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 postinhibitory 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 (approximately 10 neurons) and large (approximately 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.