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

Author:

Yutaka Jitsumatsu

Keyword:

Computer Science, Information Theory, Information Theory (cs.IT)

journal:

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date:

2023-12-06 00:00:00

Abstract

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.