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Locality in Index Coding for Large Min-Rank by Natarajan, Lakshmi; Dau, Hoang; Krishnan, Prasad; Lalitha, V. is a scholarly article available to read on EtoBox.

What is Locality in Index Coding for Large Min-Rank about?

An index code is said to be locally decodable if each receiver can decode its demand using its side information and by querying only a subset of the transmitted codeword symbols instead of observing the entire codeword. Local decodability can be a beneficial feature in some communication scenarios, such as when the receivers can afford to listen to only a part of the transmissions because of limited availability of power. The locality of an index code is the ratio of the maximum number of codeword symbols queried by a receiver to the message length. In this paper we analyze the optimum locality of linear codes for the family of index coding problems whose min-rank is one less than the number of receivers in the network. We first derive the optimal trade-off between the index coding rate and locality with vector linear coding when the side information graph is a directed cycle. We then provide the optimal trade-off achieved by scalar linear coding for a larger family of problems, viz., problems where the min-rank is only one less than the number of receivers. While the arguments used for achievability are based on known coding techniques, the converse arguments rely on new results o

Author

Natarajan, Lakshmi; Dau, Hoang; Krishnan, Prasad; Lalitha, V.

Published

2019

Language

EN