Optimal partial decode-and-forward rates for stochastically degraded Gaussian relay channels

For the Gaussian MIMO relay channel, we consider rates that can be achieved with the relay using the partial decode-and-forward (PDF) scheme, which is a generalization of the decode-and-forward (DF) scheme. Since for the general case the optimal channel input distribution for the PDF strategy is unknown, the maximum PDF rate for the Gaussian relay channel can only be determined if the best PDF strategy is equivalent to the DF strategy, point-to-point (P2P) transmission from source to destination, or if PDF achieves the cut-set bound (CSB), where Gaussian channel inputs are known to be optimal. In this paper, we identify and discuss two new such special cases, the stochastically degraded and the reversely stochastically degraded Gaussian relay channel.