  The exact values of the optimal symmetric rate point in the Cover--Leung
capacity region of the two-user union channel with complete feedback were
determined by Willems when the size of the input alphabet is 2, and by Vinck,
Hoeks and Post when the size is at least 6. We complete this line of research
when the size of the input alphabet is 3, 4 or 5. The proof hinges on the
technical lemma that concerns the maximal joint entropy of two independent
random variables in terms of their probability of equality. For the zero-error
capacity region, using superposition coding, we provide a practical
near-optimal communication scheme which improves all the previous explicit
constructions.
