Extended Shannon´s inequality and the asymptotic capacity of T-user binary adder channel

An extension of Shannon´s inequality for discrete probability distribution with an infinite number of elements is considered. As an application, the asymptotic capacity of the T-user binary adder channel is exactly determined. The previously known asymptotically good (but not very) T-user code of Chang and Weldon (1979) is shown to be far from asymptotically very good. It is thus concluded that the achievability problem of the asymptotic capacity remains open