On the Excess Distortion Exponent for Memoryless Gaussian Source-Channel Pairs

For a memoryless Gaussian source under the squared-error distortion fidelity criterion and a memoryless additive Gaussian noise channel with a quadratic power constraint at the channel input, upper and lower bounds for the joint source-channel coding excess distortion exponent (which is the exponent of the probability of excess distortion) are established. A necessary and sufficient condition for which the two bounds coincide is provided, thus exactly determining the exponent. This condition is observed to hold for a wide range of source-channel parameters