TABLE OF CONTENTS When multiple users share the same channel, the channel capacity can no longer be characterized by a single number. At the extreme, if only one user occupies all signaling dimensions in the channel then the region reduces to the single-user capacity described in Chapter 4. However, since there is an infinite number of ways to divide the channel between many users, the multiuser channel capacity is characterized by a rate region, where each point in the region is a vector of achievable rates that can be maintained by all the users simultaneously with arbitrarily small error probability. The union of achievable rate vectors under all multiuser transmission strategies is called the capacity region of the multiuser system. The channel capacity is different for uplink channels and downlink channels because of the fundamental differences between these channel models. However, the fact that downlink and uplink channels seem to be mirror images implies that there might be a connection between their capacities. In fact, there is a duality between these channels that allows the capacity region of either channel to be obtained from the capacity region of the other. Note that, in the analysis of channel capacity, the downlink is commonly referred to as the broadcast channel (BC) and the uplink is commonly referred to as the multiple access channel (MAC [5]), and we will use this terminology in our capacity discussions. In this section we describe the capacity region of the BC, Section...
