Forward error correction
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In telecommunication, forward error correction (FEC) is a system of error control for data transmission. It differs from standard error detection and correction in that the technique is specifically designed to allow the receiver to correct some errors without having to request a retransmission of data. The maximum fraction of errors that can corrected is determined in advance by the design of the code, so different forward error correcting codes are suitable for different conditions.
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How it works
FEC is accomplished by adding redundancy to the transmitted information using a predetermined algorithm. Each redundant bit is invariably a complex function of many original information bits. The original information may or may not appear in the encoded output; codes that include the unmodified input in the output are systematic, while those that do not are nonsystematic.
An extremely simple example would be to transmit each bit of information three times over, and for the receiver to assume the correct output is given by the most frequently occurring value in each group of three.
| Triplet received | Interpreted as |
|---|---|
| 000 | 0 |
| 001 | 0 |
| 010 | 0 |
| 100 | 0 |
| 111 | 1 |
| 110 | 1 |
| 101 | 1 |
| 011 | 1 |
This allows any single bit error to be compensated for - whether the bit is 'flipped' or simply unreadable.
It should be noted that this is a very poor FEC, but simply illustrates the principle.
In standard telecommunications applications, the parity bits or checksums applied to data simply allow for the detection of errors, and not their correction - the normal behaviour being to detect an error and request a retransmission.
Averaging noise to reduce errors
FEC could be said to work by "averaging noise"; since each data bit affects many transmitted symbols, the corruption of some symbols by noise usually allows the original user data to be extracted from the other, uncorrupted received symbols that also depend on the same user data. This is somewhat analogous to the way that insurance companies and mutual funds manage and spread risk.
- Because of this "risk-pooling" effect, digital communication systems that use FEC tend to work perfectly above a certain minimum signal-to-noise ratio and not at all below it.
- This all-or-nothing tendency becomes more pronounced as stronger codes are used that more closely approach the theoretical limit imposed by the Shannon limit.
Types of FEC
The two main categories of FEC are block coding and convolutional coding.
- Block codes work on fixed-size blocks (packets) of bits or symbols of predetermined size.
- Convolutional codes work on bit or symbol streams of arbitrary length.
- A convolutional code can be turned into a block code, if desired.
- Convolutional codes are most often decoded with the Viterbi algorithm, though other algorithms are sometimes used.
There are many types of block codes, but the most important by far is Reed-Solomon coding because of its widespread use on the Compact disc, the DVD, and in computer hard drives. Golay, BCH and Hamming codes are other examples of block codes. Nearly all block codes apply the algebraic properties of finite fields.
Concatenate FEC codes to reduce errors
Block and convolutional codes are frequently combined in concatenated coding schemes in which the convolutional code does most of the work and the block code (usually Reed-Solomon) "mops up" any errors made by the convolutional decoder.
- This has been standard practice in satellite and deep space communications since Voyager 2 first used the technique in its 1986 encounter with Uranus.
Turbo Codes
The most recent (early 1990s) development in error correction is turbo coding, a scheme that combines two or more relatively simple convolutional codes and an interleaver to produce a block code that can perform to within a fraction of a decibel of the Shannon limit.
- One of the earliest commercial applications of turbo coding was the CDMA2000 1x (TIA IS-2000) digital cellular technology developed by Qualcomm and sold by Verizon Wireless, Sprint, and other carriers.
- The evolution of CDMA2000 1x specifically for Internet access, 1xEV-DO (TIA IS-856), also uses turbo coding. Like 1x, EV-DO was developed by Qualcomm and is sold by Verizon Wireless, Sprint, and other carriers (Verizon's marketing name for 1xEV-DO is Broadband Access, Sprint's consumer and business marketing names for 1xEV-DO are Power Vision and Mobile Broadband, respectively.).
Further information
External links
- {{cite web
| last = | first = | authorlink = | coauthors = Charles Wang, Dean Sklar, and Diana Johnson | year = Volume 3, Number 1 (Winter 2001/2002) | url = http://www.aero.org/publications/crosslink/winter2002/04.html | title = Forward Error-Correction Coding | format = | work = Crosslink - The Aerospace Corporation magazine of advances in aerospace technology | publisher = The Aerospace Corporation | accessdate = 05 March | accessyear = 2006
}}
- {{cite web
| last = | first = | authorlink = | coauthors = Charles Wang, Dean Sklar, and Diana Johnson | year = | url = http://www.aero.org/publications/crosslink/winter2002/04_sidebar1.html | title = How Forward Error-Correcting Codes Work | format = | work = Crosslink - The Aerospace Corporation magazine of advances in aerospace technology | publisher = The Aerospace Corporation | accessdate = 05 March | accessyear = 2006
}}
- {{cite web
| last = Morelos-Zaragoza | first = Robert | authorlink = | coauthors = | year = 2004 | url = http://www.eccpage.com/ | title = The Error Correcting Codes (ECC) Page | format = | work = | publisher = | accessdate = 05 March | accessyear = 2006
}}
Literature
- Clark and Cain, "Error Correction Coding for Digital Communications", Plenum 1988
- Lin and Costello, "Error Control Coding: Fundamentals and Applications", Prentice-Hall 1983
- Wicker, "Error Control Systems for Digital Communication and Storage", Prentice-Hall 1995
- Wilson, "Digital Modulation and Coding", Prentice-Hall 1996de:Vorwärtsfehlerkorrektur