Crate ad_ess 

This crate contains the arbitrary-distribution enumerative sphere shaping (AD-ESS) algorithm¹. The algorithm is accessible via the struct ad_ess::AdEss.

A second algorithm named reverse trellis shaping rts::RTS is also located in this repository. Unlike AD-ESS it uses energy based ordering of the sequences and thus always has minimal rate loss. Its complexity is the same as Laroias 1st algorithm².

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1. https://arxiv.org/pdf/2512.16808. ↩

2. R. Laroia, N. Farvardin and S. A. Tretter, “On optimal shaping of multidimensional constellations,” in IEEE Transactions on Information Theory, vol. 40, no. 4, pp. 1044-1056, July 1994, doi: 10.1109/18.335969. ↩

Modules

ad_ess

Arbitrary-Distribution ESS

rts

Reverse Trellis Shaping

trellis

Implementation of a trellis used in ad_ess::AdEss and rts::RTS

trellis_utils

utils