---
_id: '14083'
abstract:
- lang: eng
text: "In this work we consider the list-decodability and list-recoverability of
arbitrary q-ary codes, for all integer values of q ≥ 2. A code is called (p,L)_q-list-decodable
if every radius pn Hamming ball contains less than L codewords; (p,\U0001D4C1,L)_q-list-recoverability
is a generalization where we place radius pn Hamming balls on every point of a
combinatorial rectangle with side length \U0001D4C1 and again stipulate that there
be less than L codewords.\r\nOur main contribution is to precisely calculate the
maximum value of p for which there exist infinite families of positive rate (p,\U0001D4C1,L)_q-list-recoverable
codes, the quantity we call the zero-rate threshold. Denoting this value by p_*,
we in fact show that codes correcting a p_*+ε fraction of errors must have size
O_ε(1), i.e., independent of n. Such a result is typically referred to as a \"Plotkin
bound.\" To complement this, a standard random code with expurgation construction
shows that there exist positive rate codes correcting a p_*-ε fraction of errors.
We also follow a classical proof template (typically attributed to Elias and Bassalygo)
to derive from the zero-rate threshold other tradeoffs between rate and decoding
radius for list-decoding and list-recovery.\r\nTechnically, proving the Plotkin
bound boils down to demonstrating the Schur convexity of a certain function defined
on the q-simplex as well as the convexity of a univariate function derived from
it. We remark that an earlier argument claimed similar results for q-ary list-decoding;
however, we point out that this earlier proof is flawed."
acknowledgement: "Nicolas Resch: Research supported in part by ERC H2020 grant No.74079
(ALGSTRONGCRYPTO). Chen Yuan: Research supported in part by the National Key Research
and Development Projects under Grant 2022YFA1004900 and Grant 2021YFE0109900, the
National Natural Science Foundation of China under Grant 12101403 and Grant 12031011.\r\nAcknowledgements
YZ is grateful to Shashank Vatedka, Diyuan Wu and Fengxing Zhu for inspiring discussions."
alternative_title:
- LIPIcs
article_number: '99'
article_processing_charge: Yes
author:
- first_name: Nicolas
full_name: Resch, Nicolas
last_name: Resch
- first_name: Chen
full_name: Yuan, Chen
last_name: Yuan
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
citation:
ama: 'Resch N, Yuan C, Zhang Y. Zero-rate thresholds and new capacity bounds for
list-decoding and list-recovery. In: 50th International Colloquium on Automata,
Languages, and Programming. Vol 261. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik; 2023. doi:10.4230/LIPIcs.ICALP.2023.99'
apa: 'Resch, N., Yuan, C., & Zhang, Y. (2023). Zero-rate thresholds and new
capacity bounds for list-decoding and list-recovery. In 50th International
Colloquium on Automata, Languages, and Programming (Vol. 261). Paderborn,
Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2023.99'
chicago: Resch, Nicolas, Chen Yuan, and Yihan Zhang. “Zero-Rate Thresholds and New
Capacity Bounds for List-Decoding and List-Recovery.” In 50th International
Colloquium on Automata, Languages, and Programming, Vol. 261. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2023. https://doi.org/10.4230/LIPIcs.ICALP.2023.99.
ieee: N. Resch, C. Yuan, and Y. Zhang, “Zero-rate thresholds and new capacity bounds
for list-decoding and list-recovery,” in 50th International Colloquium on Automata,
Languages, and Programming, Paderborn, Germany, 2023, vol. 261.
ista: 'Resch N, Yuan C, Zhang Y. 2023. Zero-rate thresholds and new capacity bounds
for list-decoding and list-recovery. 50th International Colloquium on Automata,
Languages, and Programming. ICALP: International Colloquium on Automata, Languages,
and Programming, LIPIcs, vol. 261, 99.'
mla: Resch, Nicolas, et al. “Zero-Rate Thresholds and New Capacity Bounds for List-Decoding
and List-Recovery.” 50th International Colloquium on Automata, Languages, and
Programming, vol. 261, 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023, doi:10.4230/LIPIcs.ICALP.2023.99.
short: N. Resch, C. Yuan, Y. Zhang, in:, 50th International Colloquium on Automata,
Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023.
