---
_id: '17893'
abstract:
- lang: eng
  text: Strong data processing inequalities (SDPI) are an important object of study
    in Information Theory and have been well studied for f -divergences. Universal
    upper and lower bounds have been provided along with several applications, connecting
    them to impossibility (converse) results, concentration of measure, hypercontractivity,
    and so on. In this paper, we study Renyi divergence and the corresponding SDPI
    constant whose behavior seems to deviate from that of ordinary <1>-divergences.
    In particular, one can find examples showing that the universal upper bound relating
    its SDPI constant to the one of Total Variation does not hold in general. In this
    work, we prove, however, that the universal lower bound involving the SDPI constant
    of the Chi-square divergence does indeed hold. Furthermore, we also provide a
    characterization of the distribution that achieves the supremum when is equal
    to 2 and consequently compute the SDPI constant for Renyi divergence of the general
    binary channel.
acknowledgement: "The work in this paper was supported in part by the Swiss National
  Science Foundation under Grant 200364.\r\n"
article_processing_charge: No
arxiv: 1
author:
- first_name: Lifu
  full_name: Jin, Lifu
  last_name: Jin
- first_name: Amedeo Roberto
  full_name: Esposito, Amedeo Roberto
  id: 9583e921-e1ad-11ec-9862-cef099626dc9
  last_name: Esposito
- first_name: Michael
  full_name: Gastpar, Michael
  last_name: Gastpar
citation:
  ama: 'Jin L, Esposito AR, Gastpar M. Properties of the strong data processing constant
    for Rényi divergence. In: <i>Proceedings of the 2024 IEEE International Symposium
    on Information Theory</i>. Institute of Electrical and Electronics Engineers;
    2024:3178-3183. doi:<a href="https://doi.org/10.1109/ISIT57864.2024.10619367">10.1109/ISIT57864.2024.10619367</a>'
  apa: 'Jin, L., Esposito, A. R., &#38; Gastpar, M. (2024). Properties of the strong
    data processing constant for Rényi divergence. In <i>Proceedings of the 2024 IEEE
    International Symposium on Information Theory</i> (pp. 3178–3183). Athens, Greece:
    Institute of Electrical and Electronics Engineers. <a href="https://doi.org/10.1109/ISIT57864.2024.10619367">https://doi.org/10.1109/ISIT57864.2024.10619367</a>'
  chicago: Jin, Lifu, Amedeo Roberto Esposito, and Michael Gastpar. “Properties of
    the Strong Data Processing Constant for Rényi Divergence.” In <i>Proceedings of
    the 2024 IEEE International Symposium on Information Theory</i>, 3178–83. Institute
    of Electrical and Electronics Engineers, 2024. <a href="https://doi.org/10.1109/ISIT57864.2024.10619367">https://doi.org/10.1109/ISIT57864.2024.10619367</a>.
  ieee: L. Jin, A. R. Esposito, and M. Gastpar, “Properties of the strong data processing
    constant for Rényi divergence,” in <i>Proceedings of the 2024 IEEE International
    Symposium on Information Theory</i>, Athens, Greece, 2024, pp. 3178–3183.
  ista: 'Jin L, Esposito AR, Gastpar M. 2024. Properties of the strong data processing
    constant for Rényi divergence. Proceedings of the 2024 IEEE International Symposium
    on Information Theory. ISIT: International Symposium on Information Theory, 3178–3183.'
  mla: Jin, Lifu, et al. “Properties of the Strong Data Processing Constant for Rényi
    Divergence.” <i>Proceedings of the 2024 IEEE International Symposium on Information
    Theory</i>, Institute of Electrical and Electronics Engineers, 2024, pp. 3178–83,
    doi:<a href="https://doi.org/10.1109/ISIT57864.2024.10619367">10.1109/ISIT57864.2024.10619367</a>.
  short: L. Jin, A.R. Esposito, M. Gastpar, in:, Proceedings of the 2024 IEEE International
    Symposium on Information Theory, Institute of Electrical and Electronics Engineers,
    2024, pp. 3178–3183.
conference:
  end_date: 2024-07-12
  location: Athens, Greece
  name: 'ISIT: International Symposium on Information Theory'
  start_date: 2024-07-07
corr_author: '1'
date_created: 2024-09-08T22:01:12Z
date_published: 2024-08-19T00:00:00Z
date_updated: 2025-09-08T09:18:00Z
day: '19'
department:
- _id: MaMo
doi: 10.1109/ISIT57864.2024.10619367
external_id:
  arxiv:
  - '2403.10656'
  isi:
  - '001304426903055'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: 'https://doi.org/10.48550/arXiv.2403.10656 '
month: '08'
oa: 1
oa_version: Preprint
page: 3178-3183
publication: Proceedings of the 2024 IEEE International Symposium on Information Theory
publication_identifier:
  isbn:
  - '9798350382846'
  issn:
  - 2157-8095
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Properties of the strong data processing constant for Rényi divergence
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...
