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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.

enter image description here

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.

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

1 Answer 1

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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:

http://ecee.colorado.edu/~mathys/ecen5682/slides/convperf99.pdf

enter image description here

so no, you don't modify Eb to allow for the fact that the redundancy of the code has increased the transmitted bit rate.

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  • \$\begingroup\$ But if you want to transmit the information rate at the same rate, you must increase the bit rate "to make room" for the extra FEC (redundant) bits. If you increase the bit rate, you reduce the energy per bit since E = PT_bit. Naturally, if you do not care about this, and makes no difference between information and redundant FEC bits, you can carry on and transmit at the same rate, and if so E = PT_bit would not change. But that case I am not interested in. Thanks. \$\endgroup\$
    – Riker_ncc
    May 20, 2021 at 18:27
  • \$\begingroup\$ The reason for plotting the coded BER against the information Eb is to allow for easy evaluation of the benefit of the FEC. If the FEC gives 6dB coding gain at the BER you are interested in, then this is equivalent to 6dB extra link margin, same as increasing tx power by 6dB for example. Of course, in evaluating the coding gain you have to evaluate the performance of the FEC case and you do have to allow for the fact that the channel Eb is reduced by the code rate, but for the top level system design, it's the coding gain that matters. Using FEC increases the channel bit rate, so bandwidth \$\endgroup\$
    – Tesla23
    May 20, 2021 at 20:31
  • \$\begingroup\$ Imagine you had plots of BER vs Eb/No for the coded and uncoded case, where the Eb was the energy of the actual channel bit, you would need to adjust for the code rate to do a comparison. If you need a BER of say 10^-6 and the uncoded case required 10.5dB Eb/No and the coded case 2dB, for a rate 1/2 code you would have to adjust the coded case by 3dB to see that there is a 5.5dB benefit. Showing the FEC performance against the information Eb/No allows you to make a direct comparison. \$\endgroup\$
    – Tesla23
    May 20, 2021 at 20:46
  • \$\begingroup\$ Thanks for your time tesla23. I think I agree with you here, that on a "top level system design perspective", the BER curves with uncoded & different codes simply show the coding gain, and the X axis is simply EbNo for a "channel bit". At this point, that channel bit does not care if it is an information or coding bit. Therefore, when looking at these graphs, one has not yet "paid the price" of using FEC, which would be to increase the bit rate, thereby reducing Eb (assuming that the designer even wants to consider this effect). \$\endgroup\$
    – Riker_ncc
    May 21, 2021 at 6:50
  • \$\begingroup\$ However, now let us say that you wish to consider this effect, and say that I will use FEC, but I do not want to change the original information rate. As mentioned, we will then increase the bit rate to account for the extra FEC bits. It is my impression that this is usual consideration to make. It is also interesting because it highlights that FEC reduces required EbNo (coding gain), but also increases it (higher bit rate), but the "win" here is higher than the "loss". Otherwise, it would not be a good code. \$\endgroup\$
    – Riker_ncc
    May 21, 2021 at 6:50

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