SDA Operator’s Manual
If the distribution is governed by only two Gaussians of equal weight, this equation degenerates
into
And if, in addition, the two Gaussians have the same sigma (or Rj), then
This equation is disturbingly different from
This is because in the traditional Dual-Dirac discussion, we typically “forget” that the two
Gaussians are only half-strength.
In general, to approximate the traditional Dj and Rj value, we are still using the separation of the
“outermost means, and approximating Rj by the mean of the two sigmas.
We do, however, calculate Tj from the most precise estimation of the CDF from the renormalized
Q-scale fit, using correct weights and sigmas to reconstruct a theoretical PDF, using the central
region of the histogram “as is” and the extremes replaced by theoretical Gaussians of the correct
strength, sigma, and mean to estimate each extreme region. This is then reconstructed into a
CDF, so Tj(BER) becomes a simple calculation on that curve.
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SDA-OM-E Rev H 397
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