.