We study the transmission of a stationary ergodic Gaussian source over a packet erasure channel, which is a composite channel with degraded states. A broadcast channel code can be applied to a composite channel to obtain different rates in the different channel states. However, we show that a non-broadcast direct transmission strategy achieves a higher expected rate than the broadcast code, although it does not meet Shannon's definition of reliable communication since it does not guarantee which bits will be received. Each channel code has a matching source code: the multiresolution source code allows the broadcast channel code to transmit prioritized information, and the symmetric multiple description source code enables direct transmission of unprioritized information. The end-to-end expected distortions of these schemes are also compared.