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| | Reed-Solomon error correction - Wikipedia, the free encyclopedia |
 | | This code can correct up to 2 byte errors per 32-byte block. | | | If the locations of the errored symbols are not known in advance, then a Reed-Solomon code can correct up to (n−k)/2 errored symbols, i.e., it can correct half as many errors as there are redundant symbols added to the block. | | | The code was invented in 1960 by Irving S. Reed and Gustave Solomon, who were then members of MIT Lincoln Laboratory. |
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http://en.wikipedia.org/wiki/Reed-Solomon_code
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| | World Intellectual Property Organization |
| | The error magnitude 141 is provided to an error corrector, such as the error corrector 150 of FIG. | | | 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). | | | For each error that the error locator 130 locates, an error corrector 150 determines the corrected codeword c (x) 151, based on the location 131 and magnitude 141 of this error. |
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http://www.wipo.int/ipdl/IPDL-CIMAGES/view/pct/getbykey5?KEY=01/39378.010531&ELEMENT_SET=DECL
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| | ECC Technologies, Inc. ECC FAQs |
| | Error correction is the process of detecting bit errors and correcting them and can be done in software or hardware. | | | Error correction is currently being used to make high capacity storage devices such as magnetic and optical disk and tape reliable. | | | Error correction can either be done in hardware or software depending upon how fast it has to be done. |
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http://members.aol.com/mnecctek/faqs.html
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| | TRL News |
| | 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). | | | The new IBM algorithm opens up a whole new range of applications for Reed-Solomon error correction by speeding it up to a level comparable with that of Hamming code error correction. | | | IBM Japan's Tokyo Research Laboratory is planning to continue exploring this field and to develop the basic technologies needed for more reliable systems in the coming generation of information processing devices. |
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http://www.research.ibm.com/trl/news/lead_rs_e.htm
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| | Fault tolerant memory using bus bit aligned Reed-Solomon error correction code symbols - Patent 5313464 |
| | This is partly due to the fact that a data bus error or memory device failure can cause the loss of more than one ten bit symbol, thus limiting the effectiveness of the error correction code in protecting the integrity of data blocks. | | | A 640 byte data block comprising 512 ten-bit symbols using the Reed-Solomon error correction code is stored in twenty byte groups of each of thirty-two eight-bit by 128 kilobyte static RAM devices. | | | In order to more effectively utilize simple, single error correcting codes, various data organizations have been adopted that disperse the data such that a single occurrence of an error does not show up as a burst error, thus exceeding the correction capability of the code. |
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http://www.freepatentsonline.com/5313464.html
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| | reed-solomon codes |
| | These data rates are for worst case decoding (correcting the maximum number of errors in "every" code word): encoding is considerably faster since it requires less computation. | | | 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 particularly well suited to correcting burst errors (where a series of bits in the codeword are received in error). |
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http://www.4i2i.com/reed_solomon_codes.htm
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| | The Ubiquitous Reed-Solomon Codes |
| | But that kind of brute-force error correction would defeat the purpose of high-speed, high-density information processing. | | | What many might be unaware of, though, is the significance, in all this modern technology, of a five-page paper that appeared in 1960 in the Journal of the Society for Industrial and Applied Mathematics. | | | In today's byte-sized world, for example, it might make sense to let K be the field of degree 8 over $Z_2$, so that each element of K corresponds to a single byte (in computerese, there are four bits to a nibble and two nibbles to a byte). |
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http://www.siam.org/siamnews/mtc/mtc193.htm
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| | Technology Mammoth Advanced Error Correction - Exabyte |
| | To deal with these errors, digital information scientists have devised various schemes for embedding error correction information within the data. | | | 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. | | | ECC3 is used only when a data error cannot be corrected by ECC1 and ECC2. |
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http://www.exabyte.com/technology/mammoth/intro/errorcorrection.cfm
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| | PDF417 Barcode FAQ and Tutorial |
