Forward error correction

Forward error correction (of English forward error correction, short FEC; sometimes engl error detection and correction, short EDAC. ) Is a technique that is used to reduce the error rate in the storage or transmission of digital data, and represents an error correction method If forward error correction is used in a transmission system, the transmitter encodes the data to be transmitted in a redundant way, so that the receiver can detect and correct transmission errors at the sender without further inquiry. Forward error correction, for example, on compact discs ( CD), digital television (DVB) and mobile use.

Basic Techniques

Forward error correction is performed in the channel coding, and is a part of the coding theory. The first source and the encoded digital signal is added on the transmitter side in a channel encoder specific redundancy is to enable the channel decoder in the receiver to correct errors that have occurred on the transmission channel.

The addition of the data to be transmitted to a check sum is not sufficient to allow forward error correction. It allows the receiver only, to detect that an error has occurred; the receiver then needs to request the transmitter for retransmission of the faulty data block. Such a process is referred to as " backward error correction ", " requested correction transfer 'or' automatic repeat request "; it is in ARQ protocols ( Automatic Repeat Request) is used and standardized for example in the TCP protocol.

FEC algorithms can be fundamentally divided according to whether they operate on data blocks of fixed length (block code) or on a continuous data stream as the convolutional codes. Examples of block codes, the simple Hamming code or BCH code much more parametrizable and related Reed-Solomon codes. The convolutional codes are often decoded with the Viterbi algorithm.

Concatenated FEC

The FEC occurs frequently linked to that data passes through this serial several Kodierschichten, and already coded sections can be made ​​with additional algorithms robust against disturbances. In Digital Video Broadcasting (DVB) block code ( Reed -Solomon code ), convolutional code and byte interleaving are used at the level of the transport stream with blocks of 188 bytes. The same applies to the codes in the Global System for Mobile Communications (GSM ), which extend the 260 -bit blocks of the voice codec with block code and convolutional code to 456 bits, and secure with double interleaving against burst errors.

In addition to the FEC to FEC channel coding occur for block protection on other levels. The transmitted MPEG data stream of a DVB channel itself contains a long packets can be secured independently of FEC bytes, regardless of the transmission medium. Like occurs for compressed speech codecs, which can also contain error correction in addition to error detection. At this level, occur almost exclusively FEC block codes that additionally calculated FEC bytes to be inserted here in the package structure.

Applications

The error correction can be used in channel coding for interference- rich transmission links such as radio to compensate for errors resulting directly after the transfer. The more frequent errors in transmission can occur, the higher the redundancy is selected in the selection of the FEC method. Accordingly, the appended FEC data is greater, which reduces the bandwidth of a transmission path for the actual payload accordingly.

Another application is the optical data transmission in SDH networks or in optical transport networks. Where the decreasing signal to noise ratio, with increasing fiber length is compensated for by the use of the error correcting FEC. As a special function of optical transponders with FEC, the receiver can dynamically adjust the operation of the input signal: By evaluating the number of correctable errors in alternation of various operating parameters, an optimum FEC length can be determined. In Digital Video Broadcasting (DVB), the Viterbi FEC is transmitted for each channel can be selected, the possible values ​​are FEC 1/2, 2/ 3, 3/ 4, 5/ 6, 7/ 8 and 9/10. This n / m scheme means that for n bits each net - m gross bits must be spent. The Viterbi FEC 9/10 is not used for terrestrial broadcasting (DVB -T), because the radio is very susceptible to interference.

In the field of data communication is the forward error correction of a backward error correction with very fast networks and long delay times - such as when access distant geostationary earth satellite - preferable.

• Transmission technology
• Coding Theory