TY - GEN
T1 - Constructions of high-rate minimum storage regenerating codes over small fields
AU - Raviv, Netanel
AU - Silberstein, Natalia
AU - Etzion, Tuvi
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - This paper presents a new construction of high-rate minimum storage regenerating codes. In addition to a minimum storage in a node, these codes have the following two important properties: first, given storage ℓ in each node, the entire stored data can be recovered from any 2 log2 ℓ (any 3 log3 ℓ) nodes for two parities (for three parities, respectively); second, a helper node accesses the minimum number of its symbols for repair of a failed systematic node (access-optimality). The goal of this paper is to provide a construction of such optimal codes over the smallest possible finite fields. The generator matrix of these codes is based on perfect matchings of complete graphs and hypergraphs, and on a rational canonical form of matrices. For two parities, the field size is reduced by a factor of two for access-optimal codes compared to previous constructions. For three parities, the field size is 6 log3 ℓ+1 (or 3 log3 ℓ+1 for fields with characteristic 2), where only non-explicit constructions with exponential field size (in log3 ℓ) were known so far.
AB - This paper presents a new construction of high-rate minimum storage regenerating codes. In addition to a minimum storage in a node, these codes have the following two important properties: first, given storage ℓ in each node, the entire stored data can be recovered from any 2 log2 ℓ (any 3 log3 ℓ) nodes for two parities (for three parities, respectively); second, a helper node accesses the minimum number of its symbols for repair of a failed systematic node (access-optimality). The goal of this paper is to provide a construction of such optimal codes over the smallest possible finite fields. The generator matrix of these codes is based on perfect matchings of complete graphs and hypergraphs, and on a rational canonical form of matrices. For two parities, the field size is reduced by a factor of two for access-optimal codes compared to previous constructions. For three parities, the field size is 6 log3 ℓ+1 (or 3 log3 ℓ+1 for fields with characteristic 2), where only non-explicit constructions with exponential field size (in log3 ℓ) were known so far.
KW - MSR codes
KW - Regenerating codes
KW - access-optimal codes
KW - perfect matchings
KW - subspace condition
UR - http://www.scopus.com/inward/record.url?scp=84985920387&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2016.7541261
DO - 10.1109/ISIT.2016.7541261
M3 - Conference contribution
AN - SCOPUS:84985920387
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 61
EP - 65
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -