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# Topic: Reed Solomon error correction

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 ipedia.com: Reed-Solomon error correction Article   (Site not responding. Last check: 2007-10-29) Reed-Solomon error correction is a coding scheme which works by first constructing a polynomial from the data symbols to be transmitted and then sending an over-sampled plot of the polynomial instead... Reed-Solomon error correction is a coding scheme which works by first constructing a polynomial from the data symbols to be transmitted and then sending an over-sampled plot of the polynomial instead of the original symbols themselves. A Reed-Solomon code is twice as powerful at erasure correction than at error correction, and any combination of errors and erasures can be corrected as long as the equation 2E + S ≤ (n−k) is satisfied, where E is the number of errors and S is the number of erasures in the block. www.ipedia.com /reed_solomon_error_correction.html   (1090 words)

 Reed-Solomon error correction - Wikipedia, the free encyclopedia Reed-Solomon error correction is a coding scheme which works by first constructing a polynomial from the data symbols to be transmitted and then sending an over-sampled plot of the polynomial instead of the original symbols themselves. In the same sense that one can correct a curve by interpolating past a gap, a Reed-Solomon code can bridge a series of errors in a block of data to recover the coefficients of the polynomial that drew the original curve. A Reed-Solomon code is twice as powerful at erasure correction than at error correction, and any combination of errors and erasures can be corrected as long as the equation 2E + S ≤ (n−k) is satisfied, where E is the number of errors and S is the number of erasures in the block. en.wikipedia.org /wiki/Reed-Solomon_code   (1114 words)

 World Intellectual Property Organization   (Site not responding. Last check: 2007-10-29) If an error is not detected for a given symbol, the symbol in the corrected codeword c (x) 151 at this evaluated position is equal to the symbol in the received codeword r (x) 101. A Reed Solomon (R-S) decoder is presented herein as a paradigm for an error correcting decoder that utilizes an iterative polynomial evaluation to determine whether particular values are roots of the given polynomial. The decoder (500) of claim 7, wherein each error magnitude of the plurality of error magnitudes (331, 341, 351, 361) is based on a sum of a-product term from a corresponding coefficient multiplier (325a-d) in each slice element (320) of the plurality of slice elements (320, 320') in the second evaluator (300). www.wipo.int /ipdl/IPDL-CIMAGES/view/pct/getbykey5?KEY=01/39378.010531&ELEMENT_SET=DECL   (4052 words)

 Encyclopedia: Reed-Solomon error correction   (Site not responding. Last check: 2007-10-29) Irving S. Reed is a mathematician and engineer best known as co-inventor, with Gus Solomon, of the class of algebraic error-correcting and error-detecting codes known as Reed-Solomon codes. Turbo codes are a class of recently-developed high-performance error correction codes finding use in deep-space satellite communications and other applications where designers seek to achieve maximal information transfer over a limited-bandwidth communication link in the presence of data-corrupting noise. In telecommunication, forward error correction (FEC) is a system of error control for data transmission wherein the receiving device has the capability to detect and correct fewer than a predetermined number or fraction of bits or symbols corrupted by transmission errors. www.nationmaster.com /encyclopedia/Reed_Solomon-error-correction   (2039 words)

 Fault tolerant memory using bus bit aligned Reed-Solomon error correction code symbols - Patent 5313464 The ten-bit Reed-Solomon error correction code symbols are data bus bit aligned in each of a plurality of RAM devices and distributed among the plurality of RAM devices. A data converter converts the ten-bit Reed-Solomon error correction code symbols so that they are conveyable via two eight bit buses or a sixteen-bit bus, with all of the ten bits of each ten-bit symbol being conveyable via one of the sixteen bits of the bus. The Reed-Solomon error correction code data from the ECC encoder/decoder 14 is converted by data converter 18 into ten-bit Reed-Solomon error correction code symbols and stored in memory array 8 in an interleaved fashion. www.freepatentsonline.com /5313464.html   (3572 words)

