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A Practical Concatenated Coding Scheme for Noisy Shuffling Channels with Coset-based Indexing

Javad Haghighat, Tolga M. Duman

TL;DR

This paper develops a finite-length concatenated coding scheme that employs Reed-Solomon codes as outer codes and polar codes as inner codes, and utilizes an implicit indexing method based on cosets of the polar code, and derives analytical approximations for the frame error rate.

Abstract

Noisy shuffling channels capture the main characteristics of DNA storage systems where distinct segments of data are received out of order, after being corrupted by substitution errors. For realistic schemes with short-length segments, practical indexing and channel coding strategies are required to restore the order and combat the channel noise. In this paper, we develop a finite-length concatenated coding scheme that employs Reed-Solomon (RS) codes as outer codes and polar codes as inner codes, and utilizes an implicit indexing method based on cosets of the polar code. We propose a matched decoding method along with a metric for detecting the index that successfully restores the order, and correct channel errors at the receiver. Residual errors that are not corrected by the matched decoder are then corrected by the outer RS code. We derive analytical approximations for the frame error rate of the proposed scheme, and also evaluate its performance through simulations to demonstrate that the proposed implicit indexing method outperforms explicit indexing.

A Practical Concatenated Coding Scheme for Noisy Shuffling Channels with Coset-based Indexing

TL;DR

This paper develops a finite-length concatenated coding scheme that employs Reed-Solomon codes as outer codes and polar codes as inner codes, and utilizes an implicit indexing method based on cosets of the polar code, and derives analytical approximations for the frame error rate.

Abstract

Noisy shuffling channels capture the main characteristics of DNA storage systems where distinct segments of data are received out of order, after being corrupted by substitution errors. For realistic schemes with short-length segments, practical indexing and channel coding strategies are required to restore the order and combat the channel noise. In this paper, we develop a finite-length concatenated coding scheme that employs Reed-Solomon (RS) codes as outer codes and polar codes as inner codes, and utilizes an implicit indexing method based on cosets of the polar code. We propose a matched decoding method along with a metric for detecting the index that successfully restores the order, and correct channel errors at the receiver. Residual errors that are not corrected by the matched decoder are then corrected by the outer RS code. We derive analytical approximations for the frame error rate of the proposed scheme, and also evaluate its performance through simulations to demonstrate that the proposed implicit indexing method outperforms explicit indexing.
Paper Structure (6 sections, 16 equations, 5 figures)

This paper contains 6 sections, 16 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Proposed Coding Scheme
  4. Performance Analysis of the Proposed Scheme
  5. Numerical Results
  6. Conclusions

Figures (5)

  • Figure 1: Schematics of (a) noisy shuffling channel model, and (b) noisy shuffling-sampling channel model.
  • Figure 2: Block diagram of the proposed encoding and decoding scheme.
  • Figure 3: Comparison between $Pr\left(\mathcal{M}\left(\mathbf{\hat{x}}\right)\neq\mathcal{M}\left(\mathbf{x}\right)\right)$ values found by simulations and by analysis, when $n=n_{i}=128$, $R=\frac{1}{2}$, $\delta=0.05$.
  • Figure 4: FERs achieved by explicit indexing and matched decoding methods for noisy permutation channel, when $n_{0}=255$, $M=32$, $n_{i}=128$.
  • Figure 5: BER results for $k_{o}=215$ and noisy shuffling-sampling channels.