DNA diamond formulates a decomposable composite letter constellation model for DNA data storage

Oligonucleotide multiplicity is an inherent property of current DNA synthesis technology. Composite letter DNA storage exploits this property to improve logical density and reduce costs. However, letter indistinguishability and high molecular diversity pose challenges for reliable recovery. Here, we formulate a composite letter constellation model, named DNA diamond, consisting of 15 decomposable points. Inspired by set partitioning in telecommunications, we propose a two-stage letter detection framework that partitions these letters into four distinguishable subsets based on their discrete entropy. Furthermore, we incorporate encoded double-end indices to eliminate crosstalk between synthesis sites and simultaneously apply length filtering to suppress error propagation during readout. We validate the eight-letter and 15-letter composite letter DNA storage under DNA diamond model, each with 10,000 composite strands. The eight-letter system achieves a payload density of 2.5 bits per letter and enables error-free recovery at 14× coverage, surpassing the storage density of prior six-letter systems while requiring lower coverage. The full 15-letter constellation enables 3.125 bits per letter for payload with error-free recovery at 33× coverage, corresponding to a density of 2.23 bits per letter for payload plus indices. The proposed decomposable DNA diamond model advances a practical and scalable framework for high-density composite DNA data storage.