2 Error Correction
Contents |
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 2 bit error correction cannot be tolerated under any circumstances, such as for scientific or financial
Bonferroni Correction Type 2 Error
computing. Typically, ECC memory maintains a memory system immune to single-bit errors: the data that is read from each
Forward Error
word is always the same as the data that had been written to it, even if one or more bits actually stored have been flipped to the wrong state. Most non-ECC
Error Correction Code
memory cannot detect errors although some non-ECC memory with parity support allows detection but not correction. Contents 1 Problem background 2 Solutions 3 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 error correction and detection 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 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
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Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» 13,594 entries Last updated: Tue Sep 27 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Discrete Mathematics>Coding Theory> Interactive Entries>Interactive Demonstrations> Error-Correcting Code An error-correcting code is an algorithm http://mathworld.wolfram.com/Error-CorrectingCode.html for expressing a sequence of numbers such that any errors which are introduced can be detected and corrected (within certain limitations) based on the remaining numbers. The study of error-correcting codes and the associated mathematics is known as coding theory. Error detection is much simpler than error correction, and one or more "check" digits are commonly embedded in credit card numbers in order to detect mistakes. Early space probes like Mariner used a type of error-correcting code error correction called a block code, and more recent space probes use convolution codes. Error-correcting codes are also used in CD players, high speed modems, and cellular phones. Modems use error detection when they compute checksums, which are sums of the digits in a given transmission modulo some number. The ISBN used to identify books also incorporates a check digit. A powerful check for 13 digit numbers consists of the following. Write the number as a string of digits . error detection and Take and double. Now add the number of digits in odd positions which are to this number. Now add . The check number is then the number required to bring the last digit to 0. This scheme detects all single digit errors and all transpositions of adjacent digits except 0 and 9. Let denote the maximal number of (0,1)-vectors having the property that any two of the set differ in at least places. The corresponding vectors can correct errors. is the number of s with precisely 1s (Sloane and Plouffe 1995). Since it is not possible for -vectors to differ in places and since -vectors which differ in all places partition into disparate sets of two, (1) Values of can be found by labeling the (0,1)--vectors, finding all unordered pairs of -vectors which differ from each other in at least places, forming a graph from these unordered pairs, and then finding the clique number of this graph. Unfortunately, finding the size of a clique for a given graph is an NP-complete problem. Sloane1A0000792, 4, 8, 16, 32, 64, 128, ...21, 2, 4, 8, ...31, 1, 2, 2, ...4A0058641, 1, 1, 2, 4, 8, 16, 20, 40, ...51, 1, 1, 1, 2, ...6A0058651, 1, 1, 1, 1, 2, 2, 2, 4, 6, 12, ...71, 1, 1, 1, 1, 1, 2, ...8A0058661, 1, 1, 1, 1, 1, 1, 2, 2, 2,