# Why do we always use 3.8 x 10^(-3) value as Forward Error Correction (FEC) threshold?

When we want to calculate the bit error rate (BER) for any communication system, why do we always select the 3.8 x 10-3 value as Forward Error Correction (FEC) threshold? Couldn't another value be used?

Example of paper uses the FEC with value is in this link.

My focus here is on the value; where did it come from?

• Consider asking at Signal Processing SE in case you don't get and answer here. Asking same question in different SE simultaneously is not encouraged. You can try to get this question migrated there by a moderator.
– AJN
Commented Sep 26, 2022 at 12:23
• @AJN Thanks for your recommendation. Commented Sep 26, 2022 at 12:28
• I recommend you post your source for that "always" value, which is almost certainly related to a desired message length vs. FEC length or to final expected (corrected) message BER. Commented Sep 26, 2022 at 13:30
• @CarlWitthoft it does not need a reference, but always on scientific papers I find it with the same value, but if there is a source that I explain why, I need it. Commented Sep 26, 2022 at 13:34
• You missed the point: responders don't want to go searching. They want you to provide a link to the exact source (or a couple sources) so they can understand the context. Commented Sep 26, 2022 at 13:57

I found this.

Which states:

For example, for 7% overhead HD-FEC with a NCG of 9.19 dB at a corrected BER of 10−15, the pre-FEC BER should be lower than $$3.8 × 10^{−3}$$ [4], which is regarded as ‘error-free’ in the context of optical transport networks. Consequently, op- tical systems researchers usually measure the pre-FEC BER and claim error-free system opera- tion when their measured BER is below the assumed FEC threshold.

So whenever you see $$3.8 × 10^{−3}$$, you aren't always happening to read about optical communications are you? Your provided source certainly falls into that category. What about all the other places you've seen it?

Following reference [4] brings you to Appendix I.9 of ITU-T G.975.1

But to me it's gobbledegook. Maybe you understand it. The number $$3.8 × 10^{−3}$$ doesn't actually appear in there anywhere so I can't go any farther.

The closest relevant thing looks to be under "I.9.3 Error Correction Ability":

In case an erasure algorithm is used, as previously suggested, performance can be improved, obtaining, e.g., an output BER less than 10E-16 for an input BER equal to 4.00E-03.

Where, from what I saw when I initially started this whole search, 10-16 is considered the minimum acceptable error for some systems.

• I agree that the ITU spec doesn't require meeting 1E-15 BER, but I am pretty sure that the overall approach is consistent. ( I did spend several years working with fiber optic comm systems and various error-correction schemes) Commented Sep 27, 2022 at 11:16

$$BER = \frac 1 2 \ erfc \left ( {\frac Q {\sqrt 2}}\right )$$

which is calculated in Excel as:

$$FEC\ Limit\ Q = Q^2factor=20*LOG10(-NORMSINV(BER))$$

$$BER =1-NORMSDIST(10^{(0.05*Q^2factor)})$$

FEC Limit: This is the lowest Q (or highest BER) that can be corrected by the FEC. Beyond this post-FEC errors will occur.

BER is the number of errors in amount of data sent over a fixed time.

A BER of $$3.8 \times 10^{-3}$$ means a data transmission accuracy of > 99.62% and a $$Q^2$$-factor of > 8.53 dBQ. A BER below this means data can be corrected by FEC and no data is lost. Above this, the FEC can not correct errors and data is lost. How this impacts the transmission depends upon the data.

There are HD-FEC (hard decision) and SD-FEC (soft decision) solutions. The HD-FEC has an overhead of 7% and equates to a BER of $$3.8 \times 10^{-3}$$. This is available from a number of different sites / published documents.

Or does it?

In optical experiments and simulations, it is very common to define acceptable (i.e., almost error-free) performance using a FEC threshold. In most literature, however, FEC thresholds are given without a reference, or with an incorrect one. This unfortunate practice has led to numerous questionable claims, in terms of thresholds that cannot be validated and in some cases contradict other published thresholds for the same code. As an illustrative example, the presently most popular FEC threshold, which is $$3.8 \times 10^{-3}$$, was used in at least 44 papers at the Optical Fiber Communication Conference (OFC) 2017 alone, but not once with a correct reference. Three times at OFC 2017, and many more times in other publications, it was incorrectly attributed to [28, App. I.9], where this particular threshold does not appear. Similar error propagation can be observed among references for other FEC thresholds.

They summarize different FEC's with stated Overhead and BER's. There is no $$3.8 \times 10^{-3}$$.

The problem with the internet is it does not cite sources. It is a case of garbage in creates garbage out. I can't answer the question because I do not believe there is an answer.

Cite the FEC code, overhead, BER and most importantly the reference.

SSR