On the Joint Source-Channel Coding Excess Distortion Exponent for 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 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. The problem of transmitting memoryless Laplacian sources over the Gaussian channel under the magnitudeerror distortion is also carried out. We also establish a lower bound for EJ for a certain class of continuous source-channel pairs when the distortion measure is a metric. The advantage in terms of the excess distortion exponent of JSCC over traditional tandem coding for Gaussian systems is next studied. A formula for the tandem exponent is derived in terms of the Gaussian source and Gaussian channel exponents. By numerically comparing the lower bound of the joint exponent and the upper bound of the tandem exponent, it is observed that, as for the discrete systems, JSCC often substantially outperforms tandem coding.