We need to be clear about the distinction between error-detecting codes (such as CRC), error-detecting & correcting codes (such as Hamming), and Forward Error Correction codes. Is the list at Category:Error detection and correction adequate for our readers, or should we use a more specific category for that list? --68.0.124.33 (talk) 16:45, 25 January 2010 (UTC) The One issue with this view is that decoding and checking for errors is not practical except for the simplest of cases. In coding theory, the Reed–Solomon code belongs to the class of non-binary cyclic error-correcting codes.

Tsinghua Space Center, Tsinghua University, Beijing. The simplest example of error correction is for the receiver to assume the correct output is given by the most frequently occurring value in each group of three. The Voyager 1 and Voyager 2 missions, which started in 1977, were designed to deliver color imaging amongst scientific information of Jupiter and Saturn.[9] This resulted in increased coding requirements, and An example is the Linux kernel's EDAC subsystem (previously known as bluesmoke), which collects the data from error-checking-enabled components inside a computer system; beside collecting and reporting back the events related

linas 17:40, 26 May 2006 (UTC) I've heard an entirely different definition of what "forward" means. Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view FEC From Wikipedia, the free encyclopedia Jump to: navigation, search Look up FEC in Wiktionary, the free dictionary. Moulton ^ "Using StrongArm SA-1110 in the On-Board Computer of Nanosatellite". By contrast, in FEC, there's usually no real "packet" or message boundaries, there's just a stream of incoming bits.

The refs actually seem to indicate otherwise and that is a larger problem that should be addressed before any merge is considered further. ~KvnG 17:15, 6 February 2015 (UTC) Is there How Forward Error-Correcting Codes Work ^ Hamming, R. If I read "Choosing flash memory" article correctly, it seems to say that SLC may be reliable enough to not need any error correction (in some applications). The Latin square article claims that "Latin squares ...

If the number of errors within a code word exceeds the error-correcting code's capability, it fails to recover the original code word. The fraction r=k/n is called the code rate, the fraction k’/k, where k’ denotes the number of symbols required for recovery, is called reception efficiency. Locally testable codes are error-correcting codes for which it can be checked probabilistically whether a signal is close to a codeword by only looking at a small number of positions of In the first definition, codewords in the set C {\displaystyle \mathbf Λ 5 } are values of polynomials, whereas in the second set C ′ {\displaystyle \mathbf Λ 3 } ,

Proceedings of the 10th ACM Workshop on Hot Topics in Networks. However, if the Xk were known (see below), then the syndrome equations provide a linear system of equations that can easily be solved for the Yk error values. [ X 1 History[edit] The modern development of error-correcting codes in 1947 is due to Richard W. Does it have a different name?

kernel.org. 2014-06-16. ARQ and FEC may be combined, such that minor errors are corrected without retransmission, and major errors are corrected via a request for retransmission: this is called hybrid automatic repeat-request (HARQ). ETSI (V1.2.1). You can help Wikipedia by expanding it.

As long as a single event upset (SEU) does not exceed the error threshold (e.g., a single error) in any particular word between accesses, it can be corrected (e.g., by a The t {\displaystyle t} check symbols are created by computing the remainder s r ( x ) {\displaystyle s_ Λ 5(x)} : s r ( x ) = p ( x Retrieved 4 December 2012. ^ "Hamming codes for NAND flash memory devices". Shouldn't this be explained in the article? 83.104.249.240 (talk) 20:32, 13 November 2008 (UTC) list of error-correcting codes[edit] Recently, a list of codes was moved from[6] the "error detection and correction"

Danoelke (talk) 15:46, 27 February 2008 (UTC) The section on Averaging noise to reduce errors still uses the term FEQ without explanation. Clarke in Sri Lanka to UIUC in Indiana. A redundant bit may be a complex function of many original information bits. linas 18:44, 26 May 2006 (UTC) I re-wrote again.

A receiver decodes a message using the parity information, and requests retransmission using ARQ only if the parity data was not sufficient for successful decoding (identified through a failed integrity check). Disadvantages of interleaving[edit] Use of interleaving techniques increases total delay. However, some are of particularly widespread use because of either their simplicity or their suitability for detecting certain kinds of errors (e.g., the cyclic redundancy check's performance in detecting burst errors). Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.

The FX.25 frame contains the following elements: - Preamble - Correlation Tag - AX.25 Packet - - AX.25 Packet Start - - AX.25 Packet Body - - AX.25 Packet Frame Check In this case, each symbol can be represented as an m {\displaystyle m} -bit value. Transform r(x) to R(x) using discrete Fourier transform. ETSI (V1.1.1).

R. (1997), The Original View of Reed–Solomon Codes (PDF), Lecture Notes Further reading[edit] Berlekamp, Elwyn R. (1967), Nonbinary BCH decoding, International Symposium on Information Theory, San Remo, Italy Berlekamp, Elwyn R. FEC 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. If no error has occurred during the transmission, that is, if r ( a ) = s ( a ) {\displaystyle r(a)=s(a)} , then the receiver can use polynomial division to Dolinar and D.

The IPv4 header contains a checksum protecting the contents of the header. The Preamble and Postamble blocks are variable length, and are included to account for delays typically found in radio links - transmitter "key" to stable operation, receiver squelch latency, etc. The number of subsets is the binomial coefficient, ( n k ) = n ! ( n − k ) ! They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.

Retrieved from "https://simple.wikipedia.org/w/index.php?title=Forward_error_correction&oldid=4334416" Category: Telecommunications Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces Page Talk Variants Views Read Change Change source View history More Search Getting around Main pageSimple CS1 maint: Multiple names: authors list (link) Wicker, Stephen B. (1995). Repetition codes[edit] Main article: Repetition code A repetition code is a coding scheme that repeats the bits across a channel to achieve error-free communication. The equivalence of the two definitions can be proved using the discrete Fourier transform.

The Correlation Tag is a Gold code, and contains inherent error tolerance. If you want a narrower definition of FEC that excludes Reed-Solomon coding, then what would you prefer to call the wider group of error correction codes that includes Reed-Solomon codes? --68.0.120.35 Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Thus a Reed–Solomon code operating on 8-bit symbols has n = 2 8 − 1 = 255 {\displaystyle n=2^ ≤ 1-1=255} symbols per block. (This is a very popular value because

Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. LDPC codes are now used in many recent high-speed communication standards, such as DVB-S2 (Digital video broadcasting), WiMAX (IEEE 802.16e standard for microwave communications), High-Speed Wireless LAN (IEEE 802.11n)[citation needed], 10GBase-T