On the Asymptotic Capacity of a Multiple-Access Channel

The asymptotic capacity for the memoryless $T$-user $q$-ary noiseless channel is studied under the condition that $T\to\infty$ and $q\to\infty$. Both coordinated and uncoordinated transmission are considered. It is shown that for both cases the maximum capacity is achieved for $T=q\ln 2$. For the coordinated case, the total capacity for T users is found to be $C_T\simeq q$, while for the uncoordinated case, $C_T\simeq\ln 2$.