Abstract:We derive lower and upper bounds on the identification capacity of inverse Gaussian 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 inverse Gaussian 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., $\sim 2^{(n \log n)R_n}$, where $R_n$ is the coding rate.
From: Mohammad Javad Salariseddigh [view email]
[v1]
Thu, 7 May 2026 12:20:19 UTC (34 KB)
[v2]
Fri, 21 Aug 2026 08:07:05 UTC (41 KB)
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