Ecc 2 bit error correction

ECC memory

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Error-correcting code memory ECC memory is a type of 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 financial computing. Typically, ECC memory maintains a memory system immune to single-bit errors: Most non-ECC memory cannot detect errors although some non-ECC memory with parity support allows detection but not correction.

Electrical or magnetic interference inside a computer system can cause a single bit of dynamic ecc 2 bit error correction 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 occur as a result of background radiationchiefly 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.

As an example, the spacecraft Cassini—Huygenslaunched incontains two identical flight recorders, each with 2. 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. However, on November 6,during the first month in ecc 2 bit error correction, 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. There was some concern that as DRAM density increases further, and thus the components on chips get smaller, while at the same time operating voltages continue to fall, DRAM chips will be affected by such radiation more frequently—since lower-energy particles will be able to change a memory cell's state.

Recent studies [5] show that single event upsets due to cosmic radiation have been dropping dramatically with process geometry and previous concerns over increasing bit cell error rates are unfounded. The consequence of a memory error is system-dependent. In systems without ECC, an error can lead either to a crash or to corruption of data; in large-scale production sites, memory errors are one of the most common hardware causes of machine crashes. A simulation study showed that, for a web browser, only ecc 2 bit error correction small fraction of memory errors caused data corruption, although, as many memory errors are intermittent and correlated, the effects of memory errors ecc 2 bit error correction greater than would be expected for independent soft errors.

Some tests conclude that the isolation of DRAM memory cells can be circumvented by unintended side effects of specially crafted accesses to adjacent cells. Thus, accessing data stored in DRAM causes memory cell to leak their charges and interact electrically, as a result of high cell density in modern memory, altering the content of nearby memory rows that actually were not addressed in the original memory access.

This effect is known as row hammerand it has also been used in some privilege escalation computer security exploits. An example of a single-bit error that would be ignored by a system with no error-checking, would halt a machine with parity checking, or would be invisibly corrected by ECC: Several approaches have been developed to deal with unwanted bit-flips, including immunity-aware programming ecc 2 bit error correction, RAM parity memory, and ECC memory.

This problem can be mitigated by using DRAM modules that include extra memory bits and memory ecc 2 bit error correction that exploit these bits. These extra bits are used to record parity or to use an error-correcting code Ecc 2 bit error correction.

Parity allows the detection of all single-bit errors actually, any odd number of wrong bits. The most common error correcting code, a single-error correction and double-error detection SECDED Hamming codeecc 2 bit error correction a single-bit error to be corrected and in the usual configuration, with an extra parity bit double-bit errors to be detected.

Chipkill ECC is a more effective version that also corrects for multiple bit errors, including the loss of an entire memory chip.

Seymour Cray famously said " parity is for farmers " when asked why he left this out of the CDC Many current microprocessor memory controllers, including almost all AMD bit offerings, support ECC, but many motherboards and in particular those using low-end chipsets do not. An ECC-capable memory controller can detect and correct errors of a single bit per bit " word " the unit of bus transferand detect but not correct errors of two bits per bit word.

The BIOS in some computers, when matched with operating systems such as some versions of LinuxmacOSand Windows[ citation needed ] allows counting of detected and corrected memory errors, in part to help identify failing memory modules before the problem ecc 2 bit error correction catastrophic. Error detection and correction EDAC depends on an expectation of the kinds of errors that occur. Implicitly, it is assumed that the failure of each bit in a word of memory is independent, resulting in improbability of two simultaneous errors.

This used to be the case when memory chips were one-bit wide, what was typical in the first half of the s; later developments moved many bits into the same chip. DRAM memory may provide increased protection against soft errors by relying on error correcting codes. Such error-correcting ecc 2 bit error correctionknown as ECC or EDAC-protected memory, is particularly desirable for high fault-tolerant applications, such as servers, as well as deep-space applications due to increased radiation.

Some systems also " scrub " the memory, by periodically reading all addresses and writing back corrected versions if necessary to remove soft errors. Interleaving allows for distribution of the effect of a single cosmic ray, potentially upsetting multiple physically neighboring bits across multiple words by associating neighboring bits to different words.

As long as a single event upset SEU does not exceed the error threshold e. Error-correcting memory controllers traditionally use Hamming codesalthough some use triple modular redundancy.

The latter is preferred because its hardware is faster than Hamming error correction hardware. Many early implementations of ECC memory mask correctable errors, acting "as if" the error never occurred, and only report uncorrectable errors. Modern implementations log both correctable errors CE and uncorrectable errors UE. Some people proactively replace memory modules that exhibit high error rates, in order to reduce the likelihood of uncorrectable error events. As ofthe most common error-correction codes use Hamming or Hsiao codes that provide single bit error correction and double bit error detection SEC-DED.

Early research attempted to minimize area and delay in ECC circuits. More recent research also attempts to minimize power in addition to minimizing area and delay. If an error is detected, data is recovered from ECC-protected level 2 cache. Registered, or buffered, memory is not the same as ECC; ecc 2 bit error correction strategies perform different functions. It is usual for memory used in servers to be both registered, to allow many memory modules to be used without electrical problems, and ECC, for data integrity.

Memory used in desktop computers is neither, for economy. Ultimately, there is a trade-off between protection against unusual loss ecc 2 bit error correction data, and a higher cost.

ECC protects against undetected memory data corruption, and is used in computers where such corruption is unacceptable, for example in some scientific and financial computing applications, or in file servers.

ECC also reduces the number of ecc 2 bit error correction, particularly unacceptable in multi-user server applications and maximum-availability systems. Most motherboards and processors for less critical application are not designed to support ECC so their prices can be kept lower. ECC memory usually involves a higher price when compared to non-ECC memory, due to additional hardware required for producing ECC memory modules, and due to lower production volumes of ECC memory and associated system hardware.

Motherboards, chipsets and processors that support ECC may ecc 2 bit error correction be more expensive. ECC may lower memory performance by around 2—3 percent on some systems, depending on application and implementation, due to the additional time needed for ECC memory controllers to perform error checking. From Wikipedia, the free encyclopedia. Retrieved October 20, Swift and Ecc 2 bit error correction M. Lay summary — ZDNet. Archived from ecc 2 bit error correction original on Reliability, Availability, and Serviceability".

Sadler and Daniel J. Primary computer data storage technologies. Delay line memory Selectron tube Williams tube. Bubble memory Drum memory Magnetic-core memory Twistor memory. Retrieved from " https: Computer memory Fault-tolerant computer systems. Webarchive template ecc 2 bit error correction links All articles with dead external links Articles with dead external links from September Articles with permanently dead external links All articles with unsourced statements Articles with unsourced statements from November Articles with unsourced statements from August Articles containing potentially dated statements from All articles containing potentially dated statements.

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In telecommunication , Hamming codes are a family of linear error-correcting codes. Hamming codes can detect up to two-bit errors or correct one-bit errors without detection of uncorrected errors. By contrast, the simple parity code cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are perfect codes , that is, they achieve the highest possible rate for codes with their block length and minimum distance of three.

In his original paper, Hamming elaborated his general idea, but specifically focused on the Hamming 7,4 code which adds three parity bits to four bits of data. In mathematical terms, Hamming codes are a class of binary linear codes. The parity-check matrix of a Hamming code is constructed by listing all columns of length r that are non-zero, which means that the dual code of the Hamming code is the shortened Hadamard code.

The parity-check matrix has the property that any two columns are pairwise linearly independent. Due to the limited redundancy that Hamming codes add to the data, they can only detect and correct errors when the error rate is low. This is the case in computer memory ECC memory , where bit errors are extremely rare and Hamming codes are widely used. In this context, an extended Hamming code having one extra parity bit is often used.

