  The error exponent of fixed-length lossy source coding was established by
Marton. Ahlswede showed that this exponent can be discontinuous at a rate $R$,
depending on the source distribution $P$ and the distortion measure $d(x,y)$.
The reason for the discontinuity in the error exponent is that there exists a
distortion measure $d(x,y)$ and a distortion level $\Delta$ such that the
rate-distortion function $R(\Delta|P)$ is neither concave nor quasi-concave
with respect to $P$. Arimoto's algorithm for computing the error exponent in
lossy source coding is based on Blahut's parametric representation of the error
exponent. However, Blahut's parametric representation is a lower convex
envelope of Marton's exponent, and the two do not generally agree. A major
contribution of this paper is to provide a parametric representation that
perfectly matches the inverse function of Marton's exponent, thereby preventing
the problems arising from the above-mentioned non-concavity of $R(\Delta|P)$.
For fixed parameters, an optimal distribution can be obtained using Arimoto's
algorithm. By performing a nonconvex optimization over the parameters, the
inverse function of Marton's exponent is obtained.
