# Bit-Error Rate (BER)

### Overview

The bit-error rate (BER) is the number of countable bit errors encountered in a data stream over a certain period of time. Common reasons for bit errors include channel noise, signal interference, distortion, and transmitter-receiver clock synchronization errors. BER gives the user a general idea of when they can expect signal errors to occur. The lower the BER, the better the system performance. [1] BER is typically calculated using computer simulations. However, if the channel and data sources are considered simple models, BER can be found analytically using mathematical formulas. BER is closely related to packet loss and shares similar metrics.

In wired networks, bit error rates are on the order of 1e-12. In wireless networks, BER is higher than that, usually in the 1e-9 range. Forward error correction is used in wireless networks to correct this by forcing data redundancy. [2] In fiber-optics, BER is a critical metric used to judge common fiber losses, especially pulse broadening and overlap.

For FSO, studies have been done on BER performance of single links in turbulent conditions. [3] Even in channels such as space’s vacuum, where ideally no information could be lost due to interference, the BER is still an important metric to understand the strength and performance of the link since bits can still be lost. [4]

Other variables such as receiver sensitivity and photodetector quantum limit also effect the BER. If the receiver is too sensitive and notices trace light when the transmitted bit is “0”, it may incorrectly report “1” instead. The photodetector quantum limit describes the minimum power required for a specific BER in a system, since by predicting this number all conditions are assumed ideal and performance is only limited by the photodetector’s physical statistics.

### Bit-Error Ratio

The bit-error ratio is a dimensionless number describing how many bit errors occur in a discrete number of transmitted bits. This ratio is not time-gated like the bit-error *rate*. However, bit-error rate and bit-error ratio are used interchangeably since it is generally understood that a stream of bits takes some amount of time to be sent. The bit-error rate is generally more helpful for pulsed signals, especially in fiber-optics, since it will give the user information about bit errors per pulse rather than overall bit errors. [5]

Consider the following ten-bit data stream shown below. The first line is the sent data stream. The second line is the received data stream.

*0 1 1 0 1 0 0 0 1 0*

*0 1 0 0 1 0 0 1 1 0*

There are 2 bit errors in a stream of 10 bits, so the bit-error ratio is 2/10, 0.2, or 20%.

### Related Links

Forum: Converting packet loss percentage to BER

Paper: Packet (loss) testing in free-space optical communication links over water