Achievable Rates of Frequency-based Channels of Unlimited Input Resolution

We consider a molecular channel, in which messages are encoded to the frequency of objects (or concentration of molecules) in a pool, and whose output during reading time is a noisy version of the input frequencies, as obtained by sampling with replacement from the pool. Motivated by recent DNA storage techniques, we focus on the regime in which the input resolution is unlimited. We derive an achievable bound on the capacity of such channel, and compare it to both the achievable bounds under limited input resolution, as well as to a converse bound.