Optimal Index Codes With Near-Extreme Rates

@article{Dau2014OptimalIC,
  title={Optimal Index Codes With Near-Extreme Rates},
  author={Son Hoang Dau and Vitaly Skachek and Yeow Meng Chee},
  journal={IEEE Transactions on Information Theory},
  year={2014},
  volume={60},
  pages={1515-1527}
}
The min-rank of a digraph was shown to represent the length of an optimal scalar linear solution of the corresponding instance of the Index Coding with Side Information (ICSI) problem. In this paper, the graphs and digraphs of near-extreme min-ranks are studied. Those graphs and digraphs correspond to the ICSI instances having near-extreme transmission rates when using optimal scalar linear index codes. In particular, it is shown that the decision problem whether a digraph has min-rank two is… CONTINUE READING
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