[SLS-OPT] O3K channel model

[Jon Hamkins]

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*
Lead Technologist
33   |   Communications, Tracking, and Radar Division
*O* 818-354-4764   | *M* 626-658-6220

*JPL*   |   jpl.nasa.gov
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