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Run-Length-Limited ISI-Mitigation (RLIM) Coding for Molecular Communication

Melih Şahin, Ozgur B. Akan

TL;DR

This work tackles inter-symbol interference in diffusion-based molecular communication by designing RLIM codes, a family of fixed-size run-length-limited codes $RLIM_i(n,k)$ that minimize the total number of 1-bits to boost per-symbol molecule budgets. A linear-time greedy decoder, equivalent to Viterbi decoding under a deterministic last-wins tie-break, enables efficient error correction and detection within the $(i,\infty)$-RLL constraint. Through extensive binomial and particle-tracking simulations, RLIM consistently achieves lower BER than classical RLL and other ISI-mitigation schemes across a broad range of channel parameters, detector schemes, and block lengths; dynamic thresholding further improves performance in drifting channels. The results demonstrate RLIM as a practical, low-complexity ISI-mitigation strategy for molecular communication with substantial implications for reliable nano-to-macro and bio-compatible communication systems.

Abstract

Inter-symbol interference (ISI) limits reliability in diffusion-based molecular communication (MC) channels. We propose RLIM, a family of run-length-limited (RLL) codes that form fixed-size codebooks by minimizing the total number of 1-bits, increasing the per-symbol molecule budget under standard power normalizations and thus improving reliability. We develop a provably optimal linear-time greedy decoder that is equivalent to Viterbi decoding under a deterministic last-wins tie-break and has lower computational complexity; empirically, it outperforms first-wins and random Viterbi variants on RLL baselines. Extensive binomial and particle-tracking simulations show that RLIM achieves lower bit error rate (BER) than classical RLL and other prominent coding schemes across a broad range of scenarios.

Run-Length-Limited ISI-Mitigation (RLIM) Coding for Molecular Communication

TL;DR

This work tackles inter-symbol interference in diffusion-based molecular communication by designing RLIM codes, a family of fixed-size run-length-limited codes that minimize the total number of 1-bits to boost per-symbol molecule budgets. A linear-time greedy decoder, equivalent to Viterbi decoding under a deterministic last-wins tie-break, enables efficient error correction and detection within the -RLL constraint. Through extensive binomial and particle-tracking simulations, RLIM consistently achieves lower BER than classical RLL and other ISI-mitigation schemes across a broad range of channel parameters, detector schemes, and block lengths; dynamic thresholding further improves performance in drifting channels. The results demonstrate RLIM as a practical, low-complexity ISI-mitigation strategy for molecular communication with substantial implications for reliable nano-to-macro and bio-compatible communication systems.

Abstract

Inter-symbol interference (ISI) limits reliability in diffusion-based molecular communication (MC) channels. We propose RLIM, a family of run-length-limited (RLL) codes that form fixed-size codebooks by minimizing the total number of 1-bits, increasing the per-symbol molecule budget under standard power normalizations and thus improving reliability. We develop a provably optimal linear-time greedy decoder that is equivalent to Viterbi decoding under a deterministic last-wins tie-break and has lower computational complexity; empirically, it outperforms first-wins and random Viterbi variants on RLL baselines. Extensive binomial and particle-tracking simulations show that RLIM achieves lower bit error rate (BER) than classical RLL and other prominent coding schemes across a broad range of scenarios.

Paper Structure

This paper contains 19 sections, 33 equations, 7 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. RLIM Coding and Codebook Derivation
  4. Detection
  5. Error Correction
  6. Equivalence with Viterbi Decoding and Complexity
  7. Analytical Estimation of Static Threshold
  8. Performance Evaluation
  9. Normalizations and Simulation Parameters
  10. Evaluation of Simulation Results
  11. Impact of Block Length on Performance
  12. Comparison Between RLL and RLIM
  13. Effects of Different Parameters
  14. Storage Requirements and Trade-offs
  15. Constraint-Level Coincidence with $(i,\infty)$–RLL in Drift-Free Channels
  16. ...and 4 more sections

Figures (7)

  • Figure 1: MC Channel Sahin2024
  • Figure 2: Error Correction Comparisons for RLL Codes with $t_s=200$$ms$, $\sigma_n^2=0$, and $r_0=$$10\,\, µm$
  • Figure 3: Detected Molecule Distributions for coding schemes RLIM$_i(n_i,16)$ with, $D = 79.4$$µm^2/s$, $r_R = 5$$µm$, $r_0 = 10$$µm$, $L$$= 200$, $\sigma_n^2=0$, and unnormalized signal interval and molecule counts of $t_s = 200$ ms, and $M = 1000$. This figures motivates $I_1=I_{\hat{0}}=3$ in (14) and (16).
  • Figure 4: MC Simulation Results for Different Block Lengths. Abbreviations: “o.d.” = optimal dynamic, “o.s.” = optimal static, “e.s.” = estimated static.
  • Figure 4: MC Simulation Results for Different Parameters
  • ...and 2 more figures