Identification for Inverse Gaussian Channels
Provides fundamental limits for molecular communication systems, relevant to nanonetworking and biomedical applications.
The paper derives lower and upper bounds on the identification capacity of inverse Gaussian channels, showing super-exponential growth (~2^{(n log n)R}) under a peak time constraint.
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 codebook sizes. A central result reveals that, under a mild regularity condition on the noise, i.e., the stochastic first arrival time of an information-carrying molecule propagating via diffusion and drift to the receiver, the identification capacity exhibits super-exponential growth in the codeword length, $n,$ i.e., $\sim 2^{(n \log n)R},$ where $R$ is the coding rate.