  We calculate the entanglement-assisted and unassisted channel capacities of
an exactly solvable spin star system, which models the quantum dephasing
channel. The capacities for this non-Markovian model exhibit a strong
dependence on the coupling strengths of the bath spins with the system, the
bath temperature, and the number of bath spins. For equal couplings and bath
frequencies, the channel becomes periodically noiseless.
