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

TL;DR

Two decoding mechanisms are introduced, Belief-Adaptive Maximum A Posteriori (BA-MAP) and Soft BA-MAP, that explicitly incorporate state-dependent means and variances of the molecular count channel that outperform conventional equalization and fixed-threshold methods.

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.

Figures (5)

• Figure 1: Belief-adaptive detection for molecular ISI channels with state-dependent noise. The MCvD channel is modeled as a finite-state ISI channel whose received-count statistics depend on the ISI state. The receiver maintains a causal belief over ISI states via forward recursion, and uses this belief to adapt detection. Soft BA-MAP performs symbol-wise MAP detection using belief-weighted Gaussian-mixture likelihoods, whereas BA-MAP reduces the mixture to a single belief-adaptive Gaussian surrogate via moment matching and applies a lightweight MAP threshold rule.
• Figure 2: Evolution of true-state Gaussian bands and adaptive thresholds for $N_{\mathrm{Tx}}=1000$ over 50 symbols. Shaded regions show the true-state means with $\pm1\sigma$ intervals for bit-0 and bit-1. Solid circular markers indicate the belief-adaptive MAP thresholds (BA-MAP); square markers show a fixed threshold at $\tau=90$. The point transmitter is located 12.5µm from the center of a spherical receiver of radius 5µm, with diffusion coefficient $D=79.4\frac{µm\squared }{s}$.
• Figure 3: Bit Error Rate (BER) performance of different decoding and equalization strategies, using the same system parameters as in Fig. \ref{['fig:bam_thresh']}.
• Figure 4: Maximum achievable information rates of proposed methodologies with respect to $T_s$, using the same system parameters as in Fig. \ref{['fig:bam_thresh']}.
• Figure 5: Maximum achievable throughputs of proposed methodologies with respect to $T_s$, using the same system parameters as in Fig. \ref{['fig:bam_thresh']}.