conference:
end_date: 2023-07-14
location: Paderborn, Germany
name: 'ICALP: International Colloquium on Automata, Languages, and Programming'
start_date: 2023-07-10
date_created: 2023-08-20T22:01:13Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-08-21T07:26:01Z
day: '01'
ddc:
- '000'
department:
- _id: MaMo
doi: 10.4230/LIPIcs.ICALP.2023.99
external_id:
arxiv:
- '2210.07754'
file:
- access_level: open_access
checksum: a449143fec3fbebb092cb8ef3b53c226
content_type: application/pdf
creator: dernst
date_created: 2023-08-21T07:23:18Z
date_updated: 2023-08-21T07:23:18Z
file_id: '14091'
file_name: 2023_LIPIcsICALP_Resch.pdf
file_size: 1141497
relation: main_file
success: 1
file_date_updated: 2023-08-21T07:23:18Z
has_accepted_license: '1'
intvolume: ' 261'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: 50th International Colloquium on Automata, Languages, and Programming
publication_identifier:
isbn:
- '9783959772785'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Zero-rate thresholds and new capacity bounds for list-decoding and list-recovery
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 261
year: '2023'
...
---
_id: '12838'
abstract:
- lang: eng
text: We study the problem of high-dimensional multiple packing in Euclidean space.
Multiple packing is a natural generalization of sphere packing and is defined
as follows. Let N > 0 and L ∈ Z ≽2 . A multiple packing is a set C of points in
R n such that any point in R n lies in the intersection of at most L – 1 balls
of radius √ nN around points in C . Given a well-known connection with coding
theory, multiple packings can be viewed as the Euclidean analog of list-decodable
codes, which are well-studied for finite fields. In this paper, we derive the
best known lower bounds on the optimal density of list-decodable infinite constellations
for constant L under a stronger notion called average-radius multiple packing.
To this end, we apply tools from high-dimensional geometry and large deviation
theory.
acknowledgement: "YZ thanks Jiajin Li for making the observation given by Equation
(23). He also would like to thank Nir Ailon and Ely Porat for several helpful conversations
throughout this project, and Alexander Barg for insightful comments on the manuscript.\r\nYZ
has received funding from the European Union’s Horizon 2020 research and innovation
programme under grant agreement No 682203-ERC-[Inf-Speed-Tradeoff]. The work of
SV was supported by a seed grant from IIT Hyderabad and the start-up research grant
from the Science and Engineering Research Board, India (SRG/2020/000910)."
article_processing_charge: No
article_type: original
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. Multiple packing: Lower bounds via infinite constellations.
IEEE Transactions on Information Theory. 2023;69(7):4513-4527. doi:10.1109/TIT.2023.3260950'
apa: 'Zhang, Y., & Vatedka, S. (2023). Multiple packing: Lower bounds via infinite
constellations. IEEE Transactions on Information Theory. IEEE. https://doi.org/10.1109/TIT.2023.3260950'
chicago: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via
Infinite Constellations.” IEEE Transactions on Information Theory. IEEE,
2023. https://doi.org/10.1109/TIT.2023.3260950.'
ieee: 'Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via infinite constellations,”
IEEE Transactions on Information Theory, vol. 69, no. 7. IEEE, pp. 4513–4527,
2023.'
ista: 'Zhang Y, Vatedka S. 2023. Multiple packing: Lower bounds via infinite constellations.
IEEE Transactions on Information Theory. 69(7), 4513–4527.'
mla: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Infinite
Constellations.” IEEE Transactions on Information Theory, vol. 69, no.
7, IEEE, 2023, pp. 4513–27, doi:10.1109/TIT.2023.3260950.'
short: Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory 69 (2023) 4513–4527.
date_created: 2023-04-16T22:01:09Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-12-13T11:16:46Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/TIT.2023.3260950
external_id:
arxiv:
- '2211.04407'
isi:
- '001017307000023'
intvolume: ' 69'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2211.04407
month: '07'
oa: 1
oa_version: Preprint
page: 4513-4527
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Multiple packing: Lower bounds via infinite constellations'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 69
year: '2023'
...
