Uncertainty of Reconstructing Multiple Messages from Uniform-Tandem-Duplication Noise

01/20/2020

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by   Yonatan Yehezkeally, et al.

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A growing number of works have, in recent years, been concerned with in-vivo DNA as medium for data storage. This paper extends the concept of reconstruction codes for uniform-tandem-duplication noise to the model of associative memory, by finding the uncertainty associated with m>2 strings (where a previous paper considered m=2). That uncertainty is found as an asymptotic expression assuming code-words belong to a typical set of strings, consisting a growing fraction of the space size, converging to 1. Our findings show that this uncertainty scales polynomially in the message length.