Title: Index coding with erroneous side information,
Abstract: In this paper, new index coding problems are studied, where each receiver has
erroneous side information. Although side information is a crucial part of
index coding, the existence of erroneous side information has not yet been
considered. We study an index code with receivers that have erroneous side
information symbols in the error-free broadcast channel, which is called an
index code with side information errors (ICSIE). The encoding and decoding
procedures of the ICSIE are proposed, based on the syndrome decoding. Then, we
derive the bounds on the optimal codelength of the proposed index code with
erroneous side information. Furthermore, we introduce a special graph for the
proposed index coding problem, called a $\delta_s$-cycle whose properties are
similar to those of the cycle in the conventional index coding problem.
Properties of the ICSIE are also discussed in the $\delta_s$-cycle and clique.
Finally, the proposed ICSIE is generalized to an index code for the scenario
having both additive channel errors and side information errors, called a
generalized error correcting index code (GECIC).