Details
| Original language | English |
|---|---|
| Title of host publication | 2023 IEEE International Symposium on Information Theory, ISIT 2023 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 204-209 |
| Number of pages | 6 |
| ISBN (electronic) | 9781665475549 |
| Publication status | Published - 2023 |
| Externally published | Yes |
| Event | 2023 IEEE International Symposium on Information Theory, ISIT 2023 - Taipei, Taiwan Duration: 25 Jun 2023 → 30 Jun 2023 |
Publication series
| Name | IEEE International Symposium on Information Theory - Proceedings |
|---|---|
| Volume | 2023-June |
| ISSN (Print) | 2157-8095 |
Abstract
Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent work this approach was generalized to Rényi a-entropies. However, due to the lack of a traditional chain rule for Rényi entropies the picture remained incomplete. In this work we establish the missing link by providing Rényi chain rules connecting different definitions of Rényi entropies by Hayashi and Arimoto. This allows us to provide new information combining bounds for the Arimoto Rényi entropy. In the second part, we generalize the chain rule to the quantum setting and show how they allow us to generalize results and conjectures previously only given for the von Neumann entropy. In the special case of a = 2 we give the first optimal information combining bounds with quantum side information.
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Computer Science(all)
- Information Systems
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Applied Mathematics
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2023 IEEE International Symposium on Information Theory, ISIT 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 204-209 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2023-June).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Chain Rules for Rényi Information Combining
AU - Hirche, Christoph
AU - Guan, Xinyue
AU - Tomamichel, Marco
N1 - Funding Information: ACKNOWLEDGMENTS This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. H2020-MSCA-IF-2020-101025848. This research is supported by the National Research Foundation, Singapore and A*STAR under its CQT Bridging Grant.
PY - 2023
Y1 - 2023
N2 - Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent work this approach was generalized to Rényi a-entropies. However, due to the lack of a traditional chain rule for Rényi entropies the picture remained incomplete. In this work we establish the missing link by providing Rényi chain rules connecting different definitions of Rényi entropies by Hayashi and Arimoto. This allows us to provide new information combining bounds for the Arimoto Rényi entropy. In the second part, we generalize the chain rule to the quantum setting and show how they allow us to generalize results and conjectures previously only given for the von Neumann entropy. In the special case of a = 2 we give the first optimal information combining bounds with quantum side information.
AB - Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent work this approach was generalized to Rényi a-entropies. However, due to the lack of a traditional chain rule for Rényi entropies the picture remained incomplete. In this work we establish the missing link by providing Rényi chain rules connecting different definitions of Rényi entropies by Hayashi and Arimoto. This allows us to provide new information combining bounds for the Arimoto Rényi entropy. In the second part, we generalize the chain rule to the quantum setting and show how they allow us to generalize results and conjectures previously only given for the von Neumann entropy. In the special case of a = 2 we give the first optimal information combining bounds with quantum side information.
UR - http://www.scopus.com/inward/record.url?scp=85171485919&partnerID=8YFLogxK
U2 - 10.1109/ISIT54713.2023.10206941
DO - 10.1109/ISIT54713.2023.10206941
M3 - Conference contribution
AN - SCOPUS:85171485919
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 204
EP - 209
BT - 2023 IEEE International Symposium on Information Theory, ISIT 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2023 IEEE International Symposium on Information Theory, ISIT 2023
Y2 - 25 June 2023 through 30 June 2023
ER -