Joint Source–Channel Coding Excess Distortion Exponent for Some Memoryless Continuous-Alphabet Systems

We investigate the joint source-channel coding (JSCC) excess distortion exponent
EJ
(the exponent of the probability of exceeding a prescribed distortion level) for some memoryless communication systems with continuous alphabets. We first establish upper and lower bounds for
EJ
for systems consisting of 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. 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. As an application, we study the advantage in terms of the excess distortion exponent of JSCC over traditional tandem (separate) coding for Gaussian systems. A formula for the tandem exponent is derived in terms of the Gaussian source and Gaussian channel exponents, and numerical results show that JSCC often substantially outperforms tandem coding. The problem of transmitting memoryless Laplacian sources over the Gaussian channel under the magnitude-error distortion is also carried out. Finally, we establish a lower bound for
EJ
for a certain class of continuous source-channel pairs when the distortion measure is a metric.