# Bit error rate

The bit error frequency  ( BFH ) is a measure of communications engineering for the quality of the transmission over a channel or a digital transmission path .

In many publications, based on the English term bit error rate  (BER), the term bit error rate is preferred for a bit error rate (with the dimension “number of errors per unit of time”).

## Similar terms

### Bit error ratio

In many documentaries (including the type of instruments manuals) the bit error rate is the unitless bit error ratio (Engl. Bit error ratio ) confused. In digital TV broadcasts, “BER” basically means “Bit Error Ratio” and thus the bit error ratio.

The bit error ratio is the error quotient of the number of incorrectly received bits ( bit errors ) in any given time interval and the total number of bits received in the same time interval. If the bits are stored on a storage medium , a defined time interval is not used, but a defined memory size. Example: A bit error ratio of 3 · 10 −6 means that out of 1 million transmitted or stored bits, an average of 3 bits can be incorrect.

The measurement to determine the bit error ratio on transmission links is called a BER test or BERT . It is usually carried out with the aid of check bit patterns that are sent by a measuring device and received and compared again after transmission.

### Bit error probability

In contrast to the bit error rate, the bit error probability (BEP) describes a probability of the occurrence of a bit error calculated on the basis of theoretical considerations . Closed calculations of bit error probabilities are usually only possible for idealized scenarios, but are often used to replace complex simulations and to determine the limits of the performance of communications systems.

### Excessive Bit Error Rate and Signal Degraded

Excessive Bit Error Rate , abbreviated to exBER, (in German: very high bit error rate) is an error definition that is used in the synchronous digital hierarchy and the plesiochronous digital hierarchy .

It is the most widely used quantitative characteristic for the quality of service in data communication . The exact definition of the error depends on the technology and bit rate . For example, it is common to designate the exBER error as reached in the event of 1 bit error for every 1000 bits transmitted. The seconds in which at least one exBER occurred are usually recorded and counted in a  MIB . With such counters, the quality of data communication can be measured in a defined manner during the time of use.

A similar definition is signal degraded  (SD). The error threshold of “Signal degraded” is usually reached with 1 bit error for every 1 million transmitted bits. At bit rates of 150 Mbit / s and higher, the error thresholds of exBER and SD are a few powers of ten higher. For leased lines in Germany, the exBER error is the contractually defined criterion for a failure of the leased line.

## Measurement method

Measuring the bit error rate requires high quality reference information or a reliable reference variable. That could be for example

• a comparison of the test information received,
• an idealized model target information,
• an assessment of the range of services received,
• an evaluation against a known test signal,
• error-free, independent reference information or
• a comparison over a sufficiently long measurement period with recurring information

## example

Bit error rate as a function of Eb / N0

If the signal-to-noise ratio is related to an information bit , the bit energy-to-noise power density ratio is obtained , the ratio of the energy E b used for an information bit  to the spectral noise power density N 0 . With increasing noise , i. H. as Eb / N0 decreases, the bit error rate increases. ${\ displaystyle {\ frac {E_ {b}} {N_ {0}}}}$

The BER also depends on the coding method : 16-PSK or 8-PSK have a higher information density than, for example, 2-PSK and require a higher signal-to-noise ratio . Forward error correction methods reduce the required signal quality.

The figure shows the error frequency for various power-limited coding methods as a function of Eb / N0 (shown in  dB ). For example, with a bit error ratio of 10 −4, the ratio Eb / N0 for  BPSK is about 8 dB, with FEC coding convolutional codes decoded with the Viterbi algorithm about 4 dB. An additional Reed-Solomon coding reduces the minimum Eb / N0 required to less than 3 dB. The vertical line in the figure indicates the Shannon limit , which cannot be fallen below.

## literature

• Herbert Bernstein: Measuring with the oscilloscope. Practical learning with a PC simulation program, 2nd edition, Springer Fachmedien, Wiesbaden 2016, ISBN 978-3-658-15100-3 .
• Karl Steinbuch, W. Weber (Ed.): Taschenbuch der Informatik. Volume III, Applications and Special Systems of Message Processing, Springer Verlag, Berlin / Heidelberg 1974, ISBN 978-3-642-65589-0 .
• Herbert Bernstein: Information and communication electronics . De Gruyter Verlag, Oldenburg 2015, ISBN 978-3-11-036029-5 .
• Peter Gerdsen: Digital transmission technology. BG Teubner Verlag, Stuttgart 1983, ISBN 978-3-519-00093-8 .
• Peter Welzel: Remote data transmission. Introductory basics for communication in open systems, Friedrich Vieweg & Sohn Verlag, Wiesbaden 1986, ISBN 978-3-663-00129-4 .
• Michael Dickreiter, Volker Dittel, Wolfgang Hoeg, Martin Wöhr (eds.): Manual of the recording studio technology. 8th, revised and expanded edition, 2 volumes. Walter de Gruyter, Berlin / Boston 2014, ISBN 978-3-11-028978-7 .
• Paul Dambacher: Digital technology for television broadcasting. DVB-T system technology from studio to receiver, Springer Verlag, Berlin / Heidelberg 1997, ISBN 978-3-642-64540-2 .