Forward error correction

Encyclopedia : F : FO : FOR : Forward error correction

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 errors in the currently received data without having to wait for the rest of the message to come in. The important distinction between forward correction, and other detection and correction methods, such as cyclic redundancy check (CRC) or other codes is that in CRC, you need to have all of the bits protected by the checksum received, so that you can compute the CRC of the whole. The difference between forward correction and CRC correction is that in forward correction, it is only the bits already received that are used to correct the "current" bit. In other correction codes, you may need to wait for bits that have not yet been received to determine the correct message. In general, FEC codes tend to require greater bandwidth than other error-correcting codes but FEC codes are more appropriate for correcting errors "on the fly", as data comes in. FEC devices are often located close to the receiver of an analog signal, in the first stage of digital processing after a signal has been received. That is, FEC circuits are often an integral part of the analog-to-digital conversion process. Many FEC coders can also generate a bit-error rate (BER) signal which can be used as feedback to fine-tune the analog receiving electronics. Many FEC algorithms, such as the Viterbi algorithm, can take (quasi-) analog data in, and generate digital data on output.

The maximum fraction of errors that can be corrected is determined in advance by the design of the code, so different forward error correcting codes are suitable for different conditions.

Contents

1 How it works
2 Averaging noise to reduce errors
3 Types of FEC
4 Concatenate FEC codes to reduce errors
5 Turbo Codes
6 References
7 External links

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 an analog to digital converter that samples three bits of signal strength data for every bit of transmitted data. If the three samples are mostly all zero, the transmitted bit was probably a zero, and if three samples are all one, the transmitted bit was probably a one. 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.

Triplet received Interpreted as
000 0
001 0
010 0
100 0
111 1
110 1
101 1
011 1
This allows an error in any one of the three samples to be corrected by "democratic voting". In practice, this is a very poor FEC, but it does illustrate the principle. In practice, FEC codes typically examine the last several dozen, or even the last several hundred, previously received bits to determine how to decode the current small handful of bits (typically in groups of 2 to 8 bits).

Triplet received	Interpreted as
000	0
001	0
010	0
100	0
111	1
110	1
101	1
011	1

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.).

References

Clark, George C., Jr., and J. Bibb Cain. Error-Correction Coding for Digital Communications. New York: Plenum Press, 1981. ISBN 0306406152.
Lin, Shu, and Daniel J. Costello, Jr. "Error Control Coding: Fundamentals and Applications". Englewood Cliffs, N.J.: Prentice-Hall, 1983. ISBN 013283796X.
Mackenzie, Dana. "Communication speed nears terminal velocity". New Scientist 187.2507 (9 July 2005): 38–41. ISSN 0262-4079.
Wicker, Stephen B. Error Control Systems for Digital Communication and Storage. Englewood Cliffs, N.J.: Prentice-Hall, 1995. ISBN 0132008092.
Wilson, Stephen G. Digital Modulation and Coding, Englewood Cliffs, N.J.: Prentice-Hall, 1996. ISBN 0132100711.

External links

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