  We prove the strong converse for the $N$-source Gaussian multiple access
channel (MAC). In particular, we show that any rate tuple that can be supported
by a sequence of codes with asymptotic average error probability less than one
must lie in the Cover-Wyner capacity region. Our proof consists of the
following. First, we perform an expurgation step to convert any given sequence
of codes with asymptotic average error probability less than one to codes with
asymptotic maximal error probability less than one. Second, we quantize the
input alphabets with an appropriately chosen resolution. Upon quantization, we
apply the wringing technique (by Ahlswede) on the quantized inputs to obtain
further subcodes from the subcodes obtained in the expurgation step so that the
resultant correlations among the symbols transmitted by the different sources
vanish as the blocklength grows. Finally, we derive upper bounds on achievable
sum-rates of the subcodes in terms of the type-II error of a binary hypothesis
test. These upper bounds are then simplified through judicious choices of
auxiliary output distributions. Our strong converse result carries over to the
Gaussian interference channel under strong interference as long as the sum of
the two asymptotic average error probabilities less than one.
