Deterministic Identification for Molecular Communications over the Poisson Channel

TL;DR

This paper investigates deterministic identification capacity for molecular communication over the Poisson channel, revealing large capacity bounds and implications for biological systems, with numerical error analysis for finite codes.

Contribution

It establishes the DI capacity bounds for the Poisson channel and demonstrates the large capacity, providing insights into natural molecular identification systems.

Findings

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

Bounds on DI capacity are derived

Error rates decrease with longer codewords

Abstract

Various applications of molecular communications (MC) are event-triggered, and, as a consequence, the prevalent Shannon capacity may not be the right measure for performance assessment. Thus, in this paper, we motivate and establish the identification capacity as an alternative metric. In particular, we study deterministic identification (DI) for the discrete-time Poisson channel (DTPC), subject to an average and a peak power constraint, which serves as a model for MC systems employing molecule counting receivers. It is established that the codebook size for this channel scales as $2^{(n\log n)R}$, where $n$ and $R$ are the codeword length and coding rate, respectively. Lower and upper bounds on the DI capacity of the DTPC are developed. The obtained large capacity of the DI channel sheds light on the performance of natural DI systems such as natural olfaction, which are known for their extremely large chemical discriminatory power in biology. Furthermore, numerical simulations for the empirical miss-identification and false identification error rates are provided for finite length codes. This allows us to quantify the scale of error reduction in terms of the codeword length.