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We study the transmission of a set of correlated sources $(U_1,\cdots,U_K)$over a Gaussian multiple access relay channel with time asynchronism betweenthe encoders. We assume that the maximum possible offset${\mathsf{d_{max}}}(n)$ between the transmitters grows without bound as theblock length $n \rightarrow \infty$ while the relative ratio${{\mathsf{d_{max}}}(n) / n}$ of the maximum possible offset to the blocklength asymptotically vanishes. For such a joint source-channel coding problem,and under specific gain conditions, we derive necessary and sufficientconditions for reliable communications and show that separate source andchannel coding achieves optimal performance. In particular, we first derive ageneral outer bound on the source entropy content for all channel gains as ourmain result. Then, using Slepian-Wolf source coding combined with the channelcoding scheme introduced in \cite{Cover_McEliece:81} on top of block Markovcoding, we show that the thus achieved inner bound matches the outer bound.Consequently, as a corollary, we also address the problem of sending a pair ofcorrelated sources over a two user interference channel in the same context.

Time-Asynchronous Gaussian Multiple Access Relay Channel with Correlated Sources