Low-Complexity Run-Length-Limited ISI-Mitigation (RLIM) Codes for Molecular Communication

TL;DR

This paper introduces a polynomial-space encoding and decoding scheme for run-length-limited ISI-mitigation codes in molecular communication, enabling larger codebooks and improved error performance under resource constraints.

Contribution

It replaces full codebook storage with an enumerative approach based on Cover's ranking, reducing storage from exponential to polynomial size.

Findings

The new scheme reduces storage complexity from exponential to polynomial.

Simulations show improved bit-error-rate performance with larger codebooks.

The approach is suitable for nano-scale molecular communication with limited resources.

Abstract

Molecular communication suffers from severe inter-symbol interference, which makes constrained coding essential for reliable transmission. Run-length-limited ISI-mitigation codes are attractive because they select low-weight constrained codebooks, reducing ISI while allowing more molecules to be assigned to each transmitted 1-symbol under the usual molecular-communication normalization. Previous results showed strong bit-error-rate performance for these codes, but their original realization required full codebook generation and storage. This exponential storage growth is unsuitable for resource-constrained molecular communication channels and also limits the exploration of larger information dimensions. This is particularly important for nano-scale molecular communication, where transmitter and receiver nodes are expected to operate under severe memory and computational constraints. This paper removes that realization bottleneck by replacing full codebook storage with an enumerative realization based on Cover's ranking framework, constant-weight run-length-limited counting, and cumulative weight-layer offsets. The resulting encoder and decoder preserve the selected RLIM codebooks and the original projection-based decoding behavior while storing only polynomial-size counting tables. Storage and runtime measurements confirm the resulting exponential-to-polynomial reduction, and diffusion-based molecular-communication simulations show that the newly accessible larger-dimensional RLIM regimes can improve the best attainable bit-error-rate performance in the tested settings.