Double and Triple Node-Erasure-Correcting Codes over Complete Graphs

Lev Yohananov, Yuval Efron, Eitan Yaakobi

Research output: Contribution to journalArticlepeer-review


In this paper we study array-based codes over graphs for correcting multiple node failures. These codes have applications to neural networks, associative memories, and distributed storage systems. We assume that the information is stored on the edges of a complete undirected graph and a node failure is the event where all the edges in the neighborhood of a given node have been erased. A code over graphs is called ρ-node-erasure-correcting if it allows to reconstruct the erased edges upon the failure of any ρ nodes or less. We present a binary optimal construction for double-node-erasure correction together with an efficient decoding algorithm, when the number of nodes is a prime number. Furthermore, we extend this construction for triple-node-erasure-correcting codes when the number of nodes is a prime number and two is a primitive element in mathbb Z n. These codes are at most a single bit away from optimality.

Original languageEnglish
Article number8985404
Pages (from-to)4089-4103
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - 1 Jul 2020


  • Array codes
  • codes over graphs
  • crisscross erasures
  • rank metric codes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


Dive into the research topics of 'Double and Triple Node-Erasure-Correcting Codes over Complete Graphs'. Together they form a unique fingerprint.

Cite this