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

TL;DR

This paper introduces belief-adaptive MAP detection methods for molecular communication channels with heteroscedastic noise, significantly improving detection performance by accounting for state-dependent noise variances.

Contribution

It proposes two novel decoding mechanisms, BA-MAP and Soft BA-MAP, that explicitly incorporate state-dependent noise characteristics into molecular ISI detection.

Findings

Outperform conventional equalization and fixed-threshold methods

Achieve up to 100% throughput improvement

Validated through simulation and information-theoretic analysis

Abstract

Inter-symbol interference (ISI) with heteroscedastic, or 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 means and variances of the molecular count channel. The BA-MAP method derives per-symbol adaptive MAP thresholds based on the receiver's current state beliefs, whereas the Soft BA-MAP approach computes mixture log-likelihood ratios by weighting all possible ISI states. Simulation and information-theoretic analyses confirm that the proposed detectors outperform conventional equalization and fixed-threshold methods, achieving up to 100% throughput improvement under realistic MCvD settings.