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The BER is the likelihood of a bit misinterpretation due to electrical noise ().Considering a bipolar NRZ transmission, we have = + for a "1" and () = + for a "0".Each of () and () has a period of .
As the description implies, is the signal energy associated with each user data bit; it is equal to the signal power divided by the user bit rate (not the channel symbol rate). If signal power is in watts and bit rate is in bits per second, E b {\displaystyle E_{b}} is in units of joules (watt-seconds).
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A parity bit is a bit that is added to a group of source bits to ensure that the number of set bits (i.e., bits with value 1) in the outcome is even or odd. It is a very simple scheme that can be used to detect single or any other odd number (i.e., three, five, etc.) of errors in the output.
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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