In
digital transmission
Data communication, including data transmission and data reception, is the transfer of data, transmitted and received over a point-to-point or point-to-multipoint communication channel. Examples of such channels are copper wires, optical ...
, the number of bit errors is the number of received
bits of a
data stream over a
communication channel
A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for infor ...
that have been altered due to
noise
Noise is sound, chiefly unwanted, unintentional, or harmful sound considered unpleasant, loud, or disruptive to mental or hearing faculties. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrat ...
,
interference,
distortion
In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal ...
or
bit synchronization errors.
The bit error rate (BER) is the number of bit errors per unit time. The bit error ratio (also BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval. Bit error ratio is a unitless performance measure, often expressed as a
percentage
In mathematics, a percentage () is a number or ratio expressed as a fraction (mathematics), fraction of 100. It is often Denotation, denoted using the ''percent sign'' (%), although the abbreviations ''pct.'', ''pct'', and sometimes ''pc'' are ...
.
The bit error probability ''p
e'' is the
expected value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informa ...
of the bit error ratio. The bit error ratio can be considered as an approximate estimate of the bit error probability. This estimate is accurate for a long time interval and a high number of bit errors.
Example
As an example, assume this transmitted bit sequence:
1 1 0 0 0 1 0 1 1
and the following received bit sequence:
0 1 0
1 0 1 0
0 1,
The number of bit errors (the underlined bits) is, in this case, 3. The BER is 3 incorrect bits divided by 9 transferred bits, resulting in a BER of 0.333 or 33.3%.
Packet error ratio
The packet error ratio (PER) is the number of incorrectly received
data packets divided by the total number of received packets. A packet is declared incorrect if at least one bit is erroneous. The expectation value of the PER is denoted packet error probability ''p
p'', which for a data packet length of ''N'' bits can be expressed as
:
,
assuming that the bit errors are independent of each other. For small bit error probabilities and large data packets, this is approximately
:
Similar measurements can be carried out for the transmission of
frames,
blocks, or
symbol
A symbol is a mark, Sign (semiotics), sign, or word that indicates, signifies, or is understood as representing an idea, physical object, object, or wikt:relationship, relationship. Symbols allow people to go beyond what is known or seen by cr ...
s.
The above expression can be rearranged to express the corresponding BER (''p
e'') as a function of the PER (''p
p'') and the data packet length ''N'' in bits:
: