The concept of digital channels of information flow is a serial-processing biased view of information: it applies a lot to serial systems like computers (which are still serial even with multiple "cores" since each operates independently of the other), but does not apply in the same way to massively parallel systems like the nervous system except perhaps to some very of the very low-level sensory information.
However, temporal coding has been a very active area of research. There are many different time scales on which neurons can potentially carry timing information. However, a digital bit stream is probably the least efficient one so you won't find much from neuroscience suggesting that type of pattern.
External timing is very important
Even given a very simple "analog-ish" neural code, where firing rates indicate some intensity of signal (for example, the tension on a tendon), there is also key temporal information to carry: the tension is happening now. It is not on a stack to be processed and conveyed in the most efficient encoding possible, it is happening presently, and the neuronal signal has to encode not just how much but also that it is occurring now: rate codes can do this to a fairly high precision.
Neuronal firing is a bit like a Geiger counter: the intensity is indicated by the rate of clicks, but there is a ton of additional information based on when those clicks occur. For example, as you move a Geiger counter nearer to a radiation source, the click rate increases dramatically. Any code that is more complex would introduce delays, and those delays necessarily result in a loss of temporal information.
Within the brain, there are definitely cases where temporal information is important to neural codes. The brain handles more complex information that changes over longer time scales than in the periphery, so it is possible to degrade temporal information to allow for deeper encoding schemes that combine generative models of the outside world with abstracted sensory information.
In particular, one can look at phase coding where neurons fire at a particular phase of an ongoing oscillation (Montemurro et al, 2008; Kayser et al, 2009). You could perhaps think of the ongoing oscillation as a "timing bit" because it provides a synchronizing point for relative timing of spikes.
In the hippocampus, phase coding is important for reconstruction of position information from neural spiking activity (O'Keefe et al, 1993; Jensen and Lisman, 2000).
Imagine a cortical neuron fires up to 100 Hz. You could digitize a signal by looking at spike/no spike within 10 ms bins, so every 10 ms you have 1 bit of information per neuron. Take an ensemble of 100 independent neurons, and you have 100 bits per 10 ms or 10,000 bits per second.
However, if you instead of 100 members of an ensemble, each 10 ms encodes not 1 * 100 bits, but 2^100 which is on the order of 1030 patterns every 10 ms. And this is without assuming a more complex temporal code where the order of firing within a brief window matters (Abeles et al, 1993).
There is good evidence that overlapping cell assemblies/ensembles exist (see for example Harris, 2005 for review) such that at any moment in time, the high-dimensional activity over the space of many neurons carries information, for example about the current sensory state.
Given that there are billions of neurons in a brain, ensemble coding makes bit rate not itself a limiting factor, though other constraints seem to make phase coding and other types of temporal info
Abeles, M., Bergman, H., Margalit, E., & Vaadia, E. (1993). Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. Journal of neurophysiology, 70(4), 1629-1638.
Harris, K. D. (2005). Neural signatures of cell assembly organization. Nature Reviews Neuroscience, 6(5), 399.
Jensen, O., & Lisman, J. E. (2000). Position reconstruction from an ensemble of hippocampal place cells: contribution of theta phase coding. Journal of neurophysiology, 83(5), 2602-2609.
Kayser, C., Montemurro, M. A., Logothetis, N. K., & Panzeri, S. (2009). Spike-phase coding boosts and stabilizes information carried by spatial and temporal spike patterns. Neuron, 61(4), 597-608.
Montemurro, M. A., Rasch, M. J., Murayama, Y., Logothetis, N. K., & Panzeri, S. (2008). Phase-of-firing coding of natural visual stimuli in primary visual cortex. Current biology, 18(5), 375-380.
O'Keefe, J., & Recce, M. L. (1993). Phase relationship between hippocampal place units and the EEG theta rhythm. Hippocampus, 3(3), 317-330.