Coded Information Retrieval for Block-Structured DNA-Based Data Storage

2026-03-17

AI Summary

This work addresses the challenge of efficient and recoverable block-structured data storage in DNA-based systems by formally introducing, for the first time, a “block-structured information retrieval” model. In this framework, $k$ information symbols are partitioned into two files that must be recovered atomically, with the goal of minimizing expected retrieval time. By analyzing the generator matrices of linear codes, the study establishes a linear lower bound based on disjoint recovery sets and a nonlinear bound derived from column-projective geometry. It identifies and proves a universal hyperbolic constraint, $ s_1/E_1 + s_2/E_2 \leq 1 $. Furthermore, the authors construct a proportional locality MDS code scheme that outperforms conventional global MDS codes in asymmetric scenarios and asymptotically achieves the derived bound as $ n \to \infty $, thereby generalizing and simplifying the optimality theory of MDS codes.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Other Foundations of Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Security and Privacy: Blockchains and distributed ledgers
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We study the problem of coded information retrieval for block-structured data, motivated by DNA-based storage systems where a database is partitioned into multiple files that must each be recoverable as an atomic unit. We initiate and formalize the block-structured retrieval problem, wherein $k$ information symbols are partitioned into two files $F_1$ and $F_2$ of sizes $s_1$ and $s_2 = k - s_1$. The objective is to characterize the set of achievable expected retrieval time pairs $\bigl(E_1(G), E_2(G)\bigr)$ over all $[n,k]$ linear codes with generator matrix $G$. We derive a family of linear lower bounds via mutual exclusivity of recovery sets, and develop a nonlinear geometric bound via column projection. For codes with no mixed columns, this yields the hyperbolic constraint $s_1/E_1 + s_2/E_2 \le 1$, which we conjecture to hold universally whenever $\max\{s_1,s_2\} \ge 2$. We analyze explicit codes, such as the identity code, file-dedicated MDS codes, and the systematic global MDS code, and compute their exact expected retrieval times. For file-dedicated codes we prove MDS optimality within the family and verify the hyperbolic constraint. For global MDS codes, we establish dominance by the proportional local MDS allocation via a combinatorial subset-counting argument, providing a significantly simpler proof compared to recent literature and formally extending the result to the asymmetric case. Finally, we characterize the limiting achievability region as $n \to \infty$: the hyperbolic boundary is asymptotically achieved by file-dedicated MDS codes, and is conjectured to be the exact boundary of the limiting achievability region.

Problem

• coded information retrieval
• block-structured data
• DNA-based storage
• expected retrieval time
• linear codes

Innovation

• coded information retrieval
• block-structured data
• DNA-based storage
• MDS codes
• retrieval time