| | 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. | | | 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. |
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http://www.idautomation.com/pdf417faq.html
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| | SourceForge: Welcome |
| | 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. | | | This implementation of the Reed-Solomon codes provide convenient 'byte-sized' block coding which is convenient for adding protection to data which is stored as eight-bit bytes (i.e., most common computer data). |
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http://rscode.sourceforge.net
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| | Defeating Audio Cd Copy Protection [1/1] |
| | 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. | | | BLER (Block Error Rate) measures the number of blocks of data per second that have one occurrence of un corrected data. | | | BERL (Burst Error Length), counts the number of consecutive blocks in error. |
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http://www.cdfreaks.com/document.php3?Doc=49
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| | Modified Reed-Solomon error correction system using (W+i+1)-bit representations of symbols of GF(2w+i) - US ... |
| | 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. | | | Then the selected bits, which are now the same as the known truncation pattern, are ignored and the remaining 8 bits of each of the ECC symbols and the modified pseudo data bytes are stored along with the data bytes as the code word. | | | Again, the modified pseudo data bytes and the remaining 8 bits of the ECC symbols contain all the information necessary to allow the decoding and error correction of the code word as bytes. |
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http://www.patentstorm.us/patents/5948117.html
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| | DDJ - January 1997 |
| | For any number of reasons, Reed-Solomon error correction is commonly implemented in hardware. | | | Here, Hugo presents a highly optimized software implementation of Reed-Solomon error correction, written in C++ and assembly language. | | | 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. |
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http://www.cs.ubc.ca/local/reading/proceedings/ddj/2000_06/articles/1997/9701/9701toc.htm
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| | ECC Technologies' Byte-Parallel Reed-Solomon ECC |
| | Reed-Solomon codes are optimal from the standpoint of having the most error correction power for a given amount of redundancy. | | | The error-correcting system can be used with raw error rates as high as one byte in error for every thousand bytes transferred. | | | The error-correcting system can be used with real-time digital video data and will correct for errors with no slowdown of the video. |
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http://members.aol.com/mnecctek/prs.html
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| | Memory Error Correction - Hamming vs Reed-Solomon Codes - White Paper |
| | errors in main memory, and Reed-Solomon codes to correct errors in peripheral devices such as tape and | | | Single-bit error correction using a Hamming code is not a viable solution without | | | multi-bit errors increase significantly and more error correction is needed. |
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http://www.imperialtechnology.com/technology_whitepapers_ecc.htm
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| | IT Production Services |
| | There are two types of Data Matrix symbology: ECC 000-140 with several available levels of convolutional error correction and ECC 200, which uses Reed-Solomon error correction. |
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http://www.ics.uci.edu/~pederson/docs/2dbarcode.html
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| | U.S. Pregrant 20030192007 - Code-programmable field-programmable architecturally-systolic Reed-Solomon BCH error ... |
| | 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. | | | The syndrome computation module calculates syndromes which are intermediate values required to find error locations and values. | | | Translator and inverse-translator circuits are employed that allow optimal choice of the internal on-chip Galois field representation for maximizing chip speed and minimizing chip gate count by making possible the use of a novel quadratic-subfield modular multiplier and a novel power-subfield integrated Galois-field divider. |
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http://cxp.paterra.com/uspregrant20030192007.html
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| | Reed Solomon Codes: Sofware and Hardware from 4i2i |
| | The RSDecoder function takes as its input a received codeword of n symbols and returns k decoded data symbols, together with a count of the number of symbol errors corrected (or a flag indicating that more than t errors were present). | | | These highly optimized software libraries support rapid encoding and decoding of the widely used Reed-Solomon Error Correcting Codes. | | | The following table shows approximate worst-case data rates on a 1.8GHz Pentium 4 (encoding and decoding, correcting the maximum t errors every code word). |