---
_id: '14665'
abstract:
- lang: eng
text: We derive lower bounds on the maximal rates for multiple packings in high-dimensional
Euclidean spaces. For any N > 0 and L ∈ Z ≥2 , a multiple packing is a set C of
points in R n such that any point in R n lies in the intersection of at most L
- 1 balls of radius √ nN around points in C . This is a natural generalization
of the sphere packing problem. We study the multiple packing problem for both
bounded point sets whose points have norm at most √ nP for some constant P > 0,
and unbounded point sets whose points are allowed to be anywhere in R n . Given
a well-known connection with coding theory, multiple packings can be viewed as
the Euclidean analog of list-decodable codes, which are well-studied over finite
fields. We derive the best known lower bounds on the optimal multiple packing
density. This is accomplished by establishing an inequality which relates the
list-decoding error exponent for additive white Gaussian noise channels, a quantity
of average-case nature, to the list-decoding radius, a quantity of worst-case
nature. We also derive novel bounds on the list-decoding error exponent for infinite
constellations and closed-form expressions for the list-decoding error exponents
for the power-constrained AWGN channel, which may be of independent interest beyond
multiple packing.
article_processing_charge: No
article_type: original
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. Multiple packing: Lower bounds via error exponents. IEEE
Transactions on Information Theory. 2023. doi:10.1109/TIT.2023.3334032'
apa: 'Zhang, Y., & Vatedka, S. (2023). Multiple packing: Lower bounds via error
exponents. IEEE Transactions on Information Theory. IEEE. https://doi.org/10.1109/TIT.2023.3334032'
chicago: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via
Error Exponents.” IEEE Transactions on Information Theory. IEEE, 2023.
https://doi.org/10.1109/TIT.2023.3334032.'
ieee: 'Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via error exponents,”
IEEE Transactions on Information Theory. IEEE, 2023.'
ista: 'Zhang Y, Vatedka S. 2023. Multiple packing: Lower bounds via error exponents.
IEEE Transactions on Information Theory.'
mla: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Error
Exponents.” IEEE Transactions on Information Theory, IEEE, 2023, doi:10.1109/TIT.2023.3334032.'
short: Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory (2023).
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-16T00:00:00Z
date_updated: 2023-12-18T07:46:45Z
day: '16'
department:
- _id: MaMo
doi: 10.1109/TIT.2023.3334032
external_id:
arxiv:
- '2211.04408'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2211.04408
month: '11'
oa: 1
oa_version: Preprint
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: epub_ahead
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Multiple packing: Lower bounds via error exponents'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14751'
abstract:
- lang: eng
text: 'We consider zero-error communication over a two-transmitter deterministic
adversarial multiple access channel (MAC) governed by an adversary who has access
to the transmissions of both senders (hence called omniscient ) and aims to maliciously
corrupt the communication. None of the encoders, jammer and decoder is allowed
to randomize using private or public randomness. This enforces a combinatorial
nature of the problem. Our model covers a large family of channels studied in
the literature, including all deterministic discrete memoryless noisy or noiseless
MACs. In this work, given an arbitrary two-transmitter deterministic omniscient
adversarial MAC, we characterize when the capacity region: 1) has nonempty interior
(in particular, is two-dimensional); 2) consists of two line segments (in particular,
has empty interior); 3) consists of one line segment (in particular, is one-dimensional);
4) or only contains (0,0) (in particular, is zero-dimensional). This extends a
recent result by Wang et al. (201 9) from the point-to-point setting to the multiple
access setting. Indeed, our converse arguments build upon their generalized Plotkin
bound and involve delicate case analysis. One of the technical challenges is to
take care of both “joint confusability” and “marginal confusability”. In particular,
the treatment of marginal confusability does not follow from the point-to-point
results by Wang et al. Our achievability results follow from random coding with
expurgation.'
acknowledgement: "The author would like to thank Amitalok J. Budkuley and Sidharth
Jaggi for many helpful discussions at the early stage of this work. He would also
like to thank Nir Ailon, Qi Cao, and Chandra Nair for discussions on a related problem
regarding zero-error binary adder MACs.\r\nThe work of Yihan Zhang was supported
by the European Union’s Horizon 2020 Research and Innovation Programme under Grant
682203-ERC-[Inf-Speed-Tradeoff]"
article_processing_charge: No
article_type: original
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
citation:
ama: Zhang Y. Zero-error communication over adversarial MACs. IEEE Transactions
on Information Theory. 2023;69(7):4093-4127. doi:10.1109/tit.2023.3257239
apa: Zhang, Y. (2023). Zero-error communication over adversarial MACs. IEEE Transactions
on Information Theory. Institute of Electrical and Electronics Engineers.
