This paper studies the four-node Multiple Access Relay Channel (MARC) under quasi-static block Rayleigh fading channels and Gaussian noise environment. A relay employs Demodulate-and-Forward (DMF) protocol in order to help two channel-encoded sources to communicate with a destination. The contributions of the paper are threefold: i) we propose a Near Optimal Joint Network/Channel decoding (NO-JNCD) algorithm at the destination. The NO-JNCD employs Cooperative Maximum Ratio Combining (C-MRC) detector and the BCJR algorithm applied to a compound code which trellis consists of all possible states of two single trellises at sources; ii) we compute extended distance spectrum of the compound code containing input weights for each source and output weights on each fading channel; and iii) from the extended distance spectrum, we derive the Bit Error Rate (BER) upper bound for the compound code as well as for each source. It is shown by simulation that the proposed decoder provides performance very close to that of the optimal JNCD with both DMF and Decode-and-Forward (DF) relaying protocols. Finally, the analysis is checked by simulation.