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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).
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 ]
If we increase the size of the bit string to four, we can detect all two-bit errors but cannot correct them (the quantity of parity bits is even); at five bits, we can both detect and correct all two-bit errors, but not all three-bit errors.
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When implemented in bit serial hardware, the generator polynomial uniquely describes the bit assignment; the first bit transmitted is always the coefficient of the highest power of , and the last bits transmitted are the CRC remainder (), starting with the coefficient of and ending with the coefficient of , a.k.a. the coefficient of 1.
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