https://doi.org/10.1109/tit.2023.3257239
chicago: Zhang, Yihan. “Zero-Error Communication over Adversarial MACs.” IEEE
Transactions on Information Theory. Institute of Electrical and Electronics
Engineers, 2023. https://doi.org/10.1109/tit.2023.3257239.
ieee: Y. Zhang, “Zero-error communication over adversarial MACs,” IEEE Transactions
on Information Theory, vol. 69, no. 7. Institute of Electrical and Electronics
Engineers, pp. 4093–4127, 2023.
ista: Zhang Y. 2023. Zero-error communication over adversarial MACs. IEEE Transactions
on Information Theory. 69(7), 4093–4127.
mla: Zhang, Yihan. “Zero-Error Communication over Adversarial MACs.” IEEE Transactions
on Information Theory, vol. 69, no. 7, Institute of Electrical and Electronics
Engineers, 2023, pp. 4093–127, doi:10.1109/tit.2023.3257239.
short: Y. Zhang, IEEE Transactions on Information Theory 69 (2023) 4093–4127.
date_created: 2024-01-08T13:04:54Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2024-01-09T08:45:24Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/tit.2023.3257239
external_id:
arxiv:
- '2101.12426'
intvolume: ' 69'
issue: '7'
keyword:
- Computer Science Applications
- Information Systems
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2101.12426
month: '07'
oa: 1
oa_version: Preprint
page: 4093-4127
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Zero-error communication over adversarial MACs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 69
year: '2023'
...
---
_id: '13269'
abstract:
- lang: eng
text: This paper is a collection of results on combinatorial properties of codes
for the Z-channel . A Z-channel with error fraction τ takes as input a length-
n binary codeword and injects in an adversarial manner up to n τ asymmetric errors,
i.e., errors that only zero out bits but do not flip 0’s to 1’s. It is known that
the largest ( L - 1)-list-decodable code for the Z-channel with error fraction
τ has exponential size (in n ) if τ is less than a critical value that we call
the ( L - 1)- list-decoding Plotkin point and has constant size if τ is larger
than the threshold. The ( L -1)-list-decoding Plotkin point is known to be L -1/L-1
– L -L/ L-1 , which equals 1/4 for unique-decoding with L -1 = 1. In this paper,
we derive various results for the size of the largest codes above and below the
list-decoding Plotkin point. In particular, we show that the largest ( L -1)-list-decodable
code ε-above the Plotkin point, for any given sufficiently small positive constant
ε > 0, has size Θ L (ε -3/2 ) for any L - 1 ≥ 1. We also devise upper and lower
bounds on the exponential size of codes below the list-decoding Plotkin point.
acknowledgement: "Nikita Polyanskii’s research was conducted in part during October
2020 - December 2021 with the Technical University of Munich and the Skolkovo Institute
of Science and Technology. His work was supported by the German Research Foundation
(Deutsche Forschungsgemeinschaft, DFG) under Grant No. WA3907/1-1 and the Russian
Foundation for Basic Research (RFBR)\r\nunder Grant No. 20-01-00559.\r\nYihan Zhang
is supported by funding from the European Union’s Horizon 2020 research and innovation
programme under grant agreement No 682203-ERC-[Inf-Speed-Tradeoff]."
article_processing_charge: No
article_type: original
author:
- first_name: Nikita
full_name: Polyanskii, Nikita
last_name: Polyanskii
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
citation:
ama: Polyanskii N, Zhang Y. Codes for the Z-channel. IEEE Transactions on Information
Theory. 2023;69(10):6340-6357. doi:10.1109/TIT.2023.3292219
apa: Polyanskii, N., & Zhang, Y. (2023). Codes for the Z-channel. IEEE Transactions
on Information Theory. Institute of Electrical and Electronics Engineers.
https://doi.org/10.1109/TIT.2023.3292219
chicago: Polyanskii, Nikita, and Yihan Zhang. “Codes for the Z-Channel.” IEEE
Transactions on Information Theory. Institute of Electrical and Electronics
Engineers, 2023. https://doi.org/10.1109/TIT.2023.3292219.
