CIF: Small: Recoverable systems, codes with local reconstruction, and interaction models

About This Grant

This project explores how information behaves in large-scale data storage systems that are designed to recover from hardware failures. Modern storage devices, such as glass-ceramic platters, arrange data in flat, grid-like patterns. To protect against data loss, information is encoded in a way that allows missing pieces to be reconstructed from surrounding bits, using a pre-set recovery rule. Over time, these systems handle vast and varied patterns of data. The research aims to understand how such data patterns evolve and organize themselves, from a statistical perspective. By identifying typical patterns and behaviors, the project will help improve the efficiency, reliability, and adaptability of storage systems—ultimately supporting better data preservation and easier access. In technical terms, the storage medium is modeled as an assignment of bits to nodes of an infinite two-dimensional grid, where the content of each node is determined by its neighbors according to a fixed recovery rule. A collection of such assignments—called a recoverable system—consists of all configurations satisfying this rule and forms the central object of study. The project aims to identify which recovery rules support systems that store the largest volume of the data on the medium, formalized as the topological entropy of the system. Introducing a temperature parameter into the model further increases in data density, assuming the system can tolerate a specified probability of errors. The system is defined through interaction energies between neighboring sites, with recoverable configurations corresponding to ground states. A key goal is to analyze equilibrium (Gibbs) distributions on the configuration space and to identify temperature regimes where phase transitions occur, leading to qualitatively different patterns of data stability. As another goal, the project aims at quantifying the system’s ability to retain information as it repeatedly restores data using the recovery rule over time, modeled as a Markov process on the space of the configurations. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.