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The error exponent of fixed-length lossy source coding was established byMarton. Ahlswede showed that this exponent can be discontinuous at a rate $R$,depending on the probability distribution $P$ of the given information sourceand the distortion measure $d(x,y)$. The reason for the discontinuity in theerror exponent is that there exists $(d,\Delta)$ such that the rate-distortionfunction $R(\Delta|P)$ is neither concave nor quasi-concave with respect to$P$. Arimoto's algorithm for computing the error exponent in lossy sourcecoding is based on Blahut's parametric representation of the error exponent.However, Blahut's parametric representation is a lower convex envelope ofMarton's exponent, and the two do not generally agree. The contribution of thispaper is to provide a parametric representation that perfectly matches with theinverse function of Marton's exponent, thus avoiding the problem of therate-distortion function being non-convex with respect to $P$. The optimaldistribution for fixed parameters can be obtained using Arimoto's algorithm.Performing a nonconvex optimization over the parameters successfully yields theinverse function of Marton's exponent.

Computing the optimal error exponential function for fixed-length lossy coding in discrete memoryless sources