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The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code. [ 5 ] FEC can be applied in situations where re-transmissions are costly or impossible, such as one-way communication links or when transmitting to multiple receivers in multicast .
An ECC-capable memory controller can generally [a] detect and correct errors of a single bit per word [b] (the unit of bus transfer), and detect (but not correct) errors of two bits per word.
The parity bit may be used within another constituent code. In an example using the DVB-S2 rate 2/3 code the encoded block size is 64800 symbols (N=64800) with 43200 data bits (K=43200) and 21600 parity bits (M=21600). Each constituent code (check node) encodes 16 data bits except for the first parity bit which encodes 8 data bits.
Error-correcting codes are used in lower-layer communication such as cellular network, high-speed fiber-optic communication and Wi-Fi, [11] [12] as well as for reliable storage in media such as flash memory, hard disk and RAM. [13] Error-correcting codes are usually distinguished between convolutional codes and block codes:
Memory scrubbing consists of reading from each computer memory location, correcting bit errors (if any) with an error-correcting code , and writing the corrected data back to the same location. [ 1 ] Due to the high integration density of modern computer memory chips , the individual memory cell structures became small enough to be vulnerable ...
Similarly, the inner code can reliably correct an input y i if less than d/2 inner symbols are erroneous. Thus, for an outer symbol y' i to be incorrect after inner decoding at least d/2 inner symbols must have been in error, and for the outer code to fail this must have happened for at least D/2 outer symbols.
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As mentioned above, there are a vast number of error-correcting codes that are actually block codes. The first error-correcting code was the Hamming(7,4) code, developed by Richard W. Hamming in 1950. This code transforms a message consisting of 4 bits into a codeword of 7 bits by adding 3 parity bits. Hence this code is a block code.