Application-Driven Error Correction and Constrained Coding Solutions for Modern Conventional and DNA Data Storage

Date

2026-8

Author

İrimağzı, Canberk

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With the continuous rise in the amounts of data being processed and stored by modern applications, requirements from data storage devices keep getting higher. DNA data storage is a new technology that promises remarkable storage density and durability gains. However, this technology suffers from certain sources of error. In particular, sequences of long homopolymers as well as unbalanced G − C content (compared with A − T) result in system instability. Moreover, because of the nature of synthesis and sequencing (writing and reading), insertion, deletion, and substitution errors also emerge. In this work, we develop efficient constrained codes, namely DNA lexicographically-ordered constrained (D-LOCO) codes, to forbid long homopolymers and achieve data stream balance globally and locally. D-LOCO codes achieve capacity, and they offer low complexity encoding and decoding. Moreover, we use bridging patterns between consecutive codewords not only to preserve the constraint, but also to perform substitution error detection. Furthermore, we devise error-correction D-LOCO (EC D-LOCO) codes that are guaranteed to correct single substitution errors. The idea is to keep only D-LOCO codewords whose indices are divisible by a specific redundancy metric R(m) for error correction. We propose syndrome-like decoding, called residue decoding, in which a table is used to map the substitution error to the received word index modulo R(m) (the residue), where m is the codeword length. We find that R(m) is of order m2, which means EC D-LOCO codes approach the constrained coding capacity. We show that EC D-LOCO codes correct double-substitution errors as well with a success rate higher than 98.20% using a list-decoding procedure. EC D-LOCO codes can also be combined with sequence reconstruction techniques to handle other types of error. To further decrease R(m), which increases the EC D-LOCO rate, we provide an algorithm to minimize the residue-decoder table size. In this work as well, we offer a novel coding solution for modern conventional stor age systems. Multi-dimensional (MD) low-density parity-check (LDPC) codes are used to mitigate various sources of error and non-uniformity in these systems. We develop MD spatially-coupled (MD-SC) codes probabilistically using the gradient descent (GD) algorithm to exploit the available degrees of freedom. We show that the proposed MD-SC codes, named GD-MD codes, offer remarkable gains compared with the available literature codes

Subject Keywords

LOCO Coding, Error Correction, Substitution, Syndrome Decoding, DNA Data Storage, Spatially-Coupled Codes, Multi-Dimensional Codes, Gradient Descent, Finite-Length Optimization

URI

https://hdl.handle.net/11511/120995

Collections

Graduate School of Applied Mathematics, Thesis