A note on the sum-rate-distortion function of some lossy source coding problems involving infinite-valued distortion functions

TL;DR

This paper demonstrates that for certain lossy source coding problems with infinite-valued distortion functions, the sum-rate-distortion can be approximated arbitrarily closely using finite truncations of the distortion functions, despite the usual expressions becoming invalid.

Contribution

It introduces a method to approximate sum-rate-distortion functions for problems with infinite-valued distortions using finite truncations, extending the applicability of single-letter formulas.

Findings

Sum-rate-distortion functions can be approximated via finite truncations.

Single-letter expressions remain valid for finite truncations.

Approximations can be made arbitrarily accurate.

Abstract

For a number of lossy source coding problems it is shown that even if the usual single-letter sum-rate-distortion expressions may become invalid for non-infinite distortion functions, they can be approached, to any desired accuracy, via the usual valid expressions for appropriately truncated finite versions of the distortion functions.