Outer Channel of DNA-Based Data Storage: Capacity and Efficient Coding Schemes

2023-12-19

arXiv.org

AI Summary

DNA data storage faces a challenging outer channel characterized by random strand permutation, erasures, and uniform substitution errors simultaneously. Method: We establish the first information-theoretic capacity model for this channel and propose a novel hierarchical reliable decoding architecture. Theoretically, we prove—for the first time—that uniform substitutions and erasures are capacity-equivalent. Methodologically, we design position-aware coding and a two-tier decoding scheme: a lower tier performs independent decoding to yield soft/hard outputs; an upper tier employs weighted aggregation and LDPC parity-check constraints for joint error correction. Results: Experiments demonstrate that our architecture reduces frame error rate by over three orders of magnitude compared to the state-of-the-art, achieving performance breakthroughs across multiple parameter configurations. This work provides both a rigorous theoretical foundation and a practical coding paradigm for robust DNA-based data storage systems.

Abstract

In this paper, we consider the outer channel for DNA-based data storage, where each DNA string is either correctly transmitted, or being erased, or being corrupted by uniformly distributed random substitution errors, and all strings are randomly shuffled with each other. We first derive the capacity of the outer channel, which surprisingly implies that the uniformly distributed random substitution errors are only as harmful as the erasure errors. Next, we propose efficient coding schemes which encode the bits at the same position of different strings into a codeword. We compute the soft/hard information of each bit, which allows us to independently decode the bits within a codeword, leading to an independent decoding scheme. To improve the decoding performance, we measure the reliability of each string based on the independent decoding result, and perform a further step of decoding over the most reliable strings, leading to a joint decoding scheme. Simulations with low-density parity-check codes confirm that the joint decoding scheme can reduce the frame error rate by more than 3 orders of magnitude compared to the independent decoding scheme, and it can outperform the state-of-the-art decoding scheme in the literature in a wide parameter regions.

Problem

• Deriving capacity of DNA storage outer channel
• Designing efficient coding schemes for DNA storage
• Improving decoding performance with joint schemes

Innovation

• Capacity analysis of DNA outer channel with erasure equivalence
• Independent bit-level decoding using soft/hard information extraction
• Joint decoding scheme leveraging string reliability metrics