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http://www.4i2i.com/reed_solomon_software.htm
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| | Algorithms in the Real World: Error Correcting Codes |
| | Reed Solomon Codes explained by 4i2i a company that "designs algorithms, components and systems for the communications industry." Here is a local copy. | | | A very brief Understanding Reed-Solomon Error Correction from Multimedia Systems Design Magazine. | | | A Commonsense Approach to the Theory of Error-Correcting Codes. |
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http://www-2.cs.cmu.edu/afs/cs.cmu.edu/project/pscico-guyb/realworld/www/errorcorrecting.html
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| | Radio Design Group - RS-FEC Reed-Solomon Software |
| | As an example: using an interleave factor of 8, a 16 symbol correction code can be constructed that would permit correction of error rates up to 1% or burst errors as long as 1017 bits. | | | RS-FEC is a robust symbol oriented error correction coding system. | | | Decode rates are similar in a no error environment. |
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http://www.radiodesign.com/rs_sale.htm
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| | AIM - The global trade assocation for automatic identification |
| | Selectable error correction levels: 4 levels of Reed-Solomon error correction, plus one for error detection only. | | | Code type: Constant height two-dimensional matrix; length dependent on amount of data encoded and error correction level in use. | | | Multilingual encoding: (Inherent) A new conceptual method for dividing languages into language groups and code planes permits the encoding of most natural languages with the Ultracode symbology, including multiple languages within an Ultracode symbol. |
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http://www.aimglobal.org/standards/symbinfo/ultracode_overview.asp
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| | The Error Correcting Codes (ECC) Page |
| | This page contains several computer programs, written in C/C++ language (and some Matlab scripts), that implement encoding and decoding routines of popular error correcting codes (ECC), such as Reed-Solomon codes, BCH codes, the binary Golay code, a binary Goppa code, a Viterbi decoder and more. | | | The program computes the generator polynomial of any binary BCH code, plus encoding and decoding using the BM algorithm. | | | Decoding the Berlekamp-Masssey (BM) algorithm, with error evaluation as explained in Lin and Costello's book. |
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http://www.eccpage.com
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| | Monarch Frame Sync [PCI] / Telemetry & Command / Products / Avtec.com - the Web site of Avtec Systems, Inc. |
| | It performs RS (255,223) VCDU error correction with interleaving depth from 1 to 8, RS (10,6) VCDU header error correction, and real-time quality generation and annotation. | | | The Monarch-E Reed-Solomon Error Correction chip accepts parallel data from the board's Serial Input Logic. | | | The Monarch-E Serial Input Channel accepts serial clock and data, then outputs processed frame data to the PCI Bus. |
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http://www.avtec.com/content/view/full/205
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| | EDN: Reed-Solomon gains favor: makers of disk-control ICs anticipate strong demand for error-correction scheme. (Cirrus ... |
| | The RS error correction scheme offers superior error correction and the promise of significantly increasing the storage capacity of 3.5-inch or smaller drives with no large investment in new read-write heads or disk media. | | | Cirrus Logic Inc's (Milpitas, CA) new CL-SH360 24M-bps disk-control integrated circuit (IC) for the IBM PC/XT/AT environment is the first of similar forthcoming products from several chip vendors to provide 88-bit Reed-Solomon (RS) error correction to disk-drive control. | | | How much improvement in disk storage is debated, with estimates ranging from 20 percent to almost... |
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http://www.highbeam.com/library/doc0.asp?docid=1G1:8661378&refid=ink_tptd_mag
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| | CSD - May 1999 - Building Blocks: Reed-Solomon from the Ground Up. |
| | The example shown in Figure 1 is one in which bursts of errors are likely. | | | As error correction methods move completely into the mainstream in modern communications, everyone keeps mentioning these Reed and Solomon fellows. | | | For CRC-7, the correctable percentage for a length of eight errors is about 99.4%, and above 99% for lengths greater than eight errors. |
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http://www.commsdesign.com/main/1999/05/9905building.htm
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| | 12.5 MBytes/sec Reed-Solomon Error Correction IC |
| | Programmable error correction capabilities from 1 to 10 errors and 2 to 20 erasures | | | The AHA4013 is a member of the AHA PerFEC high performance, single-chip Reed-Solomon Forward Error Correction (FEC) devices. | | | AHA4013B Specification - 12.5 MBytes/sec Reed-Solomon Error Correction IC |
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http://www.aha.com/show_prod.php?id=16
