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

A single unicast index coding problem (SUICP) with symmetric neighboring interference (SNI) has equal number of K messages and K receivers, the kth receiver Rk wanting the kth message xk and having the side-information Kk = (Ik ∪ xk) , where Ik = {xk−U , . . . , xk−2, xk−1} ∪ {xk+1, xk+2, . . . , xk+D} is the interference with D messages after and U messages before its desired message. Maleki, Cadambe and Jafar obtained the capacity of this single unicast index coding problem with symmetric neighboring interference (SUICP-SNI) withK tending to infinity and Blasiak, Kleinberg and Lubetzky for the special case of (D = U = 1) with K being finite. In our previous work, we proved the capacity of SUICP-SNI for arbitrary K and D with U = gcd(K,D+1)− 1. This paper deals with nearoptimal linear code construction for SUICP-SNI with arbitrary K,U and D. For SUICP-SNI with arbitrary K,U and D, we define a set of 2-tuples such that for every (a, b) in that set the rate D + 1 + a b is achieved by using vector linear index codes over every field. We prove that the set S consists of (a, b) such that the rate of constructed vector linear index codes are at most K mod (D+1) ⌊ K D+1 ⌋ away from a known lower bound on broadcast rate of SUICP-SNI. The three known results on the exact capacity of the SUICP-SNI are recovered as special cases of our results. Also, we give a low complexity decoding procedure for the proposed vector linear index codes for the SUICP-SNI.