We consider joint source-channel coding for a memoryless Gaussian source and an additive white Gaussian noise (AWGN) channel. A code is said to be robust if its performance is arbitrarily close to the theoretical limit for a wide range of channel noise conditions. The existence of robust codes depends on the ratio of the channel bandwidth to the source bandwidth-a quantity we called /spl rho/. We first show that when /spl rho/=1, robust codes do indeed exist. Secondly, no robust code exists for /spl rho//spl ne/1.