 Reed-Solomon error correction The Reed-Solomon error correction is an error-correcting code which encodes blocks of n-bit symbols. In the same sense that one can correct a curve by interpolating past a gap, a Reed-Solomon code can bridge a series of errors in a block of data to recover the coeeficients of the polynomial that drew the original curve. Reed-Solomon codes are unusual in that they correct bursts of errors with very little additional data. www.ebroadcast.com.au /lookup/encyclopedia/re/Reed-Solomon_code.html   (281 words)

 The Ubiquitous Reed-Solomon Codes Careful engineering can reduce the error rate to what may sound like a negligible level--the industry standard for hard disk drives is 1 in 10 billion--but given the volume of information processing done these days, that "negligible" level is an invitation to daily disaster. Reed, now a professor of electrical engineering at the University of Southern California, is still working on problems in coding theory. Reed was among the first to recognize the significance of abstract algebra as the basis for error-correcting codes. www.siam.org /siamnews/mtc/mtc193.htm   (1356 words)

 ECC Technologies, Inc. ECC FAQs   (Site not responding. Last check: 2007-10-29) Error correction is needed to ensure the accuracy and integrity of data and, in some cases, to create fault-tolerance (where components can fail with no loss of performance or data). Error correction is currently being used to make high capacity storage devices such as magnetic and optical disk and tape reliable. Error correction can be used to extend the battery life of portable computers and other battery-powered electronic devices by allowing a significant decrease in the DRAM refresh rate. members.aol.com /mnecctek/faqs.html   (1761 words)

 reed-solomon codes Errors occur during transmission or storage for a number of reasons (for example noise or interference, scratches on a CD, etc). Reed Solomon codes are a subset of BCH codes and are linear block codes. One symbol error occurs when 1 bit in a symbol is wrong or when all the bits in a symbol are wrong. www.4i2i.com /reed_solomon_codes.htm   (1507 words)

 AHA4011C.pdf - 10 MBytes/sec Reed-Solomon Error Correction Device AHA4011C.pdf - 10 MBytes/sec Reed-Solomon Error Correction Device DataSheet4U.com is a free electronic engineering tool that enables you to locate product datasheets from hundreds of electronic component manufacturers worldwide. .11 PS4011C-0200 iii Advanced Hardware Architectures, Inc. 1.0 INTRODUCTION The AHA4011C is a single chip integrated circuit that implements a high speed Reed-Solomon Forward Error Correction algorithm. www.datasheet4u.com /html/A/H/A/AHA4011C_AHA.pdf.html   (256 words)

 Reed-Solomon error correction: Definition and Links by Encyclopedian.com - All about Reed-Solomon error correction   (Site not responding. Last check: 2007-10-29) The Reed-Solomon error correction is an error-correcting code which encodes blocks of n-bit symbols. In the same sense that one can correct a curve by interpolating past a gap, a Reed-Solomon code can bridge a series of errors in a block of data to recover the coeeficients of the polynomial that drew the original curve. Reed-Solomon codes are unusual in that they correct bursts of errors with very little additional data. www.encyclopedian.com /re/Reed-Solomon-code.html   (314 words)

 TRL | News Thanks to their simple error correction processes, Hamming codes can be decoded in parallel, which allows very fast error correction at speeds much greater than 1 Gb/s (a billion bits per second). For example, when the new algorithm was used in a random 4-byte error correction circuit designed and fabricated by using standard 0.35-um ASIC technology, the algorithm provided parallel processing of a 320-bit-long sequence of data in 45 nanoseconds (45 billionths of a second). Designed to correct an error in a sequence of bits (a "symbol"), Reed-Solomon error-correcting codes can correct an error in up to eight consecutive bits with single-symbol correction capability, provided a symbol consists of eight bits. www.research.ibm.com /trl/news/lead_rs_e.htm   (1004 words)

 Defeating Audio Cd Copy Protection [1/1]   (Site not responding. Last check: 2007-10-29) The error correction in normal Cd players corrects these errors by interpolating the data using the data before & after the moment of error or noise. Error correction in digital audio works in a similar fashion to spelling checkers in some word processors. The problem with BER is that it counts large and small burst errors equally and not the distribution of the errors. www.cdfreaks.com /document.php3?Doc=49   (1092 words)

