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An example of binary FSK. Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is encoded on a carrier signal by periodically shifting the frequency of the carrier between several discrete frequencies. [1]
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The Shannon–Hartley theorem says that the limit of reliable information rate (data rate exclusive of error-correcting codes) of a channel depends on bandwidth and signal-to-noise ratio according to: < (+) where
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The probability of erasure is In coding theory and information theory , a binary erasure channel ( BEC ) is a communications channel model. A transmitter sends a bit (a zero or a one), and the receiver either receives the bit correctly, or with some probability P e {\displaystyle P_{e}} receives a message that the bit was not received ("erased") .
Fano's inequality can be interpreted as a way of dividing the uncertainty of a conditional distribution into two questions given an arbitrary predictor. The first question, corresponding to the term (), relates to the uncertainty of the predictor.
It therefore suffices to exhibit an input distribution that yields a uniform probability distribution for the output . For this, note that it is a property of any binary symmetric channel that a uniform probability distribution of the input results in a uniform probability distribution of the output.