A new achievable rate for the Gaussian parallel relay channel

Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the amplify-and-forward (AF) and the decode-and-forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). A rematch-and-forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In this paper, we propose a combined amplify-and-decode forward (CADF) scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein´s setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.