  A distributed inference scheme which uses bounded transmission functions over
a Gaussian multiple access channel is considered. When the sensor measurements
are decreasingly reliable as a function of the sensor index, the conditions on
the transmission functions under which consistent estimation and reliable
detection are possible is characterized. For the distributed estimation
problem, an estimation scheme that uses bounded transmission functions is
proved to be strongly consistent provided that the variance of the noise
samples are bounded and that the transmission function is one-to-one. The
proposed estimation scheme is compared with the amplify-and-forward technique
and its robustness to impulsive sensing noise distributions is highlighted. In
contrast to amplify-and-forward schemes, it is also shown that bounded
transmissions suffer from inconsistent estimates if the sensing noise variance
goes to infinity. For the distributed detection problem, similar results are
obtained by studying the deflection coefficient. Simulations corroborate our
analytical results.
