Deterministic Identification For MC ISI-Poisson Channel

TL;DR

This paper investigates deterministic identification capacity for a Poisson molecular communication channel with inter-symbol interference, deriving bounds and revealing how codebook size scales with code length and ISI growth.

Contribution

It introduces bounds on the deterministic identification capacity for DTPC with ISI and shows how codebook size scales with code length and ISI channel taps.

Findings

Codebook size scales as 2^{(n log n) R} with ISI growth

Optimizing ISI rate leads to linear scaling of identification rate with n

Deterministic encoding differs from traditional transmission rate scaling

Abstract

Several applications of molecular communications (MC) feature an alarm-prompt behavior for which the prevalent Shannon capacity may not be the appropriate performance metric. The identification capacity as an alternative measure for such systems has been motivated and established in the literature. In this paper, we study deterministic identification (DI) for the discrete-time \emph{Poisson} channel (DTPC) with inter-symbol interference (ISI) where the transmitter is restricted to an average and a peak molecule release rate constraint. Such a channel serves as a model for diffusive MC systems featuring long channel impulse responses and employing molecule counting receivers. We derive lower and upper bounds on the DI capacity of the DTPC with ISI when the number of ISI channel taps $K$ may grow with the codeword length $n$ (e.g., due to increasing symbol rate). As a key finding, we establish that for deterministic encoding, the codebook size scales as $2^{(n\log n)R}$ assuming that the number of ISI channel taps scales as $K = 2^{\kappa \log n}$, where $R$ is the coding rate and $\kappa$ is the ISI rate. Moreover, we show that optimizing $\kappa$ leads to an effective identification rate [bits/s] that scales linearly with $n$, which is in contrast to the typical transmission rate [bits/s] that is independent of $n$.