Capacity of Symmetric Index Coding Problems With X-Network Setting With 2 x 2 Local Connectivity

In X-network setting with L x L local connectivity, we have a locally connected network where each receiver is connected to L consecutive base stations and each base station has a distinct message for each connected receiver. Maleki et al. modeled the X-network setting with L x L local connectivity as a multiple unicast index coding problem and proved that the capacity of symmetric index coding problems with locally connected X-network with K number of receivers and number of messages M = KL and K tending to infinity is (2/[L(L+1)]) and for finite number of receivers this was shown to be an upper bound on the capacity. In this letter: 1) we show that when L = 2 the upper bound is exact, i.e., the capacity is (1/3) and 2) for this case we give an explicit construction of optimal linear index codes to achieve this capacity by using interference alignment.