Constructing Low-Redundancy Codes via Distributed Graph Coloring

Yuting Li; Ryan Gabrys; Farzad Farnoud

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arXiv · 2512.04197

Constructing Low-Redundancy Codes via Distributed Graph Coloring

Yuting Li·Ryan Gabrys·Farzad Farnoud

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Abstract

We present a general framework for constructing error-correcting codes using distributed graph coloring under the LOCAL model. Building on the correspondence between independent sets in the confusion graph and valid codes, we show that the color of a single vertex - consistent with a global proper coloring - can be computed in polynomial time using a modified version of Linial's coloring algorithm, leading to efficient encoding and decoding. Our results include: i) uniquely decodable code constructions for a constant number of errors of any type with redundancy twice the Gilbert-Varshamov bound; ii) list-decodable codes via a proposed extension of graph coloring, namely, hypergraph labeling; iii) an incremental synchronization scheme with reduced average-case communication when the edit distance is not precisely known; and iv) the first asymptotically optimal codes (up to a factor of 8) for correcting bursts of unbounded-length edits. Compared to syndrome compression, our approach is more flexible and generalizable, does not rely on a good base code, and achieves improved redundancy across a range of parameters.

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Yuting Li, Ryan Gabrys, Farzad Farnoud. 2025-12-03. Constructing Low-Redundancy Codes via Distributed Graph Coloring. https://arxiv.org/abs/2512.04197

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