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

TL;DR

This paper presents a practical concatenated coding scheme combining Reed-Solomon and polar codes with implicit coset-based indexing to efficiently restore order and correct errors in noisy shuffling channels, such as DNA storage systems.

Contribution

It introduces a novel implicit indexing method using cosets of polar codes and a matched decoding approach, improving error correction and order restoration in noisy, unordered data channels.

Findings

The proposed scheme effectively restores data order in noisy shuffling channels.

Simulation results show the implicit indexing outperforms explicit indexing.

Analytical approximations accurately predict 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.