Markov State--Space Modeling and Channel Characterization for DNA-Based Molecular Communication

In this paper, we study DNA-based molecular communication with microarray-style reception under reversible hybridization, where the bound-state observation exhibits both inter-symbol interference and colored counting noise. To capture these effects in a communication-oriented form, we develop a Markov state-space framework based on a voxelized reaction--diffusion model, in which a block-structured transition matrix describes molecular transport and binding/unbinding dynamics. For the microarray specialization, this representation yields the channel impulse response, the equilibrium gain, and a settling-time-based characterization of the effective channel memory. Building on the resulting symbol-rate observation model for on--off keying, we derive a grouped-binomial counting model and obtain a closed-form expression for the covariance of the counting noise. Based on these statistics, we further develop a differential-threshold detector and a finite-memory decision-feedback equalizer. Numerical results validate the theoretical correlation behavior and show that the relative performance of the proposed receivers depends strongly on the channel-memory regime.