Editing Bit error rate (section)

==Analysis of the BER==
The BER may be evaluated using stochastic ([[Monte Carlo method|Monte Carlo]]) computer simulations. If a simple transmission [[channel model]] and [[traffic generation model|data source]] model is assumed, the BER may also be calculated analytically. An example of such a data source model is the [[Bernoulli distribution|Bernoulli]] source.

Examples of simple channel models used in [[information theory]] are:
* [[Binary symmetric channel]] (used in analysis of decoding error probability in case of [[error burst|non-bursty bit errors]] on the transmission channel)
* [[Additive white Gaussian noise]] (AWGN) channel without fading.

A worst-case scenario is a completely random channel, where noise totally dominates over the useful signal. This results in a transmission BER of 50% (provided that a [[Bernoulli distribution|Bernoulli]] binary data source and a binary symmetrical channel are assumed, see below).

[[Image:PSK BER curves.svg|thumb|right|280px|Bit-error rate curves for [[BPSK]], [[QPSK]], 8-PSK and 16-PSK, [[AWGN]] channel.]]
[[Image:Diff enc BPSK BER curves.svg|thumb|right|280px|BER comparison between BPSK and [[DPSK|differentially encoded BPSK]] with gray-coding operating in white noise.]]

In a noisy channel, the BER is often expressed as a function of the normalized [[carrier-to-noise ratio]] measure denoted [[Eb/N0]], (energy per bit to noise power spectral density ratio), or [[Es/N0]] (energy per modulation symbol to noise spectral density).

For example, in the case of [[BPSK]] modulation and AWGN channel, the BER as function of the Eb/N0 is given by:

<math>\operatorname{BER}=Q(\sqrt{2E_b/N_0})</math>,

where
<math>Q(x) := \frac{1}{\sqrt{2\pi}} \int_{x}^{ \infty } e^{-t^2/2}dt</math>. <ref>
BER calculation, Vahid Meghdadi, Université de Limoges, January, 2008
</ref>

People usually plot the BER curves to describe the performance 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.

Measuring the bit error ratio helps people choose the appropriate [[forward error correction]] codes. Since most such codes correct only bit-flips, but not bit-insertions or bit-deletions, the [[Hamming distance]] metric is the appropriate way to measure the number of bit errors. Many FEC coders also continuously measure the current BER.

A more general way of measuring the number of bit errors is the [[Levenshtein distance]].
The Levenshtein distance measurement is more appropriate for measuring raw channel performance before [[frame synchronization]], and when using error correction codes designed to correct bit-insertions and bit-deletions, such as Marker Codes and Watermark Codes.<ref>
[https://www.usenix.org/legacy/event/sec06/tech/full_papers/shah/shah_html/jbug-Usenix06.html "Keyboards and Covert Channels"]
by Gaurav Shah, Andres Molina, and Matt Blaze (2006?)
</ref>