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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 .
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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.
The normal memory reads issued by the CPU or DMA devices are checked for ECC errors, but due to data locality reasons they can be confined to a small range of addresses and keeping other memory locations untouched for a very long time. These locations can become vulnerable to more than one soft error, while scrubbing ensures the checking of the ...
Proof. We need to prove that if you add a burst of length to a codeword (i.e. to a polynomial that is divisible by ()), then the result is not going to be a codeword (i.e. the corresponding polynomial is not divisible by ()).
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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.