Capacity achieving coding for the “OR” multiple access channel

We discuss a particular method of random access communications for asynchronous multiple access. We first compare the classical synchronous capacity with the respective asynchronous capacities for three different types of multiuser channels: the OR; the OR with intensity information and the XOR. We assume that the number of active users (inputs) T is large. In particular, we show that for instance, for M-ary input asynchronous access, multiple user interference reduces the capacity for the OR channel, from (M-1) to (ln2)(M-1) bits per transmission. However, for the OR with intensity information the channel capacity reduces from log₂(T+1) to 0.83 bits per transmission. For the binary input XOR, the capacity reduces from 1 to 0.32 bits per transmission. We conclude with a capacity achieving transmission method for the M-ary input OR channel and compare the presented method with earlier results