The total capacity of two-user multiple-access channel with binary output

The total capacity is evaluated for an arbitrary two-user multiple-access channel (MAC) with a binary output. The basic idea is to subdivide the MAC into a finite number of elementary MACs, i.e., a two-user MAC with binary inputs and binary outputs. These elementary MACs are classified further into two cases by the type of channel matrix. For each case, a necessary and sufficient condition of the total capacity is established by partially converting the ordinary Kuhn-Tucker condition. The solution of the necessary and sufficient condition determines the optimal distribution that achieves the total capacity of the elementary MAC. Then, for the arbitrary two-user MAC, it is shown that the total capacity is determined by evaluating the finite number of total capacities for those elementary MACs. An iteration procedure is proposed to calculate the total capacity of the MAC.