TY - GEN

T1 - Vector network coding based on subspace codes outperforms scalar linear network coding

AU - Etzion, Tuvi

AU - Wachter-Zeh, Antonia

N1 - Publisher Copyright:
© 2016 IEEE.

PY - 2016/8/10

Y1 - 2016/8/10

N2 - This paper considers vector network coding based on rank-metric codes and subspace codes. Our main result is that vector network coding can significantly reduce the required field size compared to scalar linear network coding in the same multicast network. The achieved gap between the field size of scalar and vector network coding is in q(h-2)t2/h+o(t) for any q ≥ 2 and any even h ≥ 4, where t denotes the dimension of the vector solution and h the number of messages. If h ≥ 5 is odd, then the achieved gap of the field size between the scalar network coding solution and the vector network coding solution is q(h-3)t2/(h-1)+o(t). Previously, only a gap of constant size had been shown. This implies also the same gap between the field size in linear and non-linear scalar network coding for multicast networks. The results are obtained by considering several multicast networks which are variations of the well-known combination network.

AB - This paper considers vector network coding based on rank-metric codes and subspace codes. Our main result is that vector network coding can significantly reduce the required field size compared to scalar linear network coding in the same multicast network. The achieved gap between the field size of scalar and vector network coding is in q(h-2)t2/h+o(t) for any q ≥ 2 and any even h ≥ 4, where t denotes the dimension of the vector solution and h the number of messages. If h ≥ 5 is odd, then the achieved gap of the field size between the scalar network coding solution and the vector network coding solution is q(h-3)t2/(h-1)+o(t). Previously, only a gap of constant size had been shown. This implies also the same gap between the field size in linear and non-linear scalar network coding for multicast networks. The results are obtained by considering several multicast networks which are variations of the well-known combination network.

KW - combination network

KW - field size

KW - multicast networks

KW - rank-metric codes

KW - subspace codes

KW - vector network coding

UR - http://www.scopus.com/inward/record.url?scp=84985946841&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2016.7541639

DO - 10.1109/ISIT.2016.7541639

M3 - Conference contribution

AN - SCOPUS:84985946841

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1949

EP - 1953

BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016

Y2 - 10 July 2016 through 15 July 2016

ER -