Extended Hamming codes achieve a Hamming distance of four, which allows the decoder to distinguish between when at most one one-bit error occurs and when any two-bit errors occur. Richard Hamming, the inventor of Hamming codes, worked at Bell Labs in the s on the Bell Model V computer, an electromechanical relay-based machine with cycle times in seconds.

Input was fed in on punched paper tape , seven-eighths of an inch wide which had up to six holes per row. During weekdays, when errors in the relays were detected, the machine would stop and flash lights so that the operators could correct the problem. During after-hours periods and on weekends, when there were no operators, the machine simply moved on to the next job. Hamming worked on weekends, and grew increasingly frustrated with having to restart his programs from scratch due to detected errors.

In a taped interview Hamming said, "And so I said, 'Damn it, if the machine can detect an error, why can't it locate the position of the error and correct it? In , he published what is now known as Hamming Code, which remains in use today in applications such as ECC memory. A number of simple error-detecting codes were used before Hamming codes, but none were as effective as Hamming codes in the same overhead of space.

Parity adds a single bit that indicates whether the number of ones bit-positions with values of one in the preceding data was even or odd. If an odd number of bits is changed in transmission, the message will change parity and the error can be detected at this point; however, the bit that changed may have been the parity bit itself.

The most common convention is that a parity value of one indicates that there is an odd number of ones in the data, and a parity value of zero indicates that there is an even number of ones. If the number of bits changed is even, the check bit will be valid and the error will not be detected. Moreover, parity does not indicate which bit contained the error, even when it can detect it.

The data must be discarded entirely and re-transmitted from scratch. On a noisy transmission medium, a successful transmission could take a long time or may never occur. However, while the quality of parity checking is poor, since it uses only a single bit, this method results in the least overhead. A two-out-of-five code is an encoding scheme which uses five bits consisting of exactly three 0s and two 1s. This provides ten possible combinations, enough to represent the digits 0—9.

This scheme can detect all single bit-errors, all odd numbered bit-errors and some even numbered bit-errors for example the flipping of both 1-bits. However it still cannot correct any of these errors. Another code in use at the time repeated every data bit multiple times in order to ensure that it was sent correctly.

If the three bits received are not identical, an error occurred during transmission. If the channel is clean enough, most of the time only one bit will change in each triple. Therefore, , , and each correspond to a 0 bit, while , , and correspond to a 1 bit, with the greater quantity of digits that are the same '0' or a '1' indicating what the data bit should be. Such codes cannot correctly repair all errors, however. In our example, if the channel flips two bits and the receiver gets , the system will detect the error, but conclude that the original bit is 0, which is incorrect.

If we increase the size of the bit string to four, we can detect all two-bit errors but cannot correct them, the quantity of parity bits is even at five bits, we can correct all two-bit errors, but not all three-bit errors. Moreover, increasing the size of the parity bit string is inefficient, reducing throughput by three times in our original case, and the efficiency drops drastically as we increase the number of times each bit is duplicated in order to detect and correct more errors.

If more error-correcting bits are included with a message, and if those bits can be arranged such that different incorrect bits produce different error results, then bad bits could be identified. In a seven-bit message, there are seven possible single bit errors, so three error control bits could potentially specify not only that an error occurred but also which bit caused the error.

Hamming studied the existing coding schemes, including two-of-five, and generalized their concepts. To start with, he developed a nomenclature to describe the system, including the number of data bits and error-correction bits in a block. For instance, parity includes a single bit for any data word, so assuming ASCII words with seven bits, Hamming described this as an 8,7 code, with eight bits in total, of which seven are data.

The repetition example would be 3,1 , following the same logic. Hamming also noticed the problems with flipping two or more bits, and described this as the "distance" it is now called the Hamming distance , after him. Parity has a distance of 2, so one bit flip can be detected, but not corrected and any two bit flips will be invisible. The 3,1 repetition has a distance of 3, as three bits need to be flipped in the same triple to obtain another code word with no visible errors.

