“…These two ways of pairing lead to the following two sets of disjoint paths from the source to the destination: {P (1) i } = { (1, 1, c(3, 1)), (2, 2, c(3, 2))} and {P (2) i } = { (1, 2, c(3, 1)), (2, 1, c(3, 2))}, where the superscript j in {P (j) i } indicates a different set of path selection. By considering the equivalent channels from the source to the second relay, using the existing optimality result for dual-hop relaying [8], it is easy to see that c(3, 1) = 1 and c(3, 2) = 2 are optimal for {P (1) i }. Furthermore, we only need to show log 2 1 + γ SD (P (1) 1 ) + log 2 1 + γ SD P (1) 2 ≥ log 2 1 + γ SD P (2)…”