Glossary entry

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 $n$ total bits per codeword and $k$ data bits, the code rate is $R = k/n$ . The overhead is $(n - k)/k = (1-R)/R$ , 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 $10^{-15}$ 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%	$10^{-4}$	$\sim$ 6 dB
Hard-decision concatenated RS	7%	$10^{-3}$	$\sim$ 8 – 9 dB
LDPC (soft-decision, 7% overhead)	7%	$4 \times 10^{-3}$	$\sim$ 10 – 11 dB
LDPC (soft-decision, 20% overhead)	20%	$2 \times 10^{-2}$	$\sim$ 11.5 dB
Turbo product codes	15 – 25%	$\sim 10^{-2}$	$\sim$ 11 dB
Open FEC (oFEC, 100G/400G)	15%	$\sim 10^{-2}$	$\sim$ 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.

Hard-decision vs soft-decision FEC.

Type	Receiver input	Performance
Hard-decision	Bits (1 or 0 after decision threshold)	Lower complexity, $\sim$ 6 – 9 dB NCG
Soft-decision	Bit probabilities (e.g., log-likelihood ratios)	Higher complexity, $\sim$ 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)	LDPC oFEC	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 $\sim$ 0.5 – 1 dB from Shannon-limit performance — essentially closing the historical FEC gap.