TY - GEN
T1 - Double and Triple Node-Erasure-Correcting Codes over Graphs
AU - Yohananov, Lev
AU - Efron, Yuval
AU - Yaakobi, Eitan
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/7/1
Y1 - 2019/7/1
N2 - 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 Zn. These codes are at most a single bit away from optimality.
AB - 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 Zn. These codes are at most a single bit away from optimality.
UR - http://www.scopus.com/inward/record.url?scp=85073156076&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2019.8849379
DO - 10.1109/ISIT.2019.8849379
M3 - Conference contribution
AN - SCOPUS:85073156076
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1582
EP - 1586
BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers
T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019
Y2 - 7 July 2019 through 12 July 2019
ER -