Photonica
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Glossary entry

Bit error rate (BER)

The fraction of received bits that are decoded incorrectly. The fundamental performance metric of any digital optical communication link.

The bit error rate is

BER  =  Nerrored bitsNtransmitted bits.\text{BER} \;=\; \frac{N_\text{errored bits}}{N_\text{transmitted bits}}.

A BER of 10−910^{-9} means one in 10910^9 bits is incorrectly decoded — roughly one error per second on a 1 Gb/s link, or one error every 100 ms on a 10 Gb/s link.

Telecom reference points:

BERNotes
10−310^{-3}Pre-FEC threshold for advanced soft-decision FEC
10−410^{-4}Pre-FEC threshold for hard-decision FEC
10−910^{-9}Historical "error-free" specification for direct-detection systems
10−1210^{-12}Modern "error-free" specification for unFEC'd telecom systems
10−1510^{-15}Post-FEC specification for telecom systems (after forward error correction)

For Gaussian noise on a binary signal (NRZ OOK), BER relates to the Q-factor of the eye:

BER  =  12 erfc ⁣(Q2)  ≈  exp⁡(−Q2/2)Q2π,\text{BER} \;=\; \tfrac{1}{2} \, \text{erfc}\!\left(\frac{Q}{\sqrt{2}}\right) \;\approx\; \frac{\exp(-Q^2/2)}{Q \sqrt{2\pi}},

where Q=(μ1−μ0)/(σ1+σ0)Q = (\mu_1 - \mu_0) / (\sigma_1 + \sigma_0) is the ratio of eye opening to total noise spread (note: this is the receiver-Q, distinct from resonator Q factor). Q=6Q = 6 corresponds to BER ≈10−9\approx 10^{-9}; Q=7Q = 7 to BER ≈10−12\approx 10^{-12}.

For coherent modulation formats, the relationship between BER and required OSNR depends on the constellation:

FormatRequired OSNR (at 10−310^{-3} BER, 0.1 nm)
BPSK∼\sim 7 dB
QPSK∼\sim 10 dB
8-QAM∼\sim 14 dB
16-QAM∼\sim 17 dB
64-QAM∼\sim 25 dB

Measurement: BER is measured by a bit error rate tester (BERT) that transmits a known pseudo-random binary sequence and counts decoder errors. Confident measurement to BER =10−12= 10^{-12} requires ∼1013\sim 10^{13} bits — about 17 minutes at 10 Gb/s, or 25 seconds at 400 Gb/s.

Modern forward error correction (FEC) is the central enabler of high-speed coherent transmission: a 25 % FEC overhead can correct pre-FEC BER of 10−210^{-2} down to post-FEC BER of 10−1510^{-15}. Without FEC, the required OSNR for the same data rate would be 5 – 10 dB higher.