  In this paper, 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 index coding problem. Compared to the
maximum acyclic induced subgraph (MAIS) bound, the new bounds are always as
tight and can strictly outperform the MAIS bound. They can also be useful for
large problems, where the generally tighter polymatroidal bound is
computationally impractical. We then extend these new bounds to the
multi-server index coding problem. We also present a separate, but related
result where we identify a smaller single-server index coding instance,
compared to those identified in the literature, for which non-Shannon-type
inequalities are necessary to give a tighter converse.
