# What are coding schemes for timing channels

I know we can hide information in the inter-packet delays, e.g. we can generate a code-book that each code-word corresponds to a message and is generated by realization of a specific random process.

Is there a good, comprehensive resource about coding schemes like a “Poisson process”, or other processes?

For example: if the legitimate traffic is process $A$, can we make random variables according to that process and use permutations to represent different coderwords?

• A poisson process or a random process is not a coding scheme. Your question is not clear. – Chris Sep 2 '15 at 19:24

I am not sure if this is what you are looking for, however, the information theoretic capacity of a timing channel, where delays are manipulated, has been defined and analyzed in a number of papers, by using the Shannon formalism of maximizing the common information between the input and output to obtain/bound the capacity.

There is a tutorial which can get you started here. I am unsure if this tutorial is refereed or not, but it seems to introduce the basic concepts gently.

Basically you consider a queuing system such as ./G/1 (single server, general service time distribution) or ./M/1 (single server, exponential service time) and you manipulate the input arrival distribution to maximize the common information $I(X;Y)$ between the input $X$ and the output $Y$.

The first paper in this area was

V. Anantharam, S. Verdu, “Bits through queues”, IEEE. Trans. Inform. Theory, Vol. 42, No. 1, Jan, 1996

Also, if $C(\lambda)$ is the capacity of the pure timing channel, the quantity $$C_I = sup_{\lambda \leq \mu}≤[C(\lambda) + λC_0]$$ where $C_0$ is the information capacity of the information channel, may indeed be related to the question you asked, about not just delays, but permutations of "marked(?)" packets/impulses in some fashion.

Chasing the references to the Anantharam/Verdu paper is probably a good idea.