  We study the stability and information encoding capacity of synchronized
states in a neuronal network model that represents part of thalamic circuitry.
Our model neurons have a Hodgkin-Huxley-type low threshold Calcium channel,
display post inhibitory rebound, and are connected via GABAergic inhibitory
synapses. We find that there is a threshold in synaptic strength, $\tau_c$,
below which there are no stable spiking network states. Above threshold the
stable spiking state is a cluster state, where different groups of neurons fire
consecutively, and each neuron fires with the same cluster each time. Weak
noise destabilizes this state, but stronger noise drives the system into a
different, self-organized, stochastically synchronized state. Neuronal firing
is still organized in clusters, but individual neurons can hop from cluster to
cluster. Noise can actually induce and sustain such a state below the threshold
of synaptic strength. We do find a qualitative difference in the firing
patterns between small ($\sim 10$ neurons) and large ($\sim 1000$ neurons)
networks. We determine the information content of the spike trains in terms of
two separate contributions: the spike time jitter around cluster firing times,
and the hopping from cluster to cluster. We quantify the information loss due
to temporally correlated interspike intervals. Recent experiments on the locust
olfactory system and striatal neurons suggest that the nervous system may
actually use these two channels to encode separate and unique information.
