Bit error rate

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In digital transmission, the number of bit errors is the number of received bits of a data stream over a communication channel that have been altered due to noise, interference, distortion or bit synchronization errors.




As an example, assume this transmitted bit sequence:

0 1 1 0 0 0 1 0 1 1,

and the following received bit sequence:

0 0 1 0 1 0 1 0 0 1,


Packet error rate[edit]


p_p = 1 - (1 - p_e)^N,


p_p \approx p_eN.


Factors affecting the BER[edit]




Analysis of the BER[edit]


Examples of such simple channel models are:




For example, in the case of QPSK modulation and AWGN channel, the BER as function of the Eb/N0 is given by: \operatorname{BER}=\frac{1}{2}\operatorname{erfc}(\sqrt{E_b/N_0}).[1]




Mathematical draft[edit]

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}\right)

and x_0(t) is \mathcal{N}\left(-A,\frac{N_0}{2T}\right).

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}}\right) and  p(0|1) = 0.5\, \operatorname{erfc}\left(\frac{A-\lambda}{\sqrt{N_o/T}}\right)

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}}\right). ±§

Bit error rate test[edit]



Common types of BERT stress patterns[edit]

  • 3 in 24 – Pattern contains the longest string of consecutive zeros (15) with the lowest ones density (12.5%). This pattern simultaneously stresses minimum ones density and the maximum number of consecutive zeros. The D4 frame format of 3 in 24 may cause a D4 Yellow Alarm for frame circuits depending on the alignment of one bits to a frame.
  • 1:7 – Also referred to as “1 in 8”. It has only a single one in an 8-bit repeating sequence. This pattern stresses the minimum ones density of 12.5% and should be used when testing facilities set for B8ZS coding as the 3 in 24 pattern increases to 29.5% when converted to B8ZS.
  • All Ones (or Mark) – A pattern composed of ones only. This pattern causes the repeater to consume the maximum amount of power. If DC to the repeater is regulated properly, the repeater will have no trouble transmitting the long ones sequence. This pattern should be used when measuring span power regulation. An unframed all ones pattern is used to indicate an AIS (also known as a Blue Alarm).
  • Alternating 0s and 1s - A pattern composed of alternating ones and zeroes.

Bit error rate tester[edit]

A bit error rate tester (BERT), also known as a bit error ratio tester[citation needed] or bit error rate test solution (BERTs) is electronic test equipment used to test the quality of signal transmission of single components or complete systems.

The main building blocks of a BERT are:

  • Electrical-optical converter and optical-electrical converter for testing optical communication signals.

See also[edit]




External links[edit]