Forward error correction
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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.
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.
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, and 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.
The two main categories of FEC are block coding and convolutional coding. Block codes work on fixed-size blocks of bits or symbols of predetermined size, while 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.
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.
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 is the 1xEV-DO (TIA IS-856) digital cellular Internet access technology developed by Qualcomm and sold by Verizon Wireless and other carriers (Verizon's marketing name for 1xEV-DO is Broadband Access).
Further information
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:Kanalcodierung