# With Forward Error Correction, what bit rate should be used in a link budget?

In a typical satellite link budget, you are interested in calculating the Eb/N0, where

• Eb = S/R_b (Received power times the bit period) and
• N0 is the simply kT (noise power spectral density).

Fundamentally, I have seen two main types of FEC in satellite communications, so let's anchor the discussion in these: 1) Convolutional Encoding, and 2) Reed Solomon Block Coding.

If either one of these two FECs are used, the benefit is simply that you get a coding gain of some dBs, as shown in the figure below. Fundamentally, this is done by adding redundant FEC bits to your raw information bits. My question is now, when performing a satellite link budget, i.e. when calculating Eb, is it not appropriate to use an adjusted bit rate, that includes the redundant bits, in such a way that the information bits are still transmitted at the same rate. For instance, example calculation below

• Information rate (pure information bits) = 1 Mbps
• Convultional code rate is 1/2 = > 1 extra redundant bit for every information bit
• Reed Solomon "rate" is 255/223 => ca 14.3 % more redundant bits than raw information bits.

Hence, an adjusted bit rate would now be 1×2×1.143=2.286 Mbps. Another reason why I think it makes sense to do this is that you somehow have to "pay the price" of using coding, by increasing the bit rate, you get less energy per bit. But in the end, I would guess the total coding gain, triumphs over the negative effect of having less energy per bit.

I have been unable to find any texts here, and I've seen multiple link budgets do this differently. Hopefully, you understand my question. If possible, please provide a reference. Feel free to correct my terminology as well.

• Yes, your intuition is correct. E_b is the energy associated with each bit actually transmitted, and that includes the bits added for FEC. May 12, 2021 at 10:12

Coding gain provides an indication of the improvement in performance when you use a particular code, and for this to be meaningful the error rate curves for the encoded case are plotted against Eb/N0 where Eb is the energy per information bit actually transmitted. Here's one reference on the web: 