In the ideal case, you do not need to provide any error detection or error correction, and you do not need to compress the data: all you need to do is send information about how big the data is followed by the data itself.
But even if you have an ideal error free channel, doing some kind of lossless compression makes the transmission time shorter (well, depends on how compressible the data is), which is usually a useful property.
When you have a channel that has errors, you do not strictly need to compress the data. But (1) compressing the data will reduce the transmission time; and (2) the fewer bits you transmit, the fewer bits have a chance to be corrupted by the channel errors. Each detected but not corrected error requires retransmission which uses up channel capacity, so if you compress and so reduce total bits that can be affected by errors, you reduce the probability of needing retransmission, and so increase your average channel utilization.
There is no one answer to what kind of noisy channel needs to be used: it depends on the kind of environment you want to emulate. For example if you had random trucks driving inbetween sender and receiver, then the loss of bits is going to be more by blocks than independent such as would be the case for AWGN.
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