 Integrated reed-solomon error correction code encoder and syndrome generator - Patent 6327690 Accordingly, there is a need for an execution unit that performs both R-S ECC error encoding and R-S ECC syndrome generation while minimizing the number of transistors and logic circuits needed to implement the unit and minimizing the area this execution unit occupies on the silicon die. Error location unit 34 and error correction unit 35 are each implemented by firmware code included within ROM 37 of FIG. Firmware 32 calculates error location within error location unit 34 and error correction within error correction unit 35 based upon the syndromes (S_i) generated by integrated encoder and syndrome generator 20 of the present invention. www.freepatentsonline.com /6327690.html   (6340 words)

 Technology | Mammoth | Advanced Error Correction - Exabyte   (Site not responding. Last check: 2007-10-29) Careful engineering can reduce the error rate resulting from misinterpreted information to a seemingly negligible level, but given the vast volume of data typically being being backed up in companies today, that “negligible” level is a daily invitation to disaster. To deal with these errors, digital information scientists have devised various schemes for embedding error correction information within the data. If an error is detected, the drive automatically rewrites the data block in a later track. www.exabyte.com /technology/mammoth/intro/errorcorrection.cfm   (390 words)

 PDF417 Barcode FAQ and Tutorial The Reed Solomon error correction can add significantly to the size of the PDF417 barcode, but this is usually not a problem, because the barcode is two-dimensional, multi-row and can be printed at very small x dimensions. The error correction level depends on the amount of data that needs to be encoded, the size, and the amount of symbol damage that could occur. It is necessary to use the encoder because of the complexity of the symbology and the required Reed Solomon error correction. www.idautomation.com /pdf417faq.html   (2668 words)

 Modified Reed-Solomon error correction system using (W+i+1)-bit representations of symbols of GF(2w+i) - US ...   (Site not responding. Last check: 2007-10-29) The importance of error correction coding of data in digital computer systems has increased greatly as the density of the data recorded on mass storage media, more particularly disks, has increased. During decoding any errors in the data are detected and, if possible, corrected through manipulation of the ECC symbols For a detailed description of decoding see Peterson and Weldon, Error Correction Codes, 2d Edition, MIT Press, 1972!. To prevent this "miscorrection" a separate error detection code, or cross-check, is typically used to ensure that the modifications made using the interleaved error correction code produce the correct data symbols. www.patentstorm.us /patents/5948117.html   (5590 words)

 Memory Error Correction - Hamming vs Reed-Solomon Codes - White Paper Error detection and correction (EDAC) techniques are used to ensure that data is correct and has not been To correct a single bit out of 64 bits, only 8 additional bits are required, a 12.5% overhead. correction coding, an additional document has been prepared and is available upon request. www.imperialtechnology.com /technology_whitepapers_ecc.htm   (656 words)

 SourceForge: Welcome   (Site not responding. Last check: 2007-10-29) The RSCODE project is an implementation of a Reed-Solomon error correction algorithm. Error correcting codes are marvelous jewels of mathematics and algorithms, providing an almost supernatural ability to recover good data from a corrupted channel. There are many ways you might use error correction coding, such as a high-reliability layer on top of a real-time streaming audio protocol which is implemented atop an unreliable protocol such as UDP. rscode.sourceforge.net   (314 words)

 Algorithms in the Real World: Error Correcting Codes Error Detecting and Correcting Codes (scribe notes by Daniel Maynes-Aminzade and Andrew Faulring). Error Correcting Codes lecture notes by Jim Carlson at the University of Utah. Reed Solomon Codes explained by 4i2i a company that "designs algorithms, components and systems for the communications industry." Here is a local copy. www-2.cs.cmu.edu /afs/cs.cmu.edu/project/pscico-guyb/realworld/www/errorcorrecting.html   (307 words)

 Software : Business : Inventory : IDAutomation PDF417 Barcode Font and Encoder The Reed Solomon error correction adds significantly to the size of the PDF417 barcode, but this is usually not a problem because the barcode is two-dimensional, multi-row and can be printed at very small x dimensions. By default, if the error correction level is not defined, the encoder chooses an error correction level between 2 and 5 that is recommended by AIM standards. The error correction level automatically chosen depends on the amount of data that needs to be encoded. iovsoft.hypermart.net /popprog/idauto/pdf417.htm   (2030 words)

