  We derive universal classical-quantum superposition coding and universal
classical-quantum multiple access channel code by using generalized packing
lemmas for the type method. Using our classical-quantum universal superposition
code, we establish the capacity region of a classical-quantum compound
broadcast channel with degraded message sets. Our universal classical-quantum
multiple access channel codes have two types of codes. One is a code with joint
decoding and the other is a code with separate decoding. The former universally
achieves corner points of the capacity region and the latter universally
achieves general points of the capacity region. Combining the latter universal
code with the existing result by Quantum Inf Process. 18, 246 (2019), we
establish a single-letterized formula for the capacity region of a
classical-quantum compound multiple access channel.
