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Network coding has been widely used in the wireless uplink. To do coherent detection at the receiver, channel estimation is performed to collect the channel state information (CSI). For multi-user channels, the channel estimation overhead is sometimes formidable and may even outweigh the network coding gain. To address this issue, we study the non-coherent network coding in this work. Both the analog network coding (ANC) and digital network coding (DNC) are studied. Depending on the available CSI, we first develop the coherent and non-coherent maximum likelihood receivers. For ANC, as the non-coherent receivers have no closed form, we develop two suboptimum receivers according to the average link qualities. Next we study the error rates, and show that full diversity can always be achieved at extremely high signal-to-noise ratios (SNR) regardless of the CSI assumptions. However, the lack of perfect CSI would incur some diversity loss at modest SNRs. Besides, the performance loss of ANC is more serious due to the incapability to efficiently suppress multi-user interferences at the receivers. Extensive simulations are performed to verify our analytical results.