A New Upperbound on the Broadcast Rate of 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. The single unicast index coding problem with symmetric neighboring interference (SUICP-SNI) is motivated by topological interference management problems in wireless communication networks. Maleki, Cadambe and Jafar obtained the capacity of this SUICP-SNI with K tending to infinity and Blasiak, Kleinberg and Lubetzky for the special case of (D = U = 1) with K being finite. Finding the capacity of the SUICP-SNI for arbitrary K,D and U is a challenging open problem. In our previous work, for an SUICP-SNI with arbitrary K,D and U , we defined a set S of 2-tuples such that for every (a, b) in that set S, the rate D+1+ a b is achieved by using vector linear index codes over every finite field. In this paper, we give an algorithm to find the values of a and b such that (a, b) ∈ S and a b is minimum. We present a new upperbound on the broadcast rate of SUICP-SNI and prove that this upper bound coincides with the existing results on the exact value of the capacity of SUICP-SNI in the respective settings.