DeepAI AI Chat
Log In Sign Up

Double and Triple Erasure-Correcting-Codes over Graphs

by   Lev Yohananov, et al.

In this paper we study array-based codes over graphs for correcting multiple node failures, with 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 _n. These codes are at most a single bit away from optimality.


page 1

page 2

page 3

page 4


Double and Triple Node-Erasure-Correcting Codes over Graphs

In this paper we study array-based codes over graphs for correcting mult...

Partial MDS Codes with Regeneration

Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure cor...

Correcting One Error in Non-Binary Channels with Feedback

In this paper, the problem of correction of a single error in q-ary symm...

Storage Codes with Flexible Number of Nodes

This paper presents flexible storage codes, a class of error-correcting ...

Codes for Correcting t Limited-Magnitude Sticky Deletions

Codes for correcting sticky insertions/deletions and limited-magnitude e...

Clustering-Correcting Codes

A new family of codes, called clustering-correcting codes, is presented ...

Algorithm-Based Checkpoint-Recovery for the Conjugate Gradient Method

As computers reach exascale and beyond, the incidence of faults will inc...