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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 .
Parity check is the special case where n = k + 1.From a set of k values {}, a checksum is computed and appended to the k source values: + = =. The set of k + 1 values {} + is now consistent with regard to the checksum.
Note that bit/s is a more widespread unit of measurement for the information rate, implying that it is synonymous with net bit rate or useful bit rate exclusive of error-correction codes. See also [ edit ]
The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected. The Global Positioning System makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected.
Compute forward probabilities ; Compute backward probabilities ; Compute smoothed probabilities based on other information (i.e. noise variance for AWGN, bit crossover probability for binary symmetric channel)
The first public paper on turbo codes was "Near Shannon Limit Error-correcting Coding and Decoding: Turbo-codes". [4] This paper was published 1993 in the Proceedings of IEEE International Communications Conference. The 1993 paper was formed from three separate submissions that were combined due to space constraints.
Furthermore, given some hash value, it is typically infeasible to find some input data (other than the one given) that will yield the same hash value. If an attacker can change not only the message but also the hash value, then a keyed hash or message authentication code (MAC) can be used for additional security. Without knowing the key, it is ...
On September 23, 2017, Facebook announced that the following week, it would re-license Flow, Jest, React, and Immutable.js under a standard MIT License; the company stated that React was "the foundation of a broad ecosystem of open source software for the web", and that they did not want to "hold back forward progress for nontechnical reasons".