The Gaussian parallel relay network, introduced by Schein and Gallager, consists of a concatenation of a Gaussian additive broadcast channel from a single encoder to a layer of relays followed by a Gaussian multiple-access channel from the relays to the final destination (decoder), where all noises are independent. The original setup, with white channels of equal bandwidth, was recently extended by the authors to colored noises, by applying a coding scheme coined "Rematch and Forward" (R&F). In this work we broaden the scope of this approach in a few respects: We show that the R&F strategy may employ a variety of joint source/channel coding schemes over the broadcast section of the network, and present examples of such schemes. We make the connection to a predictive view of colored channels. We show how the R&F approach can be employed, and combined with other approaches, to a more general class of networks, which we call "Layered Networks". Finally we discuss a direction for improvement of the scheme by applying joint source/channel processing to the broadcast section as well.