1 research outputs found
Optimal Scalar Linear Index Codes for Symmetric and Neighboring Side-information Problems
A single unicast index coding problem (SUICP) is called symmetric neighboring
and consecutive (SNC) side-information problem if it has messages and
receivers, the th receiver wanting the th message and
having the side-information messages immediately after and
() messages immediately before . Maleki, Cadambe and Jafar
obtained the capacity of this SUICP(SNC) and proposed -dimensional
optimal length vector linear index codes by using Vandermonde matrices.
However, for a -dimensional vector linear index code, the transmitter needs
to wait for realizations of each message and hence the latency introduced
at the transmitter is proportional to . For any given single unicast index
coding problem (SUICP) with the side-information graph , MAIS() is used
to give a lowerbound on the broadcast rate of the ICP. In this paper, we derive
MAIS() of SUICP(SNC) with side-information graph . We construct scalar
linear index codes for SUICP(SNC) with length . We derive the
minrank() of SUICP(SNC) with side-information graph and show that the
constructed scalar linear index codes are of optimal length for SUICP(SNC) with
some combinations of and . For SUICP(SNC) with arbitrary and
, we show that the length of constructed scalar linear index codes are
atmost two index code symbols per message symbol more than the broadcast rate.
The given results for SUICP(SNC) are of practical importance due to its
relation with topological interference management problem in wireless
communication networks.Comment: 6 pages, 1 figure, 2 tables. arXiv admin note: text overlap with
arXiv:1801.0040