  As a basic information-theoretic model for fading relay channels, the
parallel relay channel is first studied, for which lower and upper bounds on
the capacity are derived. For the parallel relay channel with degraded
subchannels, the capacity is established, and is further demonstrated via the
Gaussian case, for which the synchronized and asynchronized capacities are
obtained. The capacity achieving power allocation at the source and relay nodes
among the subchannels is characterized. The fading relay channel is then
studied, for which resource allocations that maximize the achievable rates are
obtained for both the full-duplex and half-duplex cases. Capacities are
established for fading relay channels that satisfy certain conditions.
