# Bit error ratio

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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.

The bit error rate or bit error ratio (BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval. BER is a unitless performance measure, often expressed as a percentage number.

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,

The number of bit errors (the underlined bits) is in this case 3. The BER is 3 incorrect bits divided by 10 transferred bits, resulting in a BER of 0.3 or 30%.

The bit error probability pe is the expectation value of the BER. The BER can be considered as an approximate estimate of the bit error probability. This estimate is accurate for a long studied time interval and a high number of bit errors.

## Contents

### Packet error rate

The packet error rate (PER) (or symbol or block error rate) is the number of incorrectly transferred data packets (etc) divided by the number of transferred packets. A packet is assumed to be incorrect if at least one bit is incorrect. The expectation value of the PER is denoted packet error probability pp, which for a data packet length of N bits can be expressed as:

pp = 1 − (1 − pe)N,

assuming that the bit errors are independent of each other. For small bit error probabilities, this is approximately:

$p_p \approx p_eN$

### Factors affecting the BER

In a communication system, the receiver side BER may be affected by transmission channel noise, interference, distortion, bit synchronization problems, attenuation, wireless multipath fading, etc.