# [SLS-OPT] O3K channel model

Jon Hamkins Jon.Hamkins at jpl.caltech.edu
Tue Mar 17 15:55:38 UTC 2020

```Hi all,

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.

*1.  What is an appropriate channel model to discriminate between the
channel coding proposals?*

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.

Potential models (there may be others):

* Standard Gaussian model (as in RF) -- same variance
o Non-signal slots: mean mu_b, variance sigma^2
o Signal slots: mean mu_s, variance sigma^2
* Gaussian model for APD -- different variances
o Non-signal slots: mean mu_b, variance sigma_b^2
o Signal slots: mean mu_s, variance sigma_s^2
* More sophisticated APD model (Webb, McIntyre, or Conradi distribution)
o Simplified version: assume dark current and surface leakage
current is 0; assume nominal gain, ideal efficiency
o Practical version: use manufacturer data sheet to generate
representative statistical model
* Poisson model
o Non-signal slots: mean n_b (and variance n_b)
o Signal slots: mean n_s + n_b (and variance n_s + n_b)

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.

*2.  What is an appropriate performance metric for the channel codes?*

Performance (BER and CWER) may be reported vs.:

* SNR -- should define this mathematically, when the model has two
means and two variances
o E.g., (mu_s - mu_b)/(sigma_s + sigma_b)
* Photons/bit (or equivalently bits/photon)
o E.g., n_s/R

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.

----Jon

--
*Jon Hamkins*