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.

翻译：异构噪声（或称状态相关噪声）下的符号间干扰（ISI）是扩散分子通信（MCvD）的一个决定性特征。然而，在以往的检测器设计中，并未系统考虑这种跨ISI状态的噪声方差依赖性。本文介绍了两种解码机制：信念自适应最大后验概率（BA-MAP）和软BA-MAP，它们明确地结合了分子计数信道的状态相关均值与方差。BA-MAP方法基于接收机当前的状态信念推导出每符号自适应的MAP阈值，而软BA-MAP方法则通过加权所有可能的ISI状态来计算混合对数似然比。仿真与信息论分析证实，所提出的检测器性能优于传统的均衡与固定阈值方法，在现实的MCvD场景下可实现高达100%的吞吐量提升。