Feedback analysis on the rate region of multi-user channels is a problem of great importance in information and communication theory. In this paper, the Slepian-Wolf multiple access relay channel (SW-MARC) with relay-sources feedback is studied as a more general model of MARC where feedback outputs are taken into consideration. First, an inner bound on the capacity region of the discret alphabet and memoryless (DM) model of this channel (DM-SW-MARC) is obtained using partial decode and forward (DF) strategy. Second, an outer bound on the capacity region is derived by applying Fano's inequality. Third, the DM results are extended to the continuous alphabet version, where an inner bound on the capacity region of the Gaussian MARC (GMARC) with relay-sources feedback is derived. Fourth, it is shown that our results include the important previous works on multiple-access channel (MAC) with feedback (Cover-Leung rate region) and without feedback (Slepian-Wolf (SW) rate region, etc.) as special cases. Finally, we investigate the effect of feedback and show that the presence of feedback enables the sources to understand each other's messages, which in turn allows the sources to cooperate to resolve the residual uncertainty at the receiver in an efficient way and at the same time, independent fresh information from the sources is superimposed upon the resolution information.

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