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Reedb>-Solomonb> error correction - Wikipedia, the free encyclopedia

If the locations of the errored symbols are not known in advance, then a Reedb>-Solomonb> 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.
Reedb>-Solomonb> 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 Reedb>-Solomonb> 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.

http://en.wikipedia.org/wiki/Reed-Solomon_code (1114 words)



World Intellectual Property Organization

A Reedb> Solomonb> (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).
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.

http://www.wipo.int/ipdl/IPDL-CIMAGES/view/pct/getbykey5?KEY=01/39378.010531&ELEMENT_SET=DECL (4052 words)



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.

http://members.aol.com/mnecctek/faqs.html (1761 words)



TRL News

The new IBM algorithm opens up a whole new range of applications for Reedb>-Solomonb> error correction by speeding it up to a level comparable with that of Hamming code error correction.
Designed to correct an error in a sequence of bits (a "symbol"), Reedb>-Solomonb> 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.
These error-correcting codes were announced in 1960 in a paper by Irving S. Reedb> and Gustave Solomonb>.

http://www.research.ibm.com/trl/news/lead_rs_e.htm (1004 words)



Fault tolerant memory using bus bit aligned Reedb>-Solomonb> error correction code symbols - Patent 5313464

A 640 byte data block comprising 512 ten-bit symbols using the Reedb>-Solomonb> error correction code is stored in twenty byte groups of each of thirty-two eight-bit by 128 kilobyte static RAM devices.
The ten-bit Reedb>-Solomonb> 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 Reedb>-Solomonb> 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.

http://www.freepatentsonline.com/5313464.html (3572 words)



reedb>-solomonb> codes

Reedb>-Solomonb> codes are particularly well suited to correcting burst errors (where a series of bits in the codeword are received in error).
The advantage of using Reedb>-Solomonb> codes is that the probability of an error remaining in the decoded data is (usually) much lower than the probability of an error if Reedb>-Solomonb> is not used.
Reedb> Solomonb> codes are a subset of BCH codes and are linear block codes.

http://www.4i2i.com/reed_solomon_codes.htm (1507 words)



The Ubiquitous Reedb>-Solomonb> Codes

Reedb> was among the first to recognize the significance of abstract algebra as the basis for error-correcting codes.
But that kind of brute-force error correction would defeat the purpose of high-speed, high-density information processing.
Reedb>, now a professor of electrical engineering at the University of Southern California, is still working on problems in coding theory.

http://www.siam.org/siamnews/mtc/mtc193.htm (1356 words)



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.

http://www.exabyte.com/technology/mammoth/intro/errorcorrection.cfm (390 words)



PDF417 Barcode FAQ and Tutorial

It is necessary to use the encoder because of the complexity of the symbology and the required Reedb> Solomonb> error correction.
The Reedb> Solomonb> 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.

http://www.idautomation.com/pdf417faq.html (2668 words)



SourceForge: Welcome

The RSCODE project is an implementation of a Reedb>-Solomonb> error correction algorithm.
This implementation of the Reedb>-Solomonb> 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).
Error correcting codes are marvelous jewels of mathematics and algorithms, providing an almost supernatural ability to recover good data from a corrupted channel.

http://rscode.sourceforge.net (314 words)



Defeating Audio Cd Copy Protection [1/1]

I will list several web pages that can be studied so that the Solomonb>-Reedb> error correction is fully understood.
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.

http://www.cdfreaks.com/document.php3?Doc=49 (1092 words)



DDJ - January 1997

For any number of reasons, Reedb>-Solomonb> error correction is commonly implemented in hardware.
Here, Hugo presents a highly optimized software implementation of Reedb>-Solomonb> 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.

http://www.cs.ubc.ca/local/reading/proceedings/ddj/2000_06/articles/1997/9701/9701toc.htm (502 words)



Modified Reedb>-Solomonb> error correction system using (W+i+1)-bit representations of symbols of GF(2^w+i) - US Patent 5948117

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.
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.
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!.

http://www.patentstorm.us/patents/5948117.html (5590 words)



Memory Error Correction - Hamming vs Reedb>-Solomonb> Codes - White Paper

errors in main memory, and Reedb>-Solomonb> codes to correct errors in peripheral devices such as tape and
For those interested in obtaining more details about Imperial Technology’s use of Reedb>-Solomonb> error
Single-bit error correction using a Hamming code is not a viable solution without

http://www.imperialtechnology.com/technology_whitepapers_ecc.htm (656 words)



ECC Technologies' Byte-Parallel Reedb>-Solomonb> ECC

Reedb>-Solomonb> codes are optimal from the standpoint of having the most error correction power for a given amount of redundancy.
Our aim is to provide a generic pattern for the design of parallelized and pipelined Reedb>-Solomonb> 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 advantages of our byte-parallel Reedb>-Solomonb> error correcting system are as follows:

http://members.aol.com/mnecctek/prs.html (919 words)



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 Reedb>-Solomonb> error correction.

http://www.ics.uci.edu/~pederson/docs/2dbarcode.html (218 words)



U.S. Pregrant 20030192007 - Code-programmable field-programmable architecturally-systolic Reedb>-Solomonb> BCH error correction decoder integrated circuit and error correction decoding method

A simplified Chien-Forney algorithm is implemented that requires fewer computations to determine error magnitudes for Reedb>-Solomonb> codes with offsets compared to conventional approaches, and which allows the same circuitry to be used for different codes with arbitrary offsets.
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.
Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes

http://cxp.paterra.com/uspregrant20030192007.html (352 words)



