Year: 2025
Type: article
Abstract: In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduceredundancyto ensurerecoverabilityfrom failure. To get the most out of every byte, practitioners and theorists have introduced the framework ofmaximal recoverability(MR) to study optimal error-correcting codes in various architectures. In this survey, we dive into the study of two families of MR codes: MR locally recoverable codes (LRCs) (also known as partial MDS codes) and grid codes (GCs). For both families of codes, we discuss the primary recoverability guarantees of each class of codes as well as what is known concerning optimal constructions of each class of codes. Along the way, we discuss many surprising connections between MR codes and broader questions in computer science and mathematics. For MR LRCs, the use of skew polynomial codes has unified many previous constructions. For MR GCs, the theory of higher order MDS codes shows that MR GCs can be used to construct optimal list-decodable codes. Furthermore, the optimally recoverable patterns of MR GCs have close ties to long-standing problems on the structural rigidity of graphs.
Authors: Joshua Brakensiek, Venkatesan Guruswami
Institution: University of California, Berkeley
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4416286249
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