---
_id: '17894'
abstract:
- lang: eng
  text: 'Sibson''s α -mutual information has received renewed attention recently in
    several contexts: concentration of measure under dependence, statistical learning,
    hypothesis testing, and estimation theory. In this work, we introduce several
    variational representations of Sibson''s α -mutual information: 1) as a supremum
    over joint distributions of (a combination of) KL divergences; and 2) as a supremum
    over functions of opportune expected values. Leveraging them, we produce a variety
    of novel and known results, including a generalization of transportation-cost
    inequalities and Fano''s inequality.'
acknowledgement: The work in this paper was supported in part by the Swiss National
  Science Foundation under Grant 200364.
article_processing_charge: No
author:
- first_name: Amedeo Roberto
  full_name: Esposito, Amedeo Roberto
  id: 9583e921-e1ad-11ec-9862-cef099626dc9
  last_name: Esposito
- first_name: Michael
  full_name: Gastpar, Michael
  last_name: Gastpar
- first_name: Ibrahim
  full_name: Issa, Ibrahim
  last_name: Issa
citation:
  ama: 'Esposito AR, Gastpar M, Issa I. Variational characterizations of Sibson’s
    α-mutual information. In: <i>Proceedings of the 2024 IEEE International Symposium
    on Information Theory </i>. Institute of Electrical and Electronics Engineers;
    2024:2110-2115. doi:<a href="https://doi.org/10.1109/ISIT57864.2024.10619378">10.1109/ISIT57864.2024.10619378</a>'
  apa: 'Esposito, A. R., Gastpar, M., &#38; Issa, I. (2024). Variational characterizations
    of Sibson’s α-mutual information. In <i>Proceedings of the 2024 IEEE International
    Symposium on Information Theory </i> (pp. 2110–2115). Athens, Greece: Institute
    of Electrical and Electronics Engineers. <a href="https://doi.org/10.1109/ISIT57864.2024.10619378">https://doi.org/10.1109/ISIT57864.2024.10619378</a>'
  chicago: Esposito, Amedeo Roberto, Michael Gastpar, and Ibrahim Issa. “Variational
    Characterizations of Sibson’s α-Mutual Information.” In <i>Proceedings of the
    2024 IEEE International Symposium on Information Theory </i>, 2110–15. Institute
    of Electrical and Electronics Engineers, 2024. <a href="https://doi.org/10.1109/ISIT57864.2024.10619378">https://doi.org/10.1109/ISIT57864.2024.10619378</a>.
  ieee: A. R. Esposito, M. Gastpar, and I. Issa, “Variational characterizations of
    Sibson’s α-mutual information,” in <i>Proceedings of the 2024 IEEE International
    Symposium on Information Theory </i>, Athens, Greece, 2024, pp. 2110–2115.
  ista: 'Esposito AR, Gastpar M, Issa I. 2024. Variational characterizations of Sibson’s
    α-mutual information. Proceedings of the 2024 IEEE International Symposium on
    Information Theory . ISIT: International Symposium on Information Theory, 2110–2115.'
  mla: Esposito, Amedeo Roberto, et al. “Variational Characterizations of Sibson’s
    α-Mutual Information.” <i>Proceedings of the 2024 IEEE International Symposium
    on Information Theory </i>, Institute of Electrical and Electronics Engineers,
    2024, pp. 2110–15, doi:<a href="https://doi.org/10.1109/ISIT57864.2024.10619378">10.1109/ISIT57864.2024.10619378</a>.
  short: A.R. Esposito, M. Gastpar, I. Issa, in:, Proceedings of the 2024 IEEE International
    Symposium on Information Theory , Institute of Electrical and Electronics Engineers,
    2024, pp. 2110–2115.
conference:
  end_date: 2024-07-12
  location: Athens, Greece
  name: 'ISIT: International Symposium on Information Theory'
  start_date: 2024-07-07
corr_author: '1'
date_created: 2024-09-08T22:01:12Z
date_published: 2024-08-19T00:00:00Z
date_updated: 2025-09-08T09:18:44Z
day: '19'
department:
- _id: MaMo
doi: 10.1109/ISIT57864.2024.10619378
external_id:
  isi:
  - '001304426902023'
isi: 1
language:
- iso: eng
month: '08'
oa_version: None
page: 2110-2115
publication: 'Proceedings of the 2024 IEEE International Symposium on Information
  Theory '
publication_identifier:
  isbn:
  - '9798350382846'
  issn:
  - 2157-8095
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Variational characterizations of Sibson's α-mutual information
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...