Reedb> Solomonb> Codes: Sofware and Hardware from 4i2i

These highly optimized software libraries support rapid encoding and decoding of the widely used Reedb>-Solomonb> Error Correcting Codes.
Reedb>-Solomonb> codes are block-based error correcting codes with a wide range of applications including:
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).

http://www.4i2i.com/reed_solomon_software.htm (386 words)



Algorithms in the Real World: Error Correcting Codes

A very brief Understanding Reedb>-Solomonb> Error Correction from Multimedia Systems Design Magazine.
Reedb> Solomonb> Codes explained by 4i2i a company that "designs algorithms, components and systems for the communications industry." Here is a local copy.
Error Correcting Codes lecture notes by Jim Carlson at the University of Utah.

http://www-2.cs.cmu.edu/afs/cs.cmu.edu/project/pscico-guyb/realworld/www/errorcorrecting.html (307 words)



Radio Design Group - RS-FEC Reedb>-Solomonb> 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.
This coding system provides superior burst error correcting capability while maintaining an excellent ability to correct random errors.

http://www.radiodesign.com/rs_sale.htm (530 words)



AIM - The global trade assocation for automatic identification

Selectable error correction levels: 4 levels of Reedb>-Solomonb> error correction, plus one for error detection only.
The Ultracode two-dimensional linear matrix symbology has a constant number of rows and uses Reedb>-Solomonb> error correction.
Code type: Constant height two-dimensional matrix; length dependent on amount of data encoded and error correction level in use.

http://www.aimglobal.org/standards/symbinfo/ultracode_overview.asp (473 words)



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 Reedb>-Solomonb> codes, BCH codes, the binary Golay code, a binary Goppa code, a Viterbi decoder and more.
Decoding the Berlekamp-Masssey (BM) algorithm, with error evaluation as explained in Lin and Costello's book.
The purpose of this tutorial is to introduce the reader to a forward error correction technique known as convolutional coding with Viterbi decoding.

http://www.eccpage.com (1250 words)



Monarch Frame Sync [PCI] / Telemetry & Command / Products / Avtec.com - the Web site of Avtec Systems, Inc.

The Monarch-E Reedb>-Solomonb> Error Correction chip accepts parallel data from the board's Serial Input Logic.
The board's integrated Reedb>-Solomonb> Encoder and Decoder provide complete block error detection and correction for each of the CCSDS-recommended grades of service for Advanced Orbiting Systems.
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.

http://www.avtec.com/content/view/full/205 (686 words)



EDN: Reedb>-Solomonb> gains favor: makers of disk-control ICs anticipate strong demand for error-correction scheme. (Cirrus Logic Inc introduces its CL-SH360 24M-bps disk-control integrated circuit)@ HighBeam Research

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 Reedb>-Solomonb> (RS) error correction to disk-drive control.
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.
How much improvement in disk storage is debated, with estimates ranging from 20 percent to almost...

http://www.highbeam.com/library/doc0.asp?docid=1G1:8661378&refid=ink_tptd_mag (212 words)



CSD - May 1999 - Building Blocks: Reedb>-Solomonb> from the Ground Up.

As error correction methods move completely into the mainstream in modern communications, everyone keeps mentioning these Reedb> and Solomonb> fellows.
The example shown in Figure 1 is one in which bursts of errors are likely.
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.

http://www.commsdesign.com/main/1999/05/9905building.htm (2172 words)



Decoding of Reedb> Solomonb> codes beyond the error-correction bound - Sudan (ResearchIndex)

Decoding of Reedb> Solomonb> codes beyond the error-correction bound.
Decoding of Reedb> Solomonb> codes beyond the error-correction bound (1997)
Decoding of Reedb> Solomonb> codes beyond the error-correction bound - Sudan (ResearchIndex)

http://citeseer.ist.psu.edu/499406.html (488 words)



12.5 MBytes/sec Reedb>-Solomonb> Error Correction IC

The AHA4013 is a member of the AHA PerFEC high performance, single-chip Reedb>-Solomonb> Forward Error Correction (FEC) devices.
AHA4013B Specification - 12.5 MBytes/sec Reedb>-Solomonb> Error Correction IC
AHA4013B Brief - 12.5 MBytes/sec Reedb>-Solomonb> Error Correction IC

http://www.aha.com/show_prod.php?id=16 (188 words)



Forward Error Correction

It is based on Reedb>-Solomonb> coding and it must be implemented.
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).

http://www.cs.tut.fi/tlt/stuff/adsl/node12.html (71 words)



Reedb>-Solomonb> Encoder

Reedb>-Solomonb> error correction coding techniques are employed on the 188-byte MTS packets, with the capability to correct eight errors per transport packet.
> Products > Intellectual Property > DSP > Error Detection/Correction > Reedb>-Solomonb> Encoder
Configurable solution for high data rate Reedb>-Solomonb> encoding

http://www.altera.com/products/ip/dsp/error_detection_correction/m-amp-rs-enc.html (277 words)



Byte-parallel system for implementing reedb>-solomonb> 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.
Syndrome processing unit for multibyte error correcting systems
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.

http://www.delphion.com/details?pn%3DUS05754563__ (354 words)

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Topic: Reed-Solomon <b>error<

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