In telecommunication and information theory, forward error correction (FEC) is a system of error control for data transmission, whereby the sender adds redundant data to its messages, also known as an errorcorrection code. This allows the receiver to detect and correct errors (within some bound) without the need to ask the sender for additional data. The advantages of forward error correction are that a backchannel is not required and retransmission of data can often be avoided (at the cost of higher bandwidth requirements, on average). FEC is therefore applied in situations where retransmissions are relatively costly or impossible. In particular, FEC information is usually added to most mass storage devices to protect against damage to the stored data.
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 analogtodigital conversion process, also involving digital modulation and demodulation, or line coding and decoding. Many FEC coders can also generate a biterror rate (BER) signal which can be used as feedback to finetune the analog receiving electronics. Softdecision algorithms, such as the Viterbi decoder, 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.
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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 zero, the transmitted bit was probably a zero, and if three samples are mostly 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". This is a highly inefficient 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).
Such triple modular redundancy, the simplest form of forward error correction, is widely used.
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.
Most telecommunication systems used a fixed channel code designed to tolerate the expected worstcase bit error rate, and then fail to work at all if the bit error rate is ever worse. However, some systems adapt to the given channel error conditions: hybrid automatic repeatrequest uses a fixed FEC method as long as the FEC can handle the error rate, then switches to ARQ when the error rate gets too high; adaptive modulation and coding uses a variety of FEC rates, adding more errorcorrection bits per packet when there are higher error rates in the channel, or taking them out when they are not needed.
The two main categories of FEC codes are block codes and convolutional codes.
There are many types of block codes, but among the classical ones the most notable is ReedSolomon coding because of its widespread use on the Compact disc, the DVD, and in hard disk drives. Golay, BCH, Multidimensional parity, and Hamming codes are other examples of classical block codes.
Hamming ECC is commonly used to correct NAND flash memory errors. This provides singlebit error correction and 2bit error detection. Hamming codes are only suitable for more reliable single level cell (SLC) NAND. Denser multi level cell (MLC) NAND requires stronger multibit correcting ECC such as BCH or ReedSolomon.
Classical block codes are usually implemented using harddecision algorithms^{[1]}, which means that for every input and output signal a hard decision is made whether it corresponds to a one or a zero bit. In contrast, softdecision algorithms like the Viterbi decoder process (discretized) analog signals, which allows for much higher errorcorrection performance than harddecision decoding.
Nearly all classical block codes apply the algebraic properties of finite fields.
Classical (algebraic) block codes and convolutional codes are frequently combined in concatenated coding schemes in which a short constraintlength Viterbidecoded convolutional code does most of the work and a block code (usually ReedSolomon) with larger symbol size and block length "mops up" any errors made by the convolutional decoder.
Concatenated codes have been standard practice in satellite and deep space communications since Voyager 2 first used the technique in its 1986 encounter with Uranus.
Lowdensity paritycheck (LDPC) codes are a class of recently rediscovered highly efficient linear block codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated softdecision decoding approach, at linear time complexity in terms of their block length. Practical implementations can draw heavily from the use of parallelism.
LDPC codes were first introduced by Robert G. Gallager in his PhD thesis in 1960, but due to the computational effort in implementing en and decoder and the introduction of ReedSolomon codes, they were mostly ignored until recently.
LDPC codes are now used in many recent highspeed communication standards, such as DVBS2 (Digital video broadcasting), WiMAX (IEEE 802.16e standard for microwave communications), HighSpeed Wireless LAN (IEEE 802.11n), 10GBaseT Ethernet (802.3an) and G.hn/G.9960 (ITUT Standard for networking over power lines, phone lines and coaxial cable).
Turbo coding is an iterated softdecoding 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. Predating LDPC codes in terms of practical application, they now provide similar performance.
One of the earliest commercial applications of turbo coding was the CDMA2000 1x (TIA IS2000) digital cellular technology developed by Qualcomm and sold by Verizon Wireless, Sprint, and other carriers. It is also used for the evolution of CDMA2000 1x specifically for Internet access, 1xEVDO (TIA IS856). Like 1x, EVDO was developed by Qualcomm, and is sold by Verizon Wireless, Sprint, and other carriers (Verizon's marketing name for 1xEVDO is Broadband Access, Sprint's consumer and business marketing names for 1xEVDO are Power Vision and Mobile Broadband, respectively.).
In telecommunications Forward error correction (FEC) is a special code. The sender adds parts of the data again. This is called redundancy. The receiver is then able to detect certain errors that came from the sending the data. In certain cases, the receiver can correct the error, without the need for a retransmission.
FEC adds redundancy to the transmitted information with a known algorithm. Each redundant bit is a 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 mostly 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", but is a very inefficient FEC. But in practice would not work very well, 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).
Such triple modular redundancy, the simplest form of forward error correction, is widely used.
