Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Identification over Poisson ISI Channels: Feedback and Molecular Applications

Yaning Zhao, Pau Colomer, Holger Boche, Christian Deppe

TL;DR

This work analyzes event-driven communication in molecular systems by studying deterministic identification (DI) over a discrete-time Poisson channel with inter-symbol interference (ISI) under peak and average power constraints. It delivers a tighter upper bound on DI capacity, showing $C_ ext{ID}^ ext{d}(\mathcal{P}) \le \frac{1+\kappa}{2}$ for a memory scaling $K(n,\kappa)=\lfloor 2^{\kappa \log n} \rfloor$, improving prior results. It also initiates the study of deterministic identification with feedback (DIF) on the same model, providing a constructive lower bound and proving that feedback yields double-exponential growth in code sizes, with a long-run lower bound $C_ ext{IDF}^ ext{d}(\mathcal{P}) \ge \frac{1}{2}\log(2\pi e \hat{E} T_s)$. The findings advance the theoretical understanding of event-driven MC and suggest feedback-driven strategies for more efficient, reliable biomedical signaling under memory and power constraints.

Abstract

Molecular communication (MC) enables information transfer via molecules, making it ideal for biomedical applications where traditional methods fall short. In many such scenarios, identifying specific events is more critical than decoding full messages, motivating the use of deterministic identification (DI). This paper investigates DI over discrete-time Poisson channels (DTPCs) with inter-symbol interference (ISI), a realistic setting due to channel memory effects. We improve the known upper bound on DI capacity under power constraints from $\frac{3}{2} + κ$ to $\frac{1 + κ}{2}$. Additionally, we present the first results on deterministic identification with feedback (DIF) in this context, providing a constructive lower bound. These findings enhance the theoretical understanding of MC and support more efficient, feedback-driven biomedical systems.

Identification over Poisson ISI Channels: Feedback and Molecular Applications

TL;DR

This work analyzes event-driven communication in molecular systems by studying deterministic identification (DI) over a discrete-time Poisson channel with inter-symbol interference (ISI) under peak and average power constraints. It delivers a tighter upper bound on DI capacity, showing for a memory scaling , improving prior results. It also initiates the study of deterministic identification with feedback (DIF) on the same model, providing a constructive lower bound and proving that feedback yields double-exponential growth in code sizes, with a long-run lower bound . The findings advance the theoretical understanding of event-driven MC and suggest feedback-driven strategies for more efficient, reliable biomedical signaling under memory and power constraints.

Abstract

Molecular communication (MC) enables information transfer via molecules, making it ideal for biomedical applications where traditional methods fall short. In many such scenarios, identifying specific events is more critical than decoding full messages, motivating the use of deterministic identification (DI). This paper investigates DI over discrete-time Poisson channels (DTPCs) with inter-symbol interference (ISI), a realistic setting due to channel memory effects. We improve the known upper bound on DI capacity under power constraints from to . Additionally, we present the first results on deterministic identification with feedback (DIF) in this context, providing a constructive lower bound. These findings enhance the theoretical understanding of MC and support more efficient, feedback-driven biomedical systems.
Paper Structure (6 sections, 3 theorems, 33 equations, 4 figures, 1 table)

This paper contains 6 sections, 3 theorems, 33 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model and Main Results
  3. Proof of Main Results
  4. Proof of Theorem \ref{['thm:main1']}
  5. Proof of Theorem \ref{['thm:main2']}
  6. Conclusion

Key Result

Theorem 2

Assume that the number of ISI scales sub-linearly with code length $n$, i.e., $K=\lfloor2^{\kappa\log{n}}\rfloor$, then the DI capacity of a DTPC with ISI $\mathcal{P}$ under peak power constraint $x_t\leq \hat{E}$ and average power constraint $\sum_{t=1}^nx_t\leq nE$ is bounded by

Figures (4)

  • Figure 1: DI over DTPC with ISI
  • Figure 2: DTPC with ISI for MC, with parameters $K=2$ and $[p_0,p_1,p_2]=[0.6,0.3,0.1]$
  • Figure 3: DIF over DTPC with ISI
  • Figure 4: Packing of many $S_{u_i}(n,r)$ spheres into the bigger $S_0(n,l)$, and the extended $S_0(n,l+r)$ containing them all.

Theorems & Definitions (5)

  • Definition 1
  • Theorem 2
  • Definition 3
  • Theorem 4
  • Lemma 5