It can correct one-bit errors or detect but not correct two-bit errors. A 4,1 repetition each bit is repeated four times has a distance of 4, so flipping three bits can be detected, but not corrected. When three bits flip in the same group there can be situations where attempting to correct will produce the wrong code word.

Hamming was interested in two problems at once: During the s he developed several encoding schemes that were dramatic improvements on existing codes. The key to all of his systems was to have the parity bits overlap, such that they managed to check each other as well as the data.

The following general algorithm generates a single-error correcting SEC code for any number of bits. The form of the parity is irrelevant. Even parity is mathematically simpler, but there is no difference in practice. Shown are only 20 encoded bits 5 parity, 15 data but the pattern continues indefinitely.

The key thing about Hamming Codes that can be seen from visual inspection is that any given bit is included in a unique set of parity bits. To check for errors, check all of the parity bits. The pattern of errors, called the error syndrome , identifies the bit in error.

If all parity bits are correct, there is no error. Otherwise, the sum of the positions of the erroneous parity bits identifies the erroneous bit. If only one parity bit indicates an error, the parity bit itself is in error.

As m varies, we get all the possible Hamming codes:. If, in addition, an overall parity bit bit 0 is included, the code can detect but not correct any two-bit error, making a SECDED code.

The overall parity indicates whether the total number of errors is even or odd. If the basic Hamming code detects an error, but the overall parity says that there are an even number of errors, an uncorrectable 2-bit error has occurred. Hamming codes have a minimum distance of 3, which means that the decoder can detect and correct a single error, but it cannot distinguish a double bit error of some codeword from a single bit error of a different codeword.

Thus, some double-bit errors will be incorrectly decoded as if they were single bit errors and therefore go undetected, unless no correction is attempted. To remedy this shortcoming, Hamming codes can be extended by an extra parity bit. Thus the decoder can detect and correct a single error and at the same time detect but not correct a double error. If the decoder does not attempt to correct errors, it can detect up to three errors.

This extended Hamming code is popular in computer memory systems, where it is known as SECDED abbreviated from single error correction, double error detection. Particularly popular is the 72,64 code, a truncated , Hamming code plus an additional parity bit, which has the same space overhead as a 9,8 parity code. In , Hamming introduced the [7,4] Hamming code. It encodes four data bits into seven bits by adding three parity bits. It can detect and correct single-bit errors. With the addition of an overall parity bit, it can also detect but not correct double-bit errors.

This is the construction of G and H in standard or systematic form. Regardless of form, G and H for linear block codes must satisfy. The parity-check matrix H of a Hamming code is constructed by listing all columns of length m that are pair-wise independent.

Thus H is a matrix whose left side is all of the nonzero n-tuples where order of the n-tuples in the columns of matrix does not matter. So G can be obtained from H by taking the transpose of the left hand side of H with the identity k- identity matrix on the left hand side of G.

Finally, these matrices can be mutated into equivalent non-systematic codes by the following operations: The [7,4] Hamming code can easily be extended to an [8,4] code by adding an extra parity bit on top of the 7,4 encoded word see Hamming 7,4.

This can be summed up with the revised matrices:. Note that H is not in standard form. To obtain G, elementary row operations can be used to obtain an equivalent matrix to H in systematic form:. For example, the first row in this matrix is the sum of the second and third rows of H in non-systematic form.

Using the systematic construction for Hamming codes from above, the matrix A is apparent and the systematic form of G is written as. The non-systematic form of G can be row reduced using elementary row operations to match this matrix. The addition of the fourth row effectively computes the sum of all the codeword bits data and parity as the fourth parity bit. For example, is encoded using the non-systematic form of G at the start of this section into 01 1 0 0 where blue digits are data; red digits are parity bits from the [7,4] Hamming code; and the green digit is the parity bit added by the [8,4] code.

The green digit makes the parity of the [7,4] codewords even. Finally, it can be shown that the minimum distance has increased from 3, in the [7,4] code, to 4 in the [8,4] code. Therefore, the code can be defined as [8,4] Hamming code. From Wikipedia, the free encyclopedia.

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