The pairwise error probability P ( X \ to \ widehat { X } ) is defined as the probability that, when X is transmitted, \ widehat { X } is received.
32.
This essentially gives us another encoding function E'with a corresponding decoding function D'with a decoding error probability of at most 2 ^ {-\ delta n + 1 } with the same rate.
33.
Channel capacity is the tightest upper bound on the rate of information that can be reliably transmitted over a information per unit time ) that can be achieved with arbitrarily small error probability.
34.
A 50-kiloton yield detonating on the ground produces a crater with a radius of 30 68 meters, depending on the density of the surface, effectively putting the bunker within the circular error probability.
35.
Within this context, Meuffels and Soni Consequently, there is always a lower limit of energy requirement depending on the required bit-error probability for intentionally changing a bit value in any memory device.
36.
Such factors are used to derive a Success Likelihood Index ( SLI ), a form of preference index, which is calibrated against existing data to derive a final Human Error Probability ( HEP ).
37.
Now by applying Markov's inequality, we can show the decoding error probability for the first 2 ^ { k-1 } messages to be at most 2 \ cdot 2 ^ {-\ delta n }.
38.
While Shannon could prove only that the block error probability can not become arbitrarily small if the transmission rate is above the channel capacity, Wolfowitz proved that the block error rate actually converges to one.
39.
The COMP algorithm requires no more than ed ( 1 + \ delta ) \ ln ( n ) tests to have an error probability less than or equal to n ^ {-\ delta }.
40.
The minimum error probability, P _ { H }, assuming that there is an equally likely chance of sending either \ mid \ alpha \ rangle or \ mid \ beta \ rangle, is given by
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