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| | Forward Error Correction |
| | Forward Error Correction (FEC) is used to assure optimal performance. | | | The interleaving depth values are either 16, 32 or 64 (32 or 64 for 2.048 Mbit/s based systems). | | | It is based on Reed-Solomon coding and it must be implemented. |
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http://www.cs.tut.fi/tlt/stuff/adsl/node12.html
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| | Reed-Solomon Encoder |
| | Reed-Solomon error correction coding techniques are employed on the 188-byte MTS packets, with the capability to correct eight errors per transport packet. | | | Configurable solution for high data rate Reed-Solomon encoding | | | > Products > Intellectual Property > DSP > Error Detection/Correction > Reed-Solomon Encoder |
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http://www.altera.com/products/ip/dsp/error_detection_correction/m-amp-rs-enc.html
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| | Byte-parallel system for implementing reed-solomon error-correcting codes (US5754563) |
| | Decoding is accomplished with or without byte failure location information by multiplying the received word by an error detection matrix, solving the key equation and generating the most-likely error word and code word in a parallel and pipelined fashion. | | | Parallelizing and pipelining allows inputs to be received at very high (fiber optic) rates and outputs to be delivered at correspondingly high rates with minimum delay. | | | Apparatus and method for data error detection and correction and address error detection in a memory system |
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http://www.delphion.com/details?pn%3DUS05754563__
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| | Available C++ Libraries FAQ |
| | Generate/test Reed-Solomon codes with an absolute minimal knowledge of error correcting codes | | | The author's permission is required (and usually given) to distribute in any other way, including on CD. | | | Commercial libraries (A-N) Forward Error Correction Library - Reed-Solomon Forward Error Correction |
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http://www.trumphurst.com/cpplibs/datapage.phtml?sqldata=Dataid=198
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| | TRAILMAPPER II: Protocol Analysis and Processing Software Package |
| | IDs Reed-Solomon forward error correction codes (up to 12 error correcting) | | | Decodes and corrects Reed-Solomon forward error correction encoded streams (up to 12 error correcting) | | | New Reed-Solomon error correction analysis and decoding capability |
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http://www.appsig.com/prods/trailmapper.html
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| | Embedded Papers - G.gen.bis: Considerations About the Power Penalty of Reed-Solomon Forward Error Correction in ADSL ... |
| | In this paper we present the mathematics for calculating the power penalty of error correction codes and apply this mathematics to Reed-Solomon FEC codes. | | | Previous presentations (NF-084 and BM-087), provide theoretical and simulated results comparing the uncoded ADSL data stream with Reed-Solomon FEC, with Reed-Solomon plus Trellis and Reed-Solomon and multiple concatenated Convolutional Codes (MCCC). | | | G.gen.bis: Considerations About the Power Penalty of Reed-Solomon Forward Error Correction in ADSL Systems in Regard to the Use of Inner Encoders |
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http://www.embeddedstar.com/technicalpapers/content/g/embedded1175.html
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| | EETimes.com - Xilinx, ISS to create Reed-Solomon error correction cores for FPGAs |
| | BELFAST, Northern Ireland -- Integrated Silicon Systems Ltd. here today announced a development pact with Xilinx Inc. to make available ISS's Reed-Solomon error detection/correction technology for field-programmable gate arrays. | | | Xilinx, ISS to create Reed-Solomon error correction cores for FPGAs | | | EETimes.com - Xilinx, ISS to create Reed-Solomon error correction cores for FPGAs |
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http://www.siliconstrategies.com/story/OEG19990831S0063
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| | ► » Reed Solomon and polynomial interpolation |
| | error correction coding, ii) polynomial interpolation problem and iii) | | | Can anybody help me with the relationship between i) Reed Solomon |
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http://www.science-chat.org/Reed-Solomon-and-polynomial-interpolation-3627324.html
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| | U.S. Pregrant 20030103582 - Selective reed-solomon error correction decoders in digital communication systems |
| | The Reed-Solomon block decoder corrects a combination of random errors and erasure errors where the erasure errors are chosen based on reliability metrics generated by the inner code or else the first positions of the data bursts are chosen for erasures as these are most likely to be in error relative to other positions. | | | Selective reed-solomon error correction decoders in digital communication systems | | | U.S. Pregrant 20030103582 - Selective reed-solomon error correction decoders in digital communication systems |
