Embedded bitstreams are generated by many source coders to allow the progressive reconstruction of the source at different bit rates from the prefixes of a single bitstream. In a packet transmission system, such bitstreams are packetized and transmitted over noisy channels. As part of packetization, an error correction coding scheme is often used to protect the packets against channel errors. It is well-known that the unequal error protection (UEP) of the packets usually results in a better end-to-end performance for the joint source-channel coding scheme compared to the less sophisticated equal error protection. Given a sequence of channel codes, the distortion-rate function of the source coder, and the channel conditions, the problem of assigning channel codes of different rates to different source packets under a constraint on the total bit budget or the total transmission rate is called rate allocation problem. Well-known cost functions for such an optimization problem are the average mean squared error (MSE) distortion, the average peak signal-to-noise-ratio (PSNR). We indiscriminately refer to the corresponding optimal solutions for these cost functions as distortion optimal.