ieee: N. Polyanskii and Y. Zhang, “Codes for the Z-channel,” IEEE Transactions
on Information Theory, vol. 69, no. 10. Institute of Electrical and Electronics
Engineers, pp. 6340–6357, 2023.
ista: Polyanskii N, Zhang Y. 2023. Codes for the Z-channel. IEEE Transactions on
Information Theory. 69(10), 6340–6357.
mla: Polyanskii, Nikita, and Yihan Zhang. “Codes for the Z-Channel.” IEEE Transactions
on Information Theory, vol. 69, no. 10, Institute of Electrical and Electronics
Engineers, 2023, pp. 6340–57, doi:10.1109/TIT.2023.3292219.
short: N. Polyanskii, Y. Zhang, IEEE Transactions on Information Theory 69 (2023)
6340–6357.
date_created: 2023-07-23T22:01:14Z
date_published: 2023-07-04T00:00:00Z
date_updated: 2024-01-29T11:10:54Z
day: '04'
department:
- _id: MaMo
doi: 10.1109/TIT.2023.3292219
external_id:
arxiv:
- '2105.01427'
isi:
- '001069680100011'
intvolume: ' 69'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.01427
month: '07'
oa: 1
oa_version: Preprint
page: 6340-6357
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Codes for the Z-channel
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 69
year: '2023'
...
---
_id: '12011'
abstract:
- lang: eng
text: We characterize the capacity for the discrete-time arbitrarily varying channel
with discrete inputs, outputs, and states when (a) the encoder and decoder do
not share common randomness, (b) the input and state are subject to cost constraints,
(c) the transition matrix of the channel is deterministic given the state, and
(d) at each time step the adversary can only observe the current and past channel
inputs when choosing the state at that time. The achievable strategy involves
stochastic encoding together with list decoding and a disambiguation step. The
converse uses a two-phase "babble-and-push" strategy where the adversary chooses
the state randomly in the first phase, list decodes the output, and then chooses
state inputs to symmetrize the channel in the second phase. These results generalize
prior work on specific channels models (additive, erasure) to general discrete
alphabets and models.
acknowledgement: The work of ADS and ML was supported in part by the US National Science
Foundation under awards CCF-1909468 and CCF-1909451.
article_processing_charge: No
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Sidharth
full_name: Jaggi, Sidharth
last_name: Jaggi
- first_name: Michael
full_name: Langberg, Michael
last_name: Langberg
- first_name: Anand D.
full_name: Sarwate, Anand D.
last_name: Sarwate
citation:
ama: 'Zhang Y, Jaggi S, Langberg M, Sarwate AD. The capacity of causal adversarial
channels. In: 2022 IEEE International Symposium on Information Theory.
Vol 2022. IEEE; 2022:2523-2528. doi:10.1109/ISIT50566.2022.9834709'
apa: 'Zhang, Y., Jaggi, S., Langberg, M., & Sarwate, A. D. (2022). The capacity
of causal adversarial channels. In 2022 IEEE International Symposium on Information
Theory (Vol. 2022, pp. 2523–2528). Espoo, Finland: IEEE. https://doi.org/10.1109/ISIT50566.2022.9834709'
chicago: Zhang, Yihan, Sidharth Jaggi, Michael Langberg, and Anand D. Sarwate. “The
Capacity of Causal Adversarial Channels.” In 2022 IEEE International Symposium
on Information Theory, 2022:2523–28. IEEE, 2022. https://doi.org/10.1109/ISIT50566.2022.9834709.
ieee: Y. Zhang, S. Jaggi, M. Langberg, and A. D. Sarwate, “The capacity of causal
adversarial channels,” in 2022 IEEE International Symposium on Information
Theory, Espoo, Finland, 2022, vol. 2022, pp. 2523–2528.
ista: 'Zhang Y, Jaggi S, Langberg M, Sarwate AD. 2022. The capacity of causal adversarial
channels. 2022 IEEE International Symposium on Information Theory. ISIT: Internation
Symposium on Information Theory vol. 2022, 2523–2528.'
mla: Zhang, Yihan, et al. “The Capacity of Causal Adversarial Channels.” 2022
IEEE International Symposium on Information Theory, vol. 2022, IEEE, 2022,
pp. 2523–28, doi:10.1109/ISIT50566.2022.9834709.