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http://cxp.paterra.com/uspregrant20030103582.html
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| | Forward Error Correcting Codes |
| | I've written software to implement various error correcting codes, including the Reed-Solomon block codes and the Viterbi and Fano algorithms for decoding convolutional error correcting codes. | | | Version 4.0 has native support for shortened codes and for the CCSDS standard (255,223) codec. | | | Three functions are currently provided: a dot product useful for FIR filtering and correlation; a sum-of-squares routine useful for signal energy measurement, and a peak sample detector useful for automatic gain control. |
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http://www.ka9q.net/code/fec
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| | MDL Corporation: Subsystems: Tape Drives - DLT 8000 |
| | 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 | | | 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. |
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http://www.mdlcorp.com/tape_dlt8k.html
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| | Armer Communications |
| | The QAM256 features 4QAM to 256QAM modulation, 1 to 55 Mbps data rate, 1 to 8 MHz channel spacing and Reed- Solomon Forward Error Correction. | | | Armer Communications' DVB-compliant QAM modulator meets all DVB requirements for transmission of digital video on broadband coaxial cable and microwave radio. |
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http://www.armercom.com/html/qam256.htm
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| | Comtech AHA - Hardware and IP core solutions for Lossless Data Compression, Turbo Product Codes and Forward Error ... |
| | And to reduce data size and transmission time, AHA also produces Lossless Data Compression hardware using ALDC, GZIP, and StarLite algorithms. | | | Comtech AHA - Hardware and IP core solutions for Lossless Data Compression, Turbo Product Codes and Forward Error Correction | | | A worldwide technology leader in Forward Error Correction and Lossless Data Compression solutions, Comtech AHA Corporation is winning the race to reduce the stress of bandwidth demands in data communications. |
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http://www.aha.com
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| | 3se86.htm |
| | Forward Error Correction, in "Scalable Multicast File Distribution" (J. Gemmell), May2000, 82 | | | "Algebraic Codes for Error Detection and Correction" (H. Liu), Dec90, 46 | | | Hamming forward error correction [C], in "How to Fix Line Glitches" (J. |
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http://www.cstone.net/~bachs/ddj/3se86.htm
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| | DDJ>Convolutional Error-Control Codes |
| | In my article entitled "Reed-Solomon Error Correction," (DDJ, January 1997), I discussed the Reed-Solomon class of error-correcting codes. | | | NASA and ESA developed a Deep Space Error Control Coding Standard based on convolutional codes with constraint length 7 and rates 1/2 and 1/3 for transmissions from spacecraft to Earth. | | | In this article, I'll examine a different class of codes -- convolutional error-correcting codes. |
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http://www.ddj.com/documents/s=935/ddj9711d/9711d.htm
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| | BBC - R&D - Publications - WHP031 |
| | Reed-Solomon error correction has several applications in broadcasting, in particular forming part of the specification for the ETSI digital terrestrial television standard, known as DVB-T. Hardware implementations of coders and decoders for Reed-Solomon error correction are complicated and require some knowledge of the theory of Galois fields on which they are based. | | | This note describes the underlying mathematics and the algorithms used for coding and decoding, with particular emphasis on their realisation in logic circuits. |
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http://www.bbc.co.uk/rd/pubs/whp/whp031.shtml
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| | ``A Tutorial on Reed-Solomon Coding for Fault-Tolerance in RAID-like Systems'' |
| | It is well-known that Reed-Solomon codes may be used to provide error correction for multiple failures in RAID-like systems. | | | The coding technique itself, however, is not as well-known. | | | On page 1000 of the journal article (page 8 of the tech report), there is a typographical error. |
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http://www.cs.utk.edu/~plank/plank/papers/SPE-9-97.html
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| | The page cannot be found |
| | HTTP Error 404 - File or directory not found. | | | Go to Microsoft Product Support Services and perform a title search for the words HTTP and 404. | | | Open IIS Help, which is accessible in IIS Manager (inetmgr), and search for topics titled Web Site Setup, Common Administrative Tasks, and About Custom Error Messages. |
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http://www.absoluteastronomy.com/encyclopedia/r/re/reed-solomon_error_correc...
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