Optimal scalar linear codes for single unicast neighboring interference symmetric index coding

An index coding problem is symmetric if relative to its position, each receiver has identical sets of wanted messages and side information. We provide an algorithm to construct an optimal length scalar linear code for single unicast symmetric index coding problems with neighboring interference. First we compute the minimum number of independent dimensions required to avoid interference and show this number to be equal to the minimum possible length of a scalar linear index code. A code construction is provided that gives the optimal scalar linear index code. Further, we have identified the one-sided neighboring antidotes single unicast symmetric index coding problem as a special case of the neighboring interference problem and have constructed an optimal scalar linear index code for the former.