Error-Correcting Graph Codes
Swastik Kopparty, Aditya Potukuchi, and Harry Sha

TL;DR
This paper introduces error-correcting graph codes, extending classical error correction to graph structures, and presents new theoretical bounds, constructions, and analogues of classical codes like Reed-Solomon and BCH for graphs.
Contribution
It provides nonconstructive bounds, new graph code constructions analogous to Reed-Solomon and BCH codes, and explicit large-distance graph codes, advancing the theory of graph-based error correction.
Findings
Determined optimal rate vs. distance trade-offs nonconstructively.
Constructed graph code analogues of Reed-Solomon and concatenated codes.
Developed graph code analogues of dual-BCH codes with near-maximal distance.
Abstract
In this paper, we construct Error-Correcting Graph Codes. An error-correcting graph code of distance is a family of graphs on a common vertex set of size , such that if we start with any graph in , we would have to modify the neighborhoods of at least vertices in order to obtain some other graph in . This is a natural graph generalization of the standard Hamming distance error-correcting codes for binary strings. Yohananov and Yaakobi were the first to construct codes in this metric, constructing good codes for , and optimal codes for a large-alphabet analogue. We extend their work by showing 1. Combinatorial results determining the optimal rate vs. distance trade-off nonconstructively. 2. Graph code analogues of Reed-Solomon codes and code concatenation, leading to positive distance codes for all rates and positive rate codes for all…
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Taxonomy
TopicsFerroelectric and Negative Capacitance Devices · Error Correcting Code Techniques · Protein Degradation and Inhibitors
