Belief-Adaptive MAP Detection for Molecular ISI Channels with Heteroscedastic Noise

Abstract

Inter-symbol interference (ISI) with heteroscedastic (state-dependent) noise is a defining feature of molecular communication via diffusion (MCvD). However, such noise variance dependency across ISI states has not been systematically considered in prior detector designs. This letter introduces two decoding mechanisms, Belief-Adaptive Maximum A Posteriori (BA-MAP) and Soft BA-MAP, that explicitly incorporate state-dependent count means and variances of the molecular channel. The BA-MAP method derives per-symbol adaptive MAP thresholds based on the receiver's current state beliefs, whereas Soft BA-MAP computes mixture log-likelihood ratios by weighting all possible ISI states. Simulation and analyses confirm that the proposed detectors outperform conventional equalization and fixed-threshold methods, and approach ideal zero-decision-delay MAP detection with perfect ISI-state knowledge.