  The random propagation of molecules in a fluid medium is characterized by the
spontaneous diffusion law as well as the interaction between the environment
and molecules. In this paper, we embody the anomalous diffusion theory for
modeling and analysis in molecular communication. We employ H-diffusion to
model a non-Fickian behavior of molecules in diffusive channels. H-diffusion
enables us to model anomalous diffusion as the subordinate relationship between
self-similar parent and directing processes and their corresponding probability
density functions with two H-variates in a unified fashion. In addition, we
introduce standard H-diffusion to make a bridge of normal diffusion across
well-known anomalous diffusions such as space-time fractional diffusion,
Erdelyi-Kober fractional diffusion, grey Brownian motion, fractional Brownian
motion, and Brownian motion. We then characterize the statistical properties of
uncertainty of the random propagation time of a molecule governed by
H-diffusion laws by introducing a general class of molecular noise---called
H-noise. Since H-noise can be an algebraic tailed process, we provide a concept
of H-noise power using finite logarithm moments based on zero-order statistics.
Finally, we develop a unifying framework for error probability analysis in a
timing-based molecular communication system with a concept of signal-to-noise
power ratio.