short: Y. Zhang, S. Jaggi, M. Langberg, A.D. Sarwate, in:, 2022 IEEE International
Symposium on Information Theory, IEEE, 2022, pp. 2523–2528.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:03Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2022-09-05T09:09:15Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834709
external_id:
arxiv:
- '2205.06708'
intvolume: ' 2022'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2205.06708'
month: '08'
oa: 1
oa_version: Preprint
page: 2523-2528
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: The capacity of causal adversarial channels
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12017'
abstract:
- lang: eng
text: 'In the classic adversarial communication problem, two parties communicate
over a noisy channel in the presence of a malicious jamming adversary. The arbitrarily
varying channels (AVCs) offer an elegant framework to study a wide range of interesting
adversary models. The optimal throughput or capacity over such AVCs is intimately
tied to the underlying adversary model; in some cases, capacity is unknown and
the problem is known to be notoriously hard. The omniscient adversary, one which
knows the sender’s entire channel transmission a priori, is one of such classic
models of interest; the capacity under such an adversary remains an exciting open
problem. The myopic adversary is a generalization of that model where the adversary’s
observation may be corrupted over a noisy discrete memoryless channel. Through
the adversary’s myopicity, one can unify the slew of different adversary models,
ranging from the omniscient adversary to one that is completely blind to the transmission
(the latter is the well known oblivious model where the capacity is fully characterized).In
this work, we present new results on the capacity under both the omniscient and
myopic adversary models. We completely characterize the positive capacity threshold
over general AVCs with omniscient adversaries. The characterization is in terms
of two key combinatorial objects: the set of completely positive distributions
and the CP-confusability set. For omniscient AVCs with positive capacity, we present
non-trivial lower and upper bounds on the capacity; unlike some of the previous
bounds, our bounds hold under fairly general input and jamming constraints. Our
lower bound improves upon the generalized Gilbert-Varshamov bound for general
AVCs while the upper bound generalizes the well known Elias-Bassalygo bound (known
for binary and q-ary alphabets). For the myopic AVCs, we build on prior results
known for the so-called sufficiently myopic model, and present new results on
the positive rate communication threshold over the so-called insufficiently myopic
regime (a completely insufficient myopic adversary specializes to an omniscient
adversary). We present interesting examples for the widely studied models of adversarial
bit-flip and bit-erasure channels. In fact, for the bit-flip AVC with additive
adversarial noise as well as random noise, we completely characterize the omniscient
model capacity when the random noise is sufficiently large vis-a-vis the adversary’s
budget.'
article_processing_charge: No
author:
- first_name: Anuj Kumar
full_name: Yadav, Anuj Kumar
last_name: Yadav
- first_name: Mohammadreza
full_name: Alimohammadi, Mohammadreza
last_name: Alimohammadi
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Amitalok J.
full_name: Budkuley, Amitalok J.
last_name: Budkuley
- first_name: Sidharth
full_name: Jaggi, Sidharth
last_name: Jaggi
citation:
ama: 'Yadav AK, Alimohammadi M, Zhang Y, Budkuley AJ, Jaggi S. New results on AVCs
with omniscient and myopic adversaries. In: 2022 IEEE International Symposium
on Information Theory. Vol 2022. Institute of Electrical and Electronics Engineers;
2022:2535-2540. doi:10.1109/ISIT50566.2022.9834632'
apa: 'Yadav, A. K., Alimohammadi, M., Zhang, Y., Budkuley, A. J., & Jaggi, S.
(2022). New results on AVCs with omniscient and myopic adversaries. In 2022
IEEE International Symposium on Information Theory (Vol. 2022, pp. 2535–2540).
Espoo, Finland: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT50566.2022.9834632'
chicago: Yadav, Anuj Kumar, Mohammadreza Alimohammadi, Yihan Zhang, Amitalok J.
Budkuley, and Sidharth Jaggi. “New Results on AVCs with Omniscient and Myopic
Adversaries.” In 2022 IEEE International Symposium on Information Theory,
2022:2535–40. Institute of Electrical and Electronics Engineers, 2022. https://doi.org/10.1109/ISIT50566.2022.9834632.
ieee: A. K. Yadav, M. Alimohammadi, Y. Zhang, A. J. Budkuley, and S. Jaggi, “New
results on AVCs with omniscient and myopic adversaries,” in 2022 IEEE International
Symposium on Information Theory, Espoo, Finland, 2022, vol. 2022, pp. 2535–2540.
ista: 'Yadav AK, Alimohammadi M, Zhang Y, Budkuley AJ, Jaggi S. 2022. New results
on AVCs with omniscient and myopic adversaries. 2022 IEEE International Symposium
on Information Theory. ISIT: Internation Symposium on Information Theory vol.
