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Divergence-Minimizing Distribution Matching for Parallel Channels and Channels with Memory

  • Francesca Diedolo
  • Gerhard Kramer
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Abstract

Theory for distribution matchers (DMs) is extended to distributions with memory. The divergence-minimizing DM is shown to select the sequences with the highest target probability, as in the memoryless case. A scaling law for divergence is extended to distributions driven by innovation processes. The theory is applied to parallel additive white Gaussian noise channels. A modified enumerative sphere-shaping (ESS) method with a weighted energy constraint is used in implementations. An illustrative example with three channels shows that joint ESS across channels reduces the rate loss by a large factor compared to product DMs at short blocklengths. The gains are confirmed by simulations with probabilistic amplitude shaping and a 5G-NR low-density parity-check code.

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Cite

BibTeXRIS
BibTeX
@misc{diedolo2026divergenceminimizing,
  title = {{Divergence-Minimizing Distribution Matching for Parallel Channels and Channels with Memory}},
  author = {Francesca Diedolo and Gerhard Kramer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34779},
  eprint = {2609.34779},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34779},
}
RIS
TY  - UNPB
TI  - Divergence-Minimizing Distribution Matching for Parallel Channels and Channels with Memory
AU  - Francesca Diedolo
AU  - Gerhard Kramer
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34779
UR  - https://arxiv.org/abs/2609.34779
AB  - Theory for distribution matchers (DMs) is extended to distributions with memory. The divergence-minimizing DM is shown to select the sequences with the highest target probability, as in the memoryless case. A scaling law for divergence is extended to distributions driven by innovation processes. The theory is applied to parallel additive white Gaussian noise channels. A modified enumerative sphere-shaping (ESS) method with a weighted energy constraint is used in implementations. An illustrative example with three channels shows that joint ESS across channels reduces the rate loss by a large factor compared to product DMs at short blocklengths. The gains are confirmed by simulations with probabilistic amplitude shaping and a 5G-NR low-density parity-check code.
ER  -