Forward error correction (FEC)
Channel coding that adds redundancy to transmitted data so the receiver can detect and correct errors without retransmission. Universal in modern optical communication; effectively part of every modern coherent transceiver.
In FEC, the transmitter prepends or interleaves additional bits computed from the message data (the parity bits or redundancy) into the transmitted bitstream. The receiver uses this redundancy to detect bit errors and, often, to correct them without requesting retransmission.
For an FEC code with total bits per codeword and data bits, the code rate is . The overhead is , typically expressed as a percentage. Telecom FECs run at code rates 0.7 – 0.93 (overhead 7% to 43%).
Pre-FEC vs post-FEC BER. FEC takes a raw bitstream with relatively high bit-error-rate (pre-FEC BER) and produces a corrected bitstream with very low BER (post-FEC BER, typically or below; effectively error-free for telecom standards).
| FEC code | Overhead | Pre-FEC BER threshold | Net coding gain |
|---|---|---|---|
| Reed-Solomon RS(255,239) | 6.7% | 6 dB | |
| Hard-decision concatenated RS | 7% | 9 dB | |
| LDPC (soft-decision, 7% overhead) | 7% | 10 – 11 dB | |
| LDPC (soft-decision, 20% overhead) | 20% | 11 dB | |
| Turbo product codes | 15 – 25% | 11 dB | |
| Open FEC (oFEC, 100G/400G) | 15% | 11 dB |
Net coding gain (NCG) quantifies the OSNR (or equivalent SNR) reduction allowed by FEC for the same post-FEC BER. An 11 dB NCG means the link can operate with 11 dB lower OSNR than without FEC, equivalent to a 11 dB reduction in required signal power or 11 dB extension in reach.
The gain can be traced through the bit error rate table. The KP4 code used by 100G-per-lane Ethernet, RS(544,514), corrects an input BER of to about or better, below the Ethernet target. Uncorrected, needs (16.9 dB); the KP4 threshold needs (10.9 dB); the difference is 6.1 dB of gross gain, from which the code's rate overhead of dB is subtracted to give a net coding gain near 5.8 dB. That gain does not appear as a separate line in a link budget, because the receiver sensitivity and the transmitter metrics (TDECQ, OMA) are already specified at the pre-FEC threshold; counting the coding gain again on top of a sensitivity defined at is the most common way to overstate a short-reach margin by 6 dB.
Hard-decision vs soft-decision FEC.
| Type | Receiver input | Performance |
|---|---|---|
| Hard-decision | Bits (1 or 0 after decision threshold) | Lower complexity, 6 – 9 dB NCG |
| Soft-decision | Bit probabilities (e.g., log-likelihood ratios) | Higher complexity, 10 – 12 dB NCG, approaches Shannon limit |
Modern coherent telecom transceivers use soft-decision FEC almost universally. The DSP that demodulates the coherent signal produces soft outputs natively, making soft-decision decoding essentially free in computational architecture.
Standard FEC overhead in optical telecom:
| Generation | FEC | Overhead |
|---|---|---|
| First-generation (10G) | Reed-Solomon | 7% |
| Second-generation (100G coherent) | LDPC + RS staircase | 7 – 15% |
| Third-generation (400G/800G) | CFEC (400ZR), oFEC (ZR+), proprietary soft-decision FEC | 15 – 20% |
Even at 20% overhead, the FEC pays for itself by enabling longer reach, higher modulation orders (more spectral efficiency), and lower required transmitter power. The net data throughput and economic value increase.
Shannon limit and the Shannon-limit gap. FEC efficiency is judged against the Shannon-capacity limit for the channel. Modern LDPC and turbo codes achieve 0.5 – 1 dB from Shannon-limit performance, essentially closing the historical FEC gap.
Where the FEC sits in a transceiver, with the RS(544,514) line-rate arithmetic for a 100 Gb/s lane, is shown in Bits to Light.