Generalized Alignment Chain: Improved Converse Results for Index Coding
share
In this work, we study the information theoretic converse for the index coding problem. We generalize the definition for the alignment chain, introduced by Maleki et al., to capture more flexible relations among interfering messages at each receiver. Based on this, we derive improved converse results for the single-server centralized index coding problem. The new bounds uniformly outperform the maximum acyclic induced subgraph bound, and can be useful for large problems, for which the generally tighter polymatroidal bound becomes computationally impractical. We then extend these new bounds to the multi-server distributed index coding problem. We also present a separate, but related result where we identify a smaller centralized index coding instance compared to those identified in the literature, for which non-Shannon-type inequalities are necessary to give a tighter converse.
READ FULL TEXT