  Neural networks in modern communication systems can be susceptible to
internal numerical errors that can drastically effect decision results. Such
structures are composed of many sections each of which generally contain
weighting operations and activation function evaluations. The safe use comes
from methods employing number based codes that can detect arithmetic errors in
the network's processing steps. Each set of operations generates parity values
dictated by a code in two ways. One set of parities is obtained from a
section's outputs while a second comparable set is developed directly from the
original inputs. The parity values protecting the activation functions involve
a Taylor series approximation to the activation functions. We focus on using
long numerically based convolutional codes because of the large size of data
sets. The codes are based on Discrete Fourier Transform kernels and there are
many design options available. Mathematical program simulations show our
error-detecting techniques are effective and efficient.
