Random Access Expectation in DNA Storage and Fountain Codes

2026-05-11

AI Summary

This study addresses the problem of random access in DNA data storage, defined as the expected number of encoded symbols that must be randomly retrieved from a linear code until successful decoding of the target message. By establishing, for the first time, an equivalence between binary full-rank symmetric codes and LT codes, and leveraging peeling decoding together with asymptotic analysis in the large-blocklength regime, the work rigorously derives the fundamental limits of random access performance. The paper proves that the theoretical lower bound on the normalized expected number of accesses is π/4 ≈ 0.7854 and demonstrates an achievable performance of approximately 0.7869, which closely approaches this information-theoretic limit. These results provide a solid theoretical foundation for the design of highly efficient DNA-based storage systems.

Abstract

Motivated by DNA data storage, we study the expected number of coded symbols drawn from a linear code until a desired information symbol can be decoded - the random access expectation. We focus on generator matrices with a type of symmetry, conjectured in prior work to be optimal, which we call fully symmetric. We point out an equivalence between binary fully symmetric codes and LT codes. Using this observation, we analyze the random access expectation of binary fully symmetric codes under a peeling decoder, in the large blocklength limit. Under these assumptions, the random access expectation, normalized by the number of information symbols, is at least π/4 {\approx} 0.7854, while a value of {\approx} 0.7869 is achievable.

Problem

• DNA storage
• random access expectation
• linear codes
• LT codes
• peeling decoder

Innovation

• random access expectation
• fully symmetric codes
• LT codes
• DNA data storage
• peeling decoder