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<p>Hi all,<br>
</p>
<p>As suggested by Bernie, I am sending this email to ask you to
please coordinate with your agency's technical experts to develop
an opinion regarding the following questions brought up today in
my presentation. We can discuss this at the April 14
teleconference. I put the presentation into the Monthly Telecons
20200317 folder in CWE.<br>
</p>
<p><font color="#0000ff"><b>1. What is an appropriate channel model
to discriminate between the channel coding proposals?</b></font></p>
<p>Background: We had previously agreed to discuss performance on
basis of a Gaussian channel model. Most agencies have reported
performance of their proposal in a way that implicitly assumes the
variance is the same in signal slots and non-signal slots, e.g.,
vs. "SNR". This is at odds with the nature of arriving photons
and with realistic APD models, in which the variance is higher in
the signal slots. The single-variance assumption equates to
ignoring shot noise and assuming thermal noise dominates. This is
the usual model for RF, but not necessarily appropriate for
optical.</p>
<p>Potential models (there may be others):</p>
<ul>
<li>Standard Gaussian model (as in RF) -- same variance<br>
</li>
<ul>
<li>Non-signal slots: mean mu_b, variance sigma^2</li>
<li>Signal slots: mean mu_s, variance sigma^2</li>
</ul>
<li>Gaussian model for APD -- different variances<br>
</li>
<ul>
<li>Non-signal slots: mean mu_b, variance sigma_b^2</li>
<li>Signal slots: mean mu_s, variance sigma_s^2</li>
</ul>
<li>More sophisticated APD model (Webb, McIntyre, or Conradi
distribution)</li>
<ul>
<li>Simplified version: assume dark current and surface leakage
current is 0; assume nominal gain, ideal efficiency</li>
<li>Practical version: use manufacturer data sheet to generate
representative statistical model<br>
</li>
</ul>
<li>Poisson model<br>
</li>
<ul>
<li>Non-signal slots: mean n_b (and variance n_b)</li>
<li>Signal slots: mean n_s + n_b (and variance n_s + n_b)</li>
</ul>
</ul>
<p>My initial thought is to try to keep the model simple, and
perhaps just use a Poisson model, which captures the statistical
nature of the arriving light without getting bogged down in a more
complicated model of a detector. This would allow us to properly
account for shot noise (the major feature lacking in our earlier
Gaussian model) and the design of the link which ultimately is
geared toward delivering photons to the detector. For example, we
could pick a few representative n_b values (0, 1e-4, 1e-2, 1) and
run simulations of proposed codes vs. n_s.<br>
</p>
<p><font color="#0000ff"><b>2. What is an appropriate performance
metric for the channel codes?</b></font></p>
<div class="moz-signature">
<p>Performance (BER and CWER) may be reported vs.:</p>
<ul>
<li>SNR -- should define this mathematically, when the model has
two means and two variances</li>
<ul>
<li>E.g., (mu_s - mu_b)/(sigma_s + sigma_b)</li>
</ul>
<li>Photons/bit (or equivalently bits/photon)</li>
<ul>
<li>E.g., n_s/R<br>
</li>
</ul>
</ul>
<p>My initial thought is that we should report performance vs.
photons/bit. This would allow us to properly account for link
design, which is set up to put a given light intensity on the
detector (photons/sec), not a given SNR. This metric would
result in the "C" shaped capacity curves, i.e., it would
discourage use of low rate codes, because the photons/bit would
be higher in those cases.</p>
<p> ----Jon<br>
</p>
</div>
<div class="moz-signature">-- <br>
<strong>Jon Hamkins</strong><br>
Lead Technologist<br>
33 | Communications, Tracking, and Radar Division<br>
<strong>O</strong> 818-354-4764 | <strong>M</strong>
626-658-6220 <br>
<br>
<strong>JPL</strong> | jpl.nasa.gov
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