Coding for Polymer-Based Data Storage

Polymer-based data-storage platforms use chains of binary synthetic polymers as recording media and read the content via tandem mass spectrometers. For such systems, we propose first known family codes that allows for both unique string reconstruction correction multiple errors. We consider two approaches: The approach pertains to asymmetric error-correction it is based on introducing redundancy scales linearly with number errors logarithmically length string. construction be uniquely reconstructed only its erroneous substring composition multiset. key idea behind our interleave (shifted) Catalan-Bertrand strings arbitrary “reflect” them so force prefixes suffixes same have different weights. asymptotic code rate scheme one, decoding accomplished a simplified version Backtracking algorithm used Turnpike problem. symmetric errors, polynomial characterization information adapt evaluation constructions this setting. In process, develop new efficient algorithms constant