In this study, according to whether the receiver has the channel state information (CSI) and knows the co-user's codebook or not, different maximum-likelihood (ML)-decoders are designed for a two user interference channel with slow flat fading. For each of the proposed ML-decoders, performance analysis based on pair-wise error probability is given. Although the importance of the CSI to the receiver is well investigated, these analyses reveal the fact that it also has much impact on the performance if the co-user's codebook is known to the receiver. The analyses also tell us that to decode out interference signals is not only unnecessary, but also reduces the performance, although it has been shown that the method of decoding out the interference signal first and then subtracting it from the received signal is an efficient way to achieve the capacity region of the Gaussian interference channel under some conditions and also is applied into practical systems.