  We investigate the computation of Csiszar's bounds for the joint
source-channel coding (JSCC) error exponent, E_J, of a communication system
consisting of a discrete memoryless source and a discrete memoryless channel.
We provide equivalent expressions for these bounds and derive explicit formulas
for the rates where the bounds are attained. These equivalent representations
can be readily computed for arbitrary source-channel pairs via Arimoto's
algorithm. When the channel's distribution satisfies a symmetry property, the
bounds admit closed-form parametric expressions. We then use our results to
provide a systematic comparison between the JSCC error exponent E_J and the
tandem coding error exponent E_T, which applies if the source and channel are
separately coded. It is shown that E_T <= E_J <= 2E_T. We establish conditions
for which E_J > E_T and for which E_J = 2E_T. Numerical examples indicate that
E_J is close to 2E_T for many source-channel pairs. This gain translates into a
power saving larger than 2 dB for a binary source transmitted over additive
white Gaussian noise channels and Rayleigh fading channels with finite output
quantization. Finally, we study the computation of the lossy JSCC error
exponent under the Hamming distortion measure.
