Assume a scenario which includes one source, one DF relay and one destination, and the direct link from the source to the destination is also considered.
If the CRC is employed, the relay only re-encodes and transmits the signal if it decodes correctly.
If not, the relay may transmit the erroneously decoded signal to the destination.
But I am not sure the difference between such two cases, in terms of the BER.
The BER is a property of the transmission path (not necessarily constant over time) and not affected by CRC or similar means. So there is no need for a relay station to check the CRC or decode/re-encode. BTW: BER is a fraction of the number of bits transmitted. Thus not relaying an already erroneous message will reduce the number of bits on the second leg, but normally not change the BER.
What CRC etc. are influencing: the effective error rate at the receiver location (in other terms: the probability of errors). If nothing is added, the effective error rate is the same as the BER. With CRC (adding redundancy), the correctness of the data received can be checked (erroneous data rejected), thus the effective error rate decreases.
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