Bit error ratio

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In telecommunication, an error ratio is the ratio of the number of bits, elements, characters, or blocks incorrectly received to the total number of bits, elements, characters, or blocks sent during a specified time interval. The error ratio is usually expressed in scientific notation; for example, 2.5 erroneous bits out of 100,000 bits transmitted would be 2.5 out of 105 or 2.5 × 10-5. Some software may display this as "2.5e-05".

The most commonly encountered ratio is the bit error ratio (BER) - also sometimes referred to as bit error rate.

For a given communication system, the bit error ratio will be affected by both the data transmission rate and the signal power margin.

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.

On good connections the BER should be below 10-10. The test time for a 95% confidence level at several speed links is shown here:

  • 40 Gbit/s (STM-256 or OC-768): 1 s
  • 10 Gbit/s (STM-64 or OC-192): 3 s
  • 2.5 Gbit/s (STM-16 or OC-48): 12 s
  • 622 Mbit/s (STM-4c or OC-12): 48 s
  • 155 Mbit/s (STM-1 or OC-3): 3.2 min
  • 64 Mbit/s (STM-1 or stnd)  : 6.4 min

Source: from Federal Standard 1037C and from MIL-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 also T-carrier

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. The scale of Y axis (for BER) is usually in probability scale, so that the curve looks like straight line. (Examples of such figures needed, as well as the simple BER models)

Curve fitting for such BER curve is an interesting topic, attracting many research efforts.

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