Error Correction Code (ECC) Algorithm
An Error Correction Code (ECC) Algorithm is an data encoding scheme that is used for controlling errors in data over unreliable or noisy communication channels.
- Context:
- It can (typically) add Data Redundancya and involve a trade-off between redundancy and the efficiency of data transmission or storage.
- It can range from being an Error Correcting Block Code to being an Error Correcting Convolutional Code.
- It can ensure Data Integrity in digital communication and storage.
- It can be implemented an an ECC-based System either a hardware and software solutions.
- …
- Example(s):
- Counter-Example(s):
- Text Error Correction (TEC) System,
- Neural-based Text Error Correction (TEC) System,
- Checksum method used for simple error detection, not correction.
- See: Code Design System, Claude Shannon, Computing, Telecommunication, Information Theory, Coding Theory, Error Control, Communication Channel, Cirrus Logic, Bell System Technical Journal, AT&T, Redundancy (Information Theory), Richard Hamming.
References
2024
- (GPT-4, 2024) ⇒ GPT-4. (2024). “Comprehensive Guide to Error Correction Codes (ECC)." [Knowledge Source].
- QUOTE: Purpose: ECCs are techniques used to detect and correct errors that occur during data transmission or storage. They ensure data integrity even when faced with interference, noise, or physical imperfections in storage media.
2020a
- (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Error_correction_code Retrieved:2020-10-25.
- In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. [1] The central idea is the sender encodes the message with redundant information in the form of an ECC. The redundancy allows the receiver to detect a limited number of errors that may occur anywhere in the message, and often to correct these errors without retransmission. 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.
ECC contrasts with error detection in that errors that are encountered can be corrected, not simply detected. The advantage is that a system using ECC does not require a reverse channel to request retransmission of data when an error occurs. The downside is that there is a fixed overhead that is added to the message, thereby requiring a higher forward-channel bandwidth. ECC is therefore applied in situations where retransmissions are costly or impossible, such as one-way communication links and when transmitting to multiple receivers in multicast. Long-latency connections also benefit; in the case of a satellite orbiting around Uranus, retransmission due to errors can create a delay of five hours. ECC information is usually added to mass storage devices to enable recovery of corrupted data, is widely used in modems, and is used on systems where the primary memory is ECC memory.
ECC processing in a receiver may be applied to a digital bitstream or in the demodulation of a digitally modulated carrier. For the latter, ECC is an integral part of the initial analog-to-digital conversion in the receiver. The Viterbi decoder implements a soft-decision algorithm to demodulate digital data from an analog signal corrupted by noise. Many ECC encoders/decoders can also generate a bit-error rate (BER) signal, which can be used as feedback to fine-tune the analog receiving electronics.
The maximum fractions of errors or of missing bits that can be corrected is determined by the design of the ECC code, so different error correcting codes are suitable for different conditions. In general, a stronger code induces more redundancy that needs to be transmitted using the available bandwidth, which reduces the effective bit-rate while improving the received effective signal-to-noise ratio. The noisy-channel coding theorem of Claude Shannon answers the question of how much bandwidth is left for data communication while using the most efficient code that turns the decoding error probability to zero. This establishes bounds on the theoretical maximum information transfer rate of a channel with some given base noise level. However, the proof is not constructive, and hence gives no insight of how to build a capacity achieving code. After years of research, some advanced ECC systems nowadays come very close to the theoretical maximum.
- In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. [1] The central idea is the sender encodes the message with redundant information in the form of an ECC. The redundancy allows the receiver to detect a limited number of errors that may occur anywhere in the message, and often to correct these errors without retransmission. 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.
- ↑ Hamming, R. W. (April 1950). “Error Detecting and Error Correcting Codes". Bell System Technical Journal. USA: AT&T. 29 (2): 147–160. doi:10.1002/j.1538-7305.1950.tb00463.x
2020b
- (Brillant, 2020) ⇒ https://brilliant.org/wiki/error-correcting-codes/ Retrieved:2020-10-25
- QUOTE: An error correcting code (ECC) is an encoding scheme that transmits messages as binary numbers, in such a way that the message can be recovered even if some bits are erroneously flipped. They are used in practically all cases of message transmission, especially in data storage where ECCs defend against data corruption.