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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 single unicast index coding problem with symmetric neighboringinterference (SUICP-SNI) with $K$ tending to infinity and Blasiak, Kleinbergand Lubetzky for the special case of $(D=U=1)$ with $K$ being finite. In ourprevious work, we proved the capacity of SUICP-SNI for arbitrary $K$ and $D$with $U=\text{gcd}(K,D+1)-1$. This paper deals with near-optimal linear codeconstruction for SUICP-SNI with arbitrary $K,U$ and $D.$ For SUICP-SNI witharbitrary $K,U$ and $D$, we define a set of $2$-tuples such that for every$(a,b)$ in that set the rate $D+1+\frac{a}{b}$ is achieved by using vectorlinear index codes over every field. We prove that the set$\mathcal{\mathbf{S}}$ consists of $(a,b)$ such that the rate of constructedvector linear index codes are at most $\frac{K~\text{mod}~(D+1)}{\left \lfloor\frac{K}{D+1} \right \rfloor}$ away from a known lower bound on broadcast rateof SUICP-SNI. The three known results on the exact capacity of the SUICP-SNIare recovered as special cases of our results. Also, we give a low complexitydecoding procedure for the proposed vector linear index codes for theSUICP-SNI.

Near-Optimal Vector Linear Index Codes For Single Unicast Index Coding Problems with Symmetric Neighboring Interference