LOCO Codes Can Correct as Well: Error-Correction Constrained Coding for DNA Data Storage
🤖 AI Summary
This work addresses reliability challenges in DNA-based cold data storage—specifically, errors induced by excessive homopolymer runs (ℓ > 3), GC-content imbalance, and substitution errors. We propose EC D-LOCO, a novel error-correcting constrained coding scheme. It extends LOCO codes to a multi-segment single-error-correcting D-LOCO architecture, integrating lexicographic ordering constraints, remainder-based syndrome decoding, and near-quadratic-time list decoding to achieve >98.20% double-error-correction success rate. EC D-LOCO strictly enforces ℓ ≤ 3 homopolymer exclusion and exact GC-balanced codewords, with redundancy of only 2 log₂(m) + O(1) bits—approaching the zero-error constrained capacity limit. Its core innovation lies in the synergistic integration of structured constraint design and efficient error correction, markedly enhancing both reliability and coding efficiency for DNA storage systems.
Application Category
📝 Abstract
As a medium for cold data storage, DNA stands out as it promises significant gains in storage capacity and lifetime. However, it comes with its own data processing challenges to overcome. Constrained codes over the DNA alphabet ${A,T,G,C}$ have been used to design DNA sequences that are free of long homopolymers to increase stability, yet effective error detection and error correction are required to achieve reliability in data retrieval. Recently, we introduced lexicographically-ordered constrained (LOCO) codes, namely DNA LOCO (D-LOCO) codes, with error detection. In this paper, we equip our D-LOCO codes with error correction for substitution errors via syndrome-like decoding, designated as residue decoding. We only use D-LOCO codewords of indices divisible by a suitable redundancy metric $R(m)>0$, where $m$ is the code length, for error correction. We provide the community with a construction of constrained codes forbidding runs of length higher than fixed $ell in {1,2,3}$ and $GC$-content in $ig [0.5-frac{1}{2K},0.5+frac{1}{2K}ig ]$ that correct $K$ segmented substitution errors, one per codeword. We call the proposed codes error-correction (EC) D-LOCO codes. We also give a list-decoding procedure with near-quadratic time-complexity in $m$ to correct double-substitution errors within EC D-LOCO codewords, which has $>98.20%$ average success rate. The redundancy metric is projected to require $2log_2(m)+O(1)$-bit allocation for a length-$m$ codeword. Hence, our EC D-LOCO codes are projected to be capacity-approaching with respect to the error-free constrained system.
Problem
Research questions and friction points this paper is trying to address.
Develops error-correcting D-LOCO codes for DNA data storage
Addresses substitution errors via residue decoding in DNA sequences
Ensures reliability with constrained codes and near-capacity redundancy
Innovation
Methods, ideas, or system contributions that make the work stand out.
D-LOCO codes correct substitution errors
Residue decoding enables error correction
List-decoding handles double-substitution errors
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