# Capacity of spike-based neuronal code

Assume that a neuronal population $$A$$ is connected to a neuronal population $$B$$ by a bunch of synapses - one-directional channels that propagate spikes. For simplicity assume that the current propagating through a synapse is 0 most of the time, and is 1 during a very short time-interval called a spike.

How to evaluate the maximal amount of information that can be transferred by a bunch of synapses in a unit of time under the assumption that all of the information is carried by spikes? It is known that for any given synapse the minimal distance between spikes is $$\Delta t$$. It is also known that the desired quantity of spikes, as well as their precise location is subject to noise from a known distribution.

The canonical approach to this problem in neuroscience is called rate-code:

1. Time is split into intervals of some arbitrary duration $$T$$
2. A probability distribution for the resulting number of spikes in such interval is obtained as function of the desired number of spikes.
3. Standard channel capacity methods are applied to this new discrete-time problem.

The problems with this approach are:

1. The result depends on the selected interval duration $$T$$
2. The result only uses number of spikes as information storage. It ignores that the approximate positions of individual spikes may store information in addition to that already given by their quantity

Questions:

• How to quantify the optimal capacity of such channels?
• There is a lot of literature in computational neuroscience using inter-spike-intervals as medium for information transfer, but most of it is very complicated and I'm scared that diving deeper into it may take a lot of time. Do the inter-spike-intervals fully describe all information that could be transferred by a channel? Briefly, how would one move from an inter-spike interval distribution to a bitrate of such a channel.
• I am not an expert in this, but maybe your problem is a manifestation of a general problem with timing channels. If one assumes the timing pattern is observed with infinite precision then the capacity of a timing channel is infinite. – kodlu Dec 13 '20 at 23:42
• @kodlu yes, certainly. Infinite precision in time would allow infinite information. But neurons, of course, have finite time-precision. You mention general timing channels. Can you recommend a good starting point to learn a bit about their theory? – Aleksejs Fomins Dec 14 '20 at 7:38