ISI-Aware Code Design: A Linear Approach Towards Reliable Molecular Communication

Abstract: Intersymbol Interference (ISI) is a major bottleneck in Molecular Communication via Diffusion (MCvD), degrading system performance. This paper introduces two families of linear channel codes to mitigate ISI: Zero Pad Zero Start (ZPZS) and Zero Pad (ZP) codes, ensuring that each codeword avoids consecutive bit-1s. The ZPZS and ZP codes are then combined to form a binary ZP code, offering a higher code rate than linear ZP codes and allowing simple decoding via the Majority Location Rule (MLR). Additionally, a Leading One Zero Pad (LOZP) code is proposed, which relaxes zero-padding constraints by prioritizing the placement of bit-1s, achieving a higher rate than ZP. A closed-form expression is derived to compute expected ISI, showing it depends on the average bit-1 density in the codewords. ISI and Bit Error Rate (BER) performance are evaluated under two MCvD channel models: (i) without refresh, where past bits persist longer, and (ii) with refresh, where the channel is cleared after each reception. Results show that the LOZP code performs better in the refresh channel due to initial bit-1 placement, while ZP excels without refresh by reducing average bit-1 density. The asymptotic upper bound on code rate illustrates a trade-off between ISI and rate. Simulations demonstrate that ZP and LOZP codes improve BER by controlling bit-1 positions and density, providing better reliability in ISI-dominated regimes compared to conventional error-correcting codes.