The statement that is false is that Hard Decision Forward Error Correction (HDFEC) provides a higher coding gain than Soft Decision FEC (SDFEC). In fact, the opposite is true. SDFEC provides a significantly higher net coding gain (NCG) than HDFEC. This is because SDFEC utilizes more information from the received analog signal. Instead of making a simple binary ('0' or '1') decision based on a single threshold (as HDFEC does), SDFEC quantizes the signal into multiple levels, preserving "soft" information about the reliability or probability of each bit. This additional information allows the SDFEC decoder to perform more effective error correction, resulting in a performance improvement of 1.5 to 2 dB over HDFEC.

A. This statement is true. HDFEC involves a simpler decoding algorithm with less computational complexity compared to SDFEC, which results in lower processing time and therefore less latency.

C. This statement is true. HDFEC uses a single decision threshold to distinguish between a '0' and a '1'. SDFEC uses multiple thresholds to quantize the received signal into several "soft" values.

D. This statement is true. HDFEC makes an irreversible binary decision at the very first stage of receiving the signal, thereby discarding all analog "soft" information (e.g., how strong the signal was) immediately.

1. Nokia Application Note: "Forward error correction for high-speed optical transmission systems" (Doc ID: AN-FEC-HS-OPT-TRANS-EN).

Section 3.2, "Soft-decision FEC": This document states, "Soft-decision FEC (SD-FEC) decoders can provide a coding gain improvement of up to 2 dB over hard-decision decoders for the same code rate and overhead." This directly contradicts option B, confirming it is the false statement. The same section also describes the increased complexity of SDFEC, which supports why option A is true.

2. Essiambre, R. J., & Tkach, R. W. (2012). "Capacity trends and limits of optical communication networks." Proceedings of the IEEE, 100(5), 1035-1055.

Section III-B, "Forward Error Correction": The paper explains, "Soft-decision decoding... provides a substantial improvement in performance of about 2 dB in required OSNR compared to hard-decision decoding." This academic source validates that SDFEC has a superior coding gain, making statement B false.

3. ITU-T Recommendation G.975.1 (10/2020), "Forward error correction for high bit-rate DWDM submarine-cable systems."

Appendix I, "FEC codes for high bit-rate line systems": This standard discusses various FEC schemes. It details that soft-decision decoding, by using more information from the channel output, provides a significant performance gain over hard-decision decoding. This supports the conclusion that SDFEC's coding gain is higher than HDFEC's.