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arXiv · 2303.12990

On Constant-Weight Binary $B_2$-Sequences

Jin Sima·Yun-Han Li·Ilan Shomorony·Olgica Milenkovic
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Abstract

Motivated by applications in polymer-based data storage we introduced the new problem of characterizing the code rate and designing constant-weight binary $B_2$-sequences. Binary $B_2$-sequences are collections of binary strings of length $n$ with the property that the real-valued sums of all distinct pairs of strings are distinct. In addition to this defining property, constant-weight binary $B_2$-sequences also satisfy the constraint that each string has a fixed, relatively small weight $\omega$ that scales linearly with $n$. The constant-weight constraint ensures low-cost synthesis and uniform processing of the data readout via tandem mass spectrometers. Our main results include upper bounds on the size of the codes formulated as entropy-optimization problems and constructive lower bounds based on Sidon sequences.

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Jin Sima, Yun-Han Li, Ilan Shomorony, Olgica Milenkovic. 2023-03-23. On Constant-Weight Binary $B_2$-Sequences. https://arxiv.org/abs/2303.12990

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