Salami Slicing Trellis for Synchronization Errors in DNA Coding

2026-06-27

AI Summary

This work addresses the challenge of efficiently correcting mixed substitution, insertion, and deletion errors—collectively known as synchronization errors—in DNA storage channels, which existing coding schemes struggle to handle effectively. The authors propose a novel sausage-slicing trellis structure that, for the first time, integrates decision feedback with cross-chain polar codes in a unified framework. By alternately advancing trellis-based and polar decoding stages and dynamically updating the trellis state using decoded bit feedback, the method jointly mitigates all three error types. It enables bit-level posterior probability computation and facilitates cross-chain joint decoding, thereby closely approaching the theoretical capacity of the substitution–insertion–deletion channel. Simulation results demonstrate the superior performance of the proposed approach.

Abstract

On top of substitution errors, DNA storage channels suffer from both insertions and deletions at the same time. It is therefore important to develop error-correcting codes with efficient encoders and decoders that can combat all three types of noise. This paper introduces the salami-slicing trellis, a decision-feedback trellis that computes bitwise posterior probabilities along each strand and is coupled with polar codes across strands. The decoder alternates between advancing the trellises by one position and polar-decoding the resulting cross-strand slice, feeding the decoded bits back to the trellises for the next position. Simulations suggest that the resulting coding scheme approaches the conjectured capacity of the substitution-insertion-deletion channel.

Problem

• DNA storage
• synchronization errors
• insertions
• deletions
• substitution errors

Innovation

• salami-slicing trellis
• polar codes
• insertion-deletion-substitution channel
• decision-feedback decoding
• DNA data storage