---
_id: '17895'
abstract:
- lang: eng
  text: We propose a concatenated code construction for a class of discrete-alphabet
    oblivious arbitrarily varying channels (AVCs) with cost constraints. The code
    has time and space complexity polynomial in the blocklength n . It uses a Reed-Solomon
    outer code, logarithmic blocklength random inner codes, and stochastic encoding
    by permuting the codeword before transmission. When the channel satisfies a condition
    called strong DS-nonsymmetrizability (a modified version of nonsymmetrizability
    originally due to Dobrushin and Stambler), we show that the code achieves a rate
    that for a variety of oblivious AVCs (such as classically studied error/erasure
    channels) match the known capacities.
acknowledgement: "The work of M. Langberg and A. D. Sarwate was supported in part
  by the US NSF under awards CCF-1909451 and CCF1909468. B. K. Dey was supported in
  part by the Bharti Centre\r\nfor Communication in IIT Bombay. "
article_processing_charge: No
author:
- first_name: B. K.
  full_name: Dey, B. K.
  last_name: Dey
- first_name: S.
  full_name: Jaggi, S.
  last_name: Jaggi
- first_name: M.
  full_name: Langberg, M.
  last_name: Langberg
- first_name: A. D.
  full_name: Sarwate, A. D.
  last_name: Sarwate
- first_name: Yihan
  full_name: Zhang, Yihan
  id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
  last_name: Zhang
  orcid: 0000-0002-6465-6258
citation:
  ama: 'Dey BK, Jaggi S, Langberg M, Sarwate AD, Zhang Y. Computationally efficient
    codes for strongly Dobrushin-Stambler nonsymmetrizable oblivious AVCs. In: <i>Proceedings
    of the 2024 IEEE International Symposium on Information Theory </i>. Institute
    of Electrical and Electronics Engineers; 2024:1586-1591. doi:<a href="https://doi.org/10.1109/ISIT57864.2024.10619362">10.1109/ISIT57864.2024.10619362</a>'
  apa: 'Dey, B. K., Jaggi, S., Langberg, M., Sarwate, A. D., &#38; Zhang, Y. (2024).
    Computationally efficient codes for strongly Dobrushin-Stambler nonsymmetrizable
    oblivious AVCs. In <i>Proceedings of the 2024 IEEE International Symposium on
    Information Theory </i> (pp. 1586–1591). Athens, Greece: Institute of Electrical
    and Electronics Engineers. <a href="https://doi.org/10.1109/ISIT57864.2024.10619362">https://doi.org/10.1109/ISIT57864.2024.10619362</a>'
  chicago: Dey, B. K., S. Jaggi, M. Langberg, A. D. Sarwate, and Yihan Zhang. “Computationally
    Efficient Codes for Strongly Dobrushin-Stambler Nonsymmetrizable Oblivious AVCs.”
    In <i>Proceedings of the 2024 IEEE International Symposium on Information Theory
    </i>, 1586–91. Institute of Electrical and Electronics Engineers, 2024. <a href="https://doi.org/10.1109/ISIT57864.2024.10619362">https://doi.org/10.1109/ISIT57864.2024.10619362</a>.
  ieee: B. K. Dey, S. Jaggi, M. Langberg, A. D. Sarwate, and Y. Zhang, “Computationally
    efficient codes for strongly Dobrushin-Stambler nonsymmetrizable oblivious AVCs,”
    in <i>Proceedings of the 2024 IEEE International Symposium on Information Theory
    </i>, Athens, Greece, 2024, pp. 1586–1591.
  ista: 'Dey BK, Jaggi S, Langberg M, Sarwate AD, Zhang Y. 2024. Computationally efficient
    codes for strongly Dobrushin-Stambler nonsymmetrizable oblivious AVCs. Proceedings
    of the 2024 IEEE International Symposium on Information Theory . ISIT: International
    Symposium on Information Theory, 1586–1591.'
  mla: Dey, B. K., et al. “Computationally Efficient Codes for Strongly Dobrushin-Stambler
    Nonsymmetrizable Oblivious AVCs.” <i>Proceedings of the 2024 IEEE International
    Symposium on Information Theory </i>, Institute of Electrical and Electronics
    Engineers, 2024, pp. 1586–91, doi:<a href="https://doi.org/10.1109/ISIT57864.2024.10619362">10.1109/ISIT57864.2024.10619362</a>.
  short: B.K. Dey, S. Jaggi, M. Langberg, A.D. Sarwate, Y. Zhang, in:, Proceedings
    of the 2024 IEEE International Symposium on Information Theory , Institute of
    Electrical and Electronics Engineers, 2024, pp. 1586–1591.
conference:
  end_date: 2024-07-12
  location: Athens, Greece
  name: 'ISIT: International Symposium on Information Theory'
  start_date: 2024-07-07
date_created: 2024-09-08T22:01:12Z
date_published: 2024-08-19T00:00:00Z
date_updated: 2025-09-08T09:19:25Z
day: '19'
department:
- _id: MaMo
doi: 10.1109/ISIT57864.2024.10619362
external_id:
  isi:
  - '001304426901091'
isi: 1
language:
- iso: eng
month: '08'
oa_version: None
page: 1586-1591
publication: 'Proceedings of the 2024 IEEE International Symposium on Information
  Theory '
publication_identifier:
  isbn:
  - '9798350382846'
  issn:
  - 2157-8095
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computationally efficient codes for strongly Dobrushin-Stambler nonsymmetrizable
  oblivious AVCs
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...