Non-orthogonal transmission is considered to be one of the promising techniques for improving the throughput of the existing and future wireless communication networks. We concentrate on the transmission of both independent and correlated binary sources over a non-orthogonal multiple access relay channel (MARC), which consists of two sources, one relay, and one destination. The lossy decode-and-forward (DF), developed from the conventional DF, is adopted at the relay. Two time slots are required with non-orthogonal transmission over such network setup, while three time slots are required with the conventional orthogonal transmission. We analyze the outage probability of transmission of independent binary sources over the non-orthogonal MARC based on the theorem of multiple access channel (MAC) with a helper, which combines the Slepian-Wolf rate region and the MAC capacity region. For the performance verification, we implement a practical coding-decoding chain, which is applicable to the transmission of both independent and correlated binary sources. Exclusive-OR (XOR) based multiuser complete decoding is introduced at the relay node, and iterative joint decoding is utilized at the destination by taking into consideration the estimated intra-link error probability and correlation information between the sources. The practical simulation results are well matched with the theoretical analyses. Index Terms-Multiple access channel with a helper, multiple access relay channels, outage probability, Slepian-Wolf theorem, Shannon's lossy source-channel separation theorem.