TY - GEN

T1 - Codes for graph erasures

AU - Yohananov, Lev

AU - Yaakobi, Eitan

N1 - Publisher Copyright:
© 2017 IEEE.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the information is stored on the edges of an undirected graph, and a code over graphs is a set of graphs. A node failure is the event where all edges in the neighborhood of the failed node have been erased. We say that a code over graphs can tolerate ρ node failures if it can correct the erased edges of any ρ failed nodes in the graph. While the construction of such codes can be easily accomplished by MDS codes, their field size has to be at least), O(n2) when n is the number of nodes in the graph. In this work we present several constructions of codes over graphs with smaller field size. In particular, we present optimal codes over graphs correcting two node failures over the binary field, when the number of nodes in the graph is a prime number. We also present a construction of codes over graphs correcting ρ node failures for all ρ over a field of size at least (n + 1)/2-1, and show how to improve this construction for optimal codes when ρ = 2,3.

AB - Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the information is stored on the edges of an undirected graph, and a code over graphs is a set of graphs. A node failure is the event where all edges in the neighborhood of the failed node have been erased. We say that a code over graphs can tolerate ρ node failures if it can correct the erased edges of any ρ failed nodes in the graph. While the construction of such codes can be easily accomplished by MDS codes, their field size has to be at least), O(n2) when n is the number of nodes in the graph. In this work we present several constructions of codes over graphs with smaller field size. In particular, we present optimal codes over graphs correcting two node failures over the binary field, when the number of nodes in the graph is a prime number. We also present a construction of codes over graphs correcting ρ node failures for all ρ over a field of size at least (n + 1)/2-1, and show how to improve this construction for optimal codes when ρ = 2,3.

UR - http://www.scopus.com/inward/record.url?scp=85034105888&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8006647

DO - 10.1109/ISIT.2017.8006647

M3 - Conference contribution

AN - SCOPUS:85034105888

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 844

EP - 848

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

Y2 - 25 June 2017 through 30 June 2017

ER -