Double Bit Parity Error
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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 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 parity error detection 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, proving, lets say that 2 out of 21 bits is flipped, is a skill I don't have. –Mike John Jun 2 '13 at 23:40 Here's a "simple" version of what Dave and Andy said: Each valid code word is arranged such that there are no other valid code word can be arrived at if ANY N bits in a valid word are flipped. If N=3 then you can flip one bit in any valid code word and not get to a combination that can be arr
article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (March 2013) (Learn how and when to remove this template message) This article may be too technical for
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most readers to understand. Please help improve this article to make it understandable to non-experts, without removing pci parity error the technical details. The talk page may contain suggestions. (February 2016) (Learn how and when to remove this template message) (Learn how and when to parity error 4x4 remove this template message) Binary Hamming Codes The Hamming(7,4)-code (with r = 3) Named after Richard W. Hamming Classification Type Linear block code Block length 2r − 1 where r ≥ 2 Message length 2r − r − 1 Rate 1 − http://electronics.stackexchange.com/questions/71410/single-bit-error-correction-double-bit-error-detection r/(2r − 1) Distance 3 Alphabet size 2 Notation [2r − 1, 2r − r − 1, 3]2-code Properties perfect code v t e In telecommunication, Hamming codes are a family of linear error-correcting codes that generalize the Hamming(7,4)-code, and were invented by Richard Hamming in 1950. 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 https://en.wikipedia.org/wiki/Hamming_code 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.[1] In mathematical terms, Hamming codes are a class of binary linear codes. For each integer r ≥ 2 there is a code with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal number of bit changes needed to go from any code word to any other code word is three) and block length 2r − 1. 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 punctured 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 betwe
now than a few years ago, but when you have a multi-user system, it pays to avoid system hangs and crashes. With plain memory, errors are undetected and corrupt the results until they propagate http://www.ohio.edu/people/piccard/mis300/eccram.htm to the point that the application or operating system crashes, by which time bad data may well have been stored to disk. With parity memory, single-bit or triple-bit errors are detected immediately (crashing the application or operating system before corrupting on-disk data) but double-bit or quadruple-bit errors are not detected. How is this done? For every eight bits of data written to RAM, the RAM subsystem hardware computes a ninth ("parity") bit and stores it along with the parity error eight data bits. For example, if using so-called "odd parity," the ninth bit will be given the value of one if there are an even number of bits already set to a value of one in the eight data bits. Changing any one data bit will change the computed value for the parity bit. When the RAM subsystem sends data back, it re-computes the parity bit from the eight data bits it read, and compares that with the parity double bit parity bit it read. If the two agree, it proceeds. If the two disagree, then it knows that one of the nine bits is wrong, and it signals the CPU that the data are not valid. (One time out of nine, on the average, it will be the parity bit itself that is wrong, but most of the time it is one of the eight data bits that is wrong.) Original Data and Computed Parity 01101100 1 there are four data bits with value 1, so the parity is 1 to give an odd number of bits set Recovered Data and Parity 01111100 1 ^ one bit in the data has changed! Re-computed Parity 0 there are five bits with value 1 in the recovered data so the re-computed parity is 0 to leave an odd number of bits set Because the re-computed parity does not agree with the recovered parity, we know that an error has occurred, but we don't know which bit changed. Depending on the system design, and on whether the byte being read was data or program code, this may crash the system or the application, or it may just result in an error message on the screen, but with functioning parity memory and system software designed to notice it, there will be some notification of the error. If two bits change, the re-computed parity will match the recovered parit