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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 source distribution $P$ and the distortion measure $d(x,y)$.The reason for the discontinuity in the error exponent is that there exists adistortion measure $d(x,y)$ and a distortion level $\Delta$ such that therate-distortion function $R(\Delta|P)$ is neither concave nor quasi-concavewith respect to $P$. Arimoto's algorithm for computing the error exponent inlossy source coding is based on Blahut's parametric representation of the errorexponent. However, Blahut's parametric representation is a lower convexenvelope of Marton's exponent, and the two do not generally agree. A majorcontribution of this paper is to provide a parametric representation thatperfectly matches the inverse function of Marton's exponent, thereby preventingthe problems arising from the above-mentioned non-concavity of $R(\Delta|P)$.For fixed parameters, an optimal distribution can be obtained using Arimoto'salgorithm. By performing a nonconvex optimization over the parameters, theinverse function of Marton's exponent is obtained.

Computation of the optimal error exponent function for fixed-length lossy source coding in discrete memoryless sources