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This paper investigates in frequency-flat Rayleigh fading multiple access channel (MAC) the performances of Slepian-Wolf (SW)-based iterative spatial demapping (SW-ISM) for two correlated sources. The correlation between the sources is exploited in log-likelihood ratio (LLR) exchange via the vertical iteration (VI) loop between the two outer decoders. The results via computer simulations confirm that the proposed SW-ISM structure achieves excellent performances over frequency-flat Rayleigh fading MAC. Results of the SW and MAC rate regions analysis are also presented to demonstrate the effectiveness of the technique. Potential applications of the technique investigated in this paper are sensor and/or relay networks requiring high throughput.