- Bit error ratio
In
telecommunication , an error ratio is theratio of the number ofbit s, elements, characters, or blocks incorrectly received to the total number of bits, elements, characters, or blocks sent during a specifiedtime interval.The most commonly encountered ratio is the bit error ratio (BER) - also sometimes referred to as bit error rate.
Examples of bit error ratio are (a) transmission BER, "i.e.", the number of erroneous bits received divided by the total number of bits transmitted; and (b)
information BER, "i.e.," the number of erroneous decoded (corrected) bits divided by the total number of decoded (corrected) bits.The test time for a 95%
confidence interval at several speed links is shown here:*40 Gbit/s (
STM-256 orOC-768 ): 1 s
*10 Gbit/s (STM-64 orOC-192 ): 3 s
*2.5 Gbit/s (STM-16 orOC-48 ): 12 s
*622 Mbit/s (STM-4c orOC-12 ): 48 s
*155 Mbit/s (STM-1 orOC-3 ): 3.2 min
*64 Mbit/s (STM-1 orstnd ) : 6.4 minPlease note that the above sample time is based on BER=10-10.Source: from
Federal Standard 1037C and fromMIL-STD-188 The test time t can be calculated using Gaussian error distribution to:
t = -frac{ln(1-c)}{b*r}
where c is the degree of confidence level, b = upper bound of BER and r = bit rate.
See the following technical article for measuring BER for High-speed serial communication.http://www.analogzone.com/nett1003.pdf
People usually plot the BER curves to describe the functionality of a digital communication system. In optical communication, BER(dB) vs. Received Power(dBm) is usually used; while in wireless communication, BER(dB) vs. SNR(dB) is used.
Curve fitting for such BER curve is a topic, attracting many research efforts.Mathematical draft
The BER is the likelihood of a bit misinterpretation due to electrical noise w(t). Considering a bipolar NRZ transmission, we have x_1(t) = A + w(t) for a "1" and x_0(t) = -A + w(t) for a "0". Each of x_1(t) and x_0(t) has a period of T.
Knowing that the noise has a bilateral spectral density frac{N_0}{2} ,
x_1(t) is mathcal{N}left(A,frac{N_0}{2T} ight)
and x_0(t) is mathcal{N}left(-A,frac{N_0}{2T} ight).
Returning to BER, we have the likelihood of a bit misinterpretation p_e = p(0|1) p_1 + p(1|0) p_0.
p(1|0) = 0.5, operatorname{erfc}left(frac{A+lambda}{sqrt{N_o/T ight) and p(0|1) = 0.5, operatorname{erfc}left(frac{A-lambda}{sqrt{N_o/T ight)
where lambda is the threshold of decision, set to 0 when p_1 = p_0 = 0.5.
We can use the average energy of the signal E = A^2 T to find the final expression :
p_e = 0.5, operatorname{erfc}left(sqrt{frac{E}{N_o ight).
ee also
*
T-carrier
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