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Identification for Inverse Gaussian Channels
Abstract
We derive lower and upper bounds on the identification capacity of inverse Gaussian (IG) channels, a fundamental model for molecular communications in fluid environments. The analysis considers deterministic encoding schemes under a peak time constraint and characterizes the asymptotic growth of optimal codebook sizes. In the converse, by leveraging the Borel-Cantelli lemma and the super-exponential near-zero tail behavior of the IG distribution, we establish an almost-sure lower bound on the first-passage time of drifting diffusing molecules. This leads to the conclusion that the identification capacity exhibits super-exponential growth with the codeword length n, i.e., ∼ 2(n log n)Rn, where Rn is the coding rate.
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BibTeX
@misc{salariseddigh2026identification,
title = {{Identification for Inverse Gaussian Channels}},
author = {Mohammad Javad Salariseddigh and Christian Deppe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.06103},
eprint = {2605.06103},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.06103},
}
RIS
TY - UNPB
TI - Identification for Inverse Gaussian Channels
AU - Mohammad Javad Salariseddigh
AU - Christian Deppe
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2605.06103
UR - https://arxiv.org/abs/2605.06103
AB - We derive lower and upper bounds on the identification capacity of inverse Gaussian (IG) channels, a fundamental model for molecular communications in fluid environments. The analysis considers deterministic encoding schemes under a peak time constraint and characterizes the asymptotic growth of optimal codebook sizes. In the converse, by leveraging the Borel-Cantelli lemma and the super-exponential near-zero tail behavior of the IG distribution, we establish an almost-sure lower bound on the first-passage time of drifting diffusing molecules. This leads to the conclusion that the identification capacity exhibits super-exponential growth with the codeword length n, i.e., ∼ 2^(n log n)R_n, where R_n is the coding rate.
ER -