Design a decoder-context-based frame-index code

Construct a frame-index coding scheme for reordered concatenated Gaussian sets that uses context already available to the decoder, such as the stable Morton ordering of L-GSC, to achieve a rate below 4.91 bits per Gaussian while preserving lossless frame assignment.

Background

Concatenating multiple dynamic 3DGS frames into one Gaussian set requires the decoder to determine the original frame of every decoded Gaussian. L-GSC, LGSCV, and GSCodec-S reorder the Gaussians but do not transmit a per-Gaussian frame index; the paper therefore charges these codecs a uniformly coded index cost of logâ‚‚30 = 4.91 bits per Gaussian for a 30-frame group of frames.

The paper observes that L-GSC's stable Morton ordering places co-located Gaussians from successive frames next to one another and in frame order. This suggests that a decoder-aware context model could encode the frame sequence more efficiently than a uniform code, but no such code is evaluated or designed.

References

A code below $4.91$ bits would have to use context that the decoder already has, such as the ordering of the codec: the Morton sort of L-GSC is stable, so co-located Gaussians of successive frames follow each other in frame order. We did not evaluate such a code and leave its design open.

— Robust, Estimator-Agnostic Dynamic 3DGS Compression  (2609.25633 - Wang et al., 22 Sep 2026) in Appendix, Section 'Notes on the Main Text', subsection 'Frame indices in the rates of L-GSC, LGSCV and GSCodec-S'