Identification Capacity of the Discrete-Time Poisson Channel

Christian Deppe; Holger Boche; Wafa Labidi

Identification Capacity of the Discrete-Time Poisson Channel

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arxiv 2310.16507 v3 pith:ABL35HX4 submitted 2023-10-25 cs.IT math.IT

Wafa Labidi , Christian Deppe , Holger Boche This is my paper · ORCID

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keywords capacitychanneldtpcidentificationcodesdiscrete-timemessagemetric

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Numerous applications in the field of molecular communications (MC) such as healthcare systems are often event-driven. The conventional Shannon capacity may not be the appropriate metric for assessing performance in such cases. We propose the identification (ID) capacity as an alternative metric. Particularly, we consider randomized identification (RI) over the discrete-time Poisson channel (DTPC), which is typically used as a model for MC systems that utilize molecule-counting receivers. In the ID paradigm, the receiver's focus is not on decoding the message sent. However, he wants to determine whether a message of particular significance to him has been sent or not. In contrast to Shannon transmission codes, the size of ID codes for a Discrete Memoryless Channel (DMC) grows doubly exponentially fast with the blocklength, if randomized encoding is used. In this paper, we derive the capacity formula for RI over the DTPC subject to some peak and average power constraints. Furthermore, we analyze the case of state-dependent DTPC.

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Rate-reliability tradeoff for deterministic identification
cs.IT 2025-02 conditional novelty 7.0 of 10

Imposing exponentially small identification errors removes the superlinear message growth of deterministic identification and yields linear rates governed by the Minkowski dimension of the channel output set.

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