Bit Error Correction Code
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Single Bit Error Correction Code
In information theory and coding theory with applications in computer science hamming code single bit error correction and telecommunication, error detection and correction or error control are techniques that enable reliable delivery of parity bit error correction digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a
2 Bit Error Correction
receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Contents 1 Definitions 2 History 3 Introduction 4 Implementation 5 Error detection schemes 5.1 Repetition codes 5.2 Parity bits 5.3 Checksums 5.4 Cyclic redundancy checks (CRCs) 5.5 Cryptographic hash functions 5.6 Error-correcting codes 6 Error
One Bit Error Correction
correction 6.1 Automatic repeat request (ARQ) 6.2 Error-correcting code 6.3 Hybrid schemes 7 Applications 7.1 Internet 7.2 Deep-space telecommunications 7.3 Satellite broadcasting (DVB) 7.4 Data storage 7.5 Error-correcting memory 8 See also 9 References 10 Further reading 11 External links Definitions[edit] The general definitions of the terms are as follows: Error detection is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. Error correction is the detection of errors and reconstruction of the original, error-free data. History[edit] The modern development of error-correcting codes in 1947 is due to Richard W. Hamming.[1] A description of Hamming's code appeared in Claude Shannon's A Mathematical Theory of Communication[2] and was quickly generalized by Marcel J. E. Golay.[3] Introduction[edit] The general idea for achieving error detection and correction is to add some redundancy (i.e., some extra data) to a message, which receivers can use to check consistency of the delivered message, and to recover data determined to
computer data storage that can detect and correct the most common kinds of internal data corruption. ECC memory is used in most computers where data corruption cannot be tolerated under any circumstances, such as for scientific or multiple bit error correction financial computing. Typically, ECC memory maintains a memory system immune to single-bit errors: the data
Error Correction Code Example
that is read from each word is always the same as the data that had been written to it, even if one error correction code flash memory or more bits actually stored have been flipped to the wrong state. Most non-ECC memory cannot detect errors although some non-ECC memory with parity support allows detection but not correction. Contents 1 Problem background 2 Solutions 3 https://en.wikipedia.org/wiki/Error_detection_and_correction Implementations 4 Cache 5 Registered memory 6 Advantages and disadvantages 7 References 8 External links Problem background[edit] Electrical or magnetic interference inside a computer system can cause a single bit of dynamic random-access memory (DRAM) to spontaneously flip to the opposite state. It was initially thought that this was mainly due to alpha particles emitted by contaminants in chip packaging material, but research has shown that the majority of one-off soft errors in DRAM chips https://en.wikipedia.org/wiki/ECC_memory occur as a result of background radiation, chiefly neutrons from cosmic ray secondaries, which may change the contents of one or more memory cells or interfere with the circuitry used to read or write to them.[2] Hence, the error rates increase rapidly with rising altitude; for example, compared to the sea level, the rate of neutron flux is 3.5 times higher at 1.5km and 300 times higher at 10–12km (the cruising altitude of commercial airplanes).[3] As a result, systems operating at high altitudes require special provision for reliability. As an example, the spacecraft Cassini–Huygens, launched in 1997, contains two identical flight recorders, each with 2.5gigabits of memory in the form of arrays of commercial DRAM chips. Thanks to built-in EDAC functionality, spacecraft's engineering telemetry reports the number of (correctable) single-bit-per-word errors and (uncorrectable) double-bit-per-word errors. During the first 2.5years of flight, the spacecraft reported a nearly constant single-bit error rate of about 280errors per day. However, on November 6, 1997, during the first month in space, the number of errors increased by more than a factor of four for that single day. This was attributed to a solar particle event that had been detected by the satellite GOES 9.[4] There was some concern that as DRAM density increases further, and thus the components on chips get smaller, while at the same
tour help Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings http://electronics.stackexchange.com/questions/71410/single-bit-error-correction-double-bit-error-detection and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Electrical Engineering Questions Tags Users Badges Unanswered Ask Question _ Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. Join them; it only takes a error correction minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Single Bit Error Correction & Double Bit Error Detection up vote 1 down vote favorite Can someone explain, in their own words, what Double Bit Error Detection is and how to derive it? An example bit error correction of corrupted data and how to detect the double bit would be appreciated. I can do Single Bit Error Correction using parity bits as well as correct the flipped bit. Now when I reach Double Bit Error Detection I understand there is an extra DED bit, which is somehow related to the even or odd parity of the bit sequence. However, I am lost. What I read: http://en.wikipedia.org/wiki/Error_detection_and_correction Video on Hamming Code: http://www.youtube.com/watch?v=JAMLuxdHH8o error-correction parity share|improve this question asked Jun 2 '13 at 20:49 Mike John 117126 Do you understand Hamming distance en.wikipedia.org/wiki/Hamming_distance - it might be worth reading if you don't. Basically in error detection/correction algorithms you add "redundant" bits to your data so that data+redundancy has a hamming distance of at least 4 - this allows one error to make the D+R correctable AND two errors make D+R detectable. 3 errors means you think you can correct but erroneously correct it to a wrong number. Does this make any sense? –Andy aka Jun 2 '13 at 21:47 That much I get. However, provi