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A single unicast index coding problem (SUICP) with symmetric neighboringinterference (SNI) has equal number of $K$ messages and $K$ receivers, the$k$th receiver $R_{k}$ wanting the $k$th message $x_{k}$ and having theside-information $\mathcal{K}_{k}=(\mathcal{I}_{k} \cup x_{k})^c,$ where${I}_k= \{x_{k-U},\dots,x_{k-2},x_{k-1}\}\cup\{x_{k+1},x_{k+2},\dots,x_{k+D}\}$ is the interference with $D$ messages after and $U$messages before its desired message. Maleki, Cadambe and Jafar obtained thecapacity of this symmetric neighboring interference single unicast index codingproblem (SNI-SUICP) with $(K)$ tending to infinity and Blasiak, Kleinberg andLubetzky for the special case of $(D=U=1)$ with $K$ being finite. In this work,for any finite $K$ and arbitrary $D$ we obtain the capacity for the case$U=gcd(K,D+1)-1.$ Our proof is constructive, i.e., we give an explicitconstruction of a linear index code achieving the capacity.

Capacity of Some Index Coding Problems with Symmetric Neighboring Interference