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On Designing Novel ISI-Reducing Single Error Correcting Codes in an MCvD System

Tamoghno Nath, Krishna Gopal Benerjee, Adrish Banerjee

TL;DR

This work tackles ISI and receiver noise in Molecular Communication via Diffusion (MCvD) channels by designing ISI-reducing single error-correcting codes with memory. The authors introduce the binary code family $\\mathcal{C}_{k,m}$ of length $n=k+m+1$, size $2^k$, and minimum distance $d=3$, built from recursive matrices to achieve asymptotic rates near $0.5$ and, in particular, enhanced performance for $\\mathcal{C}_{k,k+1}$. An accompanying encoding/decoding framework, including a post-encoding operation that redistributes consecutive ones, further reduces ISI and improves BER in noisy MCvD channels. Comparative simulations against Hamming, SOCC, ISI-free, and ISI-mtg codes show notable BER gains, especially under moderate noise ($\sigma_n^2$ up to about $120$) and channel memory $L=40$, highlighting practical gains for diffusion-based molecular communications. Overall, the study provides a concrete, implementable ECC design that jointly mitigates ISI and noise, with clear design rules and performance benefits demonstrated via simulations.

Abstract

Intersymbol Interference (ISI) has a detrimental impact on any Molecular Communication via Diffusion (MCvD) system. Also, the receiver noise can severely degrade the MCvD channel performance. However, the channel codes proposed in the literature for the MCvD system have only addressed one of these two challenges independently. In this paper, we have designed single Error Correcting Codes in an MCvD system with channel memory and noise. We have also provided encoding and decoding algorithms for the proposed codes, which are simple to follow despite having a non-linear code construction. Finally, through simulation results, we show that the proposed single ECCs, for given code parameters, perform better than the existing codes in the literature in combating the effect of ISI in the channel and improving the average Bit Error Rate (BER) performance in a noisy channel.

On Designing Novel ISI-Reducing Single Error Correcting Codes in an MCvD System

TL;DR

This work tackles ISI and receiver noise in Molecular Communication via Diffusion (MCvD) channels by designing ISI-reducing single error-correcting codes with memory. The authors introduce the binary code family of length , size , and minimum distance , built from recursive matrices to achieve asymptotic rates near and, in particular, enhanced performance for . An accompanying encoding/decoding framework, including a post-encoding operation that redistributes consecutive ones, further reduces ISI and improves BER in noisy MCvD channels. Comparative simulations against Hamming, SOCC, ISI-free, and ISI-mtg codes show notable BER gains, especially under moderate noise ( up to about ) and channel memory , highlighting practical gains for diffusion-based molecular communications. Overall, the study provides a concrete, implementable ECC design that jointly mitigates ISI and noise, with clear design rules and performance benefits demonstrated via simulations.

Abstract

Intersymbol Interference (ISI) has a detrimental impact on any Molecular Communication via Diffusion (MCvD) system. Also, the receiver noise can severely degrade the MCvD channel performance. However, the channel codes proposed in the literature for the MCvD system have only addressed one of these two challenges independently. In this paper, we have designed single Error Correcting Codes in an MCvD system with channel memory and noise. We have also provided encoding and decoding algorithms for the proposed codes, which are simple to follow despite having a non-linear code construction. Finally, through simulation results, we show that the proposed single ECCs, for given code parameters, perform better than the existing codes in the literature in combating the effect of ISI in the channel and improving the average Bit Error Rate (BER) performance in a noisy channel.

Paper Structure

This paper contains 6 sections, 4 theorems, 9 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Error Correction Code Design
  4. Encoding and Decoding
  5. Performance Evaluation
  6. Conclusion

Key Result

Proposition 1

For any positive integer $k$, the matrix $\mathbf{U}^{(k)}_{2^k,k}$ can be obtained recursively by with the initial condition $\mathbf{U}_{2,1}^{(1)} = \left[\right]^T$.

Figures (5)

  • Figure 1: Post-encoding operation of the code $\mathcal{C}_{k,m}$ for $m> k$.
  • Figure 2: Expected ISI comparison at $t_s = 0.3$s.
  • Figure 3: Average BER with $\sigma_n^2=0$ and $t_s = 0.4$s.
  • Figure 4: Average BER with $M = 300$ and $t_s = 0.3$s.
  • Figure 5: Average BER comparison with $\sigma_n^2 = 0$ and $t_s = 0.3$s.

Theorems & Definitions (11)

  • Proposition 1
  • Proposition 2
  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Remark 2
  • Remark 3: Post-Encoding Operation
  • Remark 4
  • ...and 1 more