  Sensory systems take continuously varying stimuli as their input and encode
features relevant for the organism's survival into a sequence of action
potentials - spike trains. The full dynamic range of complex dynamical inputs
has to be compressed into a set of discrete spike times and the question,
facing any sensory system, arises: which features of the stimulus are thereby
encoded and how does the animal decode them to recover its external sensory
world?
  Here we study this issue for the two motion-sensitive H1 neurons of the fly's
optical system, which are sensitive to horizontal velocity stimuli, each neuron
responding to oppositely pointing preferred directions. They constitute an
efficient detector for rotations of the fly's body about a vertical axis.
Surprisingly the spike trains $\rho_B(t)$ generated by an empoverished stimulus
$S_B(t)$, containing just the instants when the of velocity $S(t)$ reverses its
direction, convey the same amount of global (Shannon) information as spike
trains $\rho(t)$ generated by the complete stimulus $S(t)$. This amount of
information is just enough to encode the instants of velocity reversal. Yet
this suffices to give the motor system just one, yet vital order: go left or
right, turning the H1 neurons into efficient analog-to-digital converters.
Furthermore also probability distributions computed from $\rho(t)$ and
$\rho_B(t)$ are identical. Still there are regions in the spike trains
following velocity reversals, 80 msec long and containing about 3-6 msec long
spike intervals, where detailed stimulus properties are encoded. We suggest a
decoding scheme - how to reconstruct the stimulus from the spike train, which
is fast and works in real time.