 Reed-Solomon Error Correction Encyclopedia Article, Definition, History, Biography   (Site not responding. Last check: 2007-10-29) Looking For reed solomon error correction - Find reed solomon error correction and more at Lycos Search. Find reed solomon error correction - Your relevant result is a click away! Look for reed solomon error correction - Find reed solomon error correction at one of the best sites the Internet has to offer! www.karr.net /encyclopedia/Reed-Solomon_error_correction   (1317 words)

 ClearImage PDF417 - High Accuracy 2D, PDF417 Barcode Recognition The importance of error correction cannot be overemphasized. This high level of error correction is far more advanced than linear barcodes with check digits. The error correction levels range from 0 to 8. www.inliteresearch.com /homepage/products/pdf417.html   (395 words)

 DDJ - January 1997 Network security is a concept whose time clearly has come, and, as Jack finds out this month, DSNT chief scientist Eva Bozoki is in the thick of things, security wise. For any number of reasons, Reed-Solomon error correction is commonly implemented in hardware. Mark examines zlib, a library of C routines that can be used to compress or expand files using the same deflate algorithm popularized by PKZIP 2.0. www.cs.ubc.ca /local/reading/proceedings/ddj/2000_06/articles/1997/9701/9701toc.htm   (502 words)

 MDL Corporation: Subsystems: Tape Drives - DLT 8000 The media is rated for 1,000,000 stop/start passes or approximately 10,000 cartridge uses—up to 100 times that of other tape drives. SDLT uses an advanced Reed Solomon error correction code to provide a hard error rate of less than 1 in 10 Reed Solomon ECC, 64-bit CRC on each 4KB of data, 16-bit CRC on each record, Internal parity checking on cache buffer www.mdlcorp.com /tape_dlt8k.html   (428 words)

 Reed-Solomon error correction - Internet-Encyclopedia.com   (Site not responding. Last check: 2007-10-29) Find reed solomon error correction and more at Lycos Search. Do you get Error messages, or is your PC simply not working the way its supposed to. Read about reed solomon error correction in the free online encyclopedia and dictionary. www.internet-encyclopedia.com /ie/r/re/reed_solomon_error_correction.html   (1223 words)

 The Ubiquitous Reed-Solomon Codes (Barry A. Cipra, 1-93) In this so-called Age of Information, no one need be reminded of the importance not only of speed but also of accuracy in the storage, retrieval, and transmission of data. It's more than a question of "Garbage In, Garbage Out." Machines do make errors, and their non-man-made mistakes can turn otherwise flawless programming into worthless, even dangerous, trash. At the same time, Richard Hamming introduced an elegant approach to single-error correction and double-error detection. www.cs.utk.edu /%7Eshuford/terminal/reed_solomon_codes.html   (1404 words)

 U.S. Pregrant 20030192007 - Code-programmable field-programmable architecturally-systolic Reed-Solomon BCH error ...   (Site not responding. Last check: 2007-10-29) A programmable error-correction decoder embodied in an integrated circuit and error correction decoding method that performs high-speed error correction for digital communication channels and digital data storage applications. The decoder carries out error detection and correction for digital data in a variety of data transmission and storage applications. A simplified Chien-Forney algorithm is implemented that requires fewer computations to determine error magnitudes for Reed-Solomon codes with offsets compared to conventional approaches, and which allows the same circuitry to be used for different codes with arbitrary offsets. cxp.paterra.com /uspregrant20030192007.html   (352 words)

 ECC Technologies' Byte-Parallel Reed-Solomon ECC   (Site not responding. Last check: 2007-10-29) Our aim is to provide a generic pattern for the design of parallelized and pipelined Reed-Solomon encoders and decoders so that, given one level of error correction capability, the design of other implementations to correct more or fewer errors is readily apparent. The error-correcting system can be used with raw error rates as high as one byte in error for every thousand bytes transferred. Reed-Solomon codes are optimal from the standpoint of having the most error correction power for a given amount of redundancy. members.aol.com /mnecctek/prs.html   (919 words)

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