2022, 2535–2540.'
mla: Yadav, Anuj Kumar, et al. “New Results on AVCs with Omniscient and Myopic Adversaries.”
2022 IEEE International Symposium on Information Theory, vol. 2022, Institute
of Electrical and Electronics Engineers, 2022, pp. 2535–40, doi:10.1109/ISIT50566.2022.9834632.
short: A.K. Yadav, M. Alimohammadi, Y. Zhang, A.J. Budkuley, S. Jaggi, in:, 2022
IEEE International Symposium on Information Theory, Institute of Electrical and
Electronics Engineers, 2022, pp. 2535–2540.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:06Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2023-02-13T09:00:14Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834632
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 2535-2540
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: New results on AVCs with omniscient and myopic adversaries
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12013'
abstract:
- lang: eng
text: We consider the problem of communication over adversarial channels with feedback.
Two parties comprising sender Alice and receiver Bob seek to communicate reliably.
An adversary James observes Alice's channel transmission entirely and chooses,
maliciously, its additive channel input or jamming state thereby corrupting Bob's
observation. Bob can communicate over a one-way reverse link with Alice; we assume
that transmissions over this feedback link cannot be corrupted by James. Our goal
in this work is to study the optimum throughput or capacity over such channels
with feedback. We first present results for the quadratically-constrained additive
channel where communication is known to be impossible when the noise-to-signal
(power) ratio (NSR) is at least 1. We present a novel achievability scheme to
establish that positive rate communication is possible even when the NSR is as
high as 8/9. We also present new converse upper bounds on the capacity of this
channel under potentially stochastic encoders and decoders. We also study feedback
communication over the more widely studied q-ary alphabet channel under additive
noise. For the q -ary channel, where q > 2, it is well known that capacity is
positive under full feedback if and only if the adversary can corrupt strictly
less than half the transmitted symbols. We generalize this result and show that
the same threshold holds for positive rate communication when the noiseless feedback
may only be partial; our scheme employs a stochastic decoder. We extend this characterization,
albeit partially, to fully deterministic schemes under partial noiseless feedback.
We also present new converse upper bounds for q-ary channels under full feedback,
where the encoder and/or decoder may privately randomize. Our converse results
bring to the fore an interesting alternate expression for the well known converse
bound for the q—ary channel under full feedback which, when specialized to the
binary channel, also equals its known capacity.
article_processing_charge: No
author:
- first_name: Pranav
full_name: Joshi, Pranav
last_name: Joshi
- first_name: Amritakshya
full_name: Purkayastha, Amritakshya
last_name: Purkayastha
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Amitalok J.
full_name: Budkuley, Amitalok J.
last_name: Budkuley
- first_name: Sidharth
full_name: Jaggi, Sidharth
last_name: Jaggi
citation:
ama: 'Joshi P, Purkayastha A, Zhang Y, Budkuley AJ, Jaggi S. On the capacity of
additive AVCs with feedback. In: 2022 IEEE International Symposium on Information
Theory. Vol 2022. IEEE; 2022:504-509. doi:10.1109/ISIT50566.2022.9834850'
apa: 'Joshi, P., Purkayastha, A., Zhang, Y., Budkuley, A. J., & Jaggi, S. (2022).
On the capacity of additive AVCs with feedback. In 2022 IEEE International
Symposium on Information Theory (Vol. 2022, pp. 504–509). Espoo, Finland:
IEEE. https://doi.org/10.1109/ISIT50566.2022.9834850'
chicago: Joshi, Pranav, Amritakshya Purkayastha, Yihan Zhang, Amitalok J. Budkuley,
and Sidharth Jaggi. “On the Capacity of Additive AVCs with Feedback.” In 2022
IEEE International Symposium on Information Theory, 2022:504–9. IEEE, 2022.
https://doi.org/10.1109/ISIT50566.2022.9834850.
ieee: P. Joshi, A. Purkayastha, Y. Zhang, A. J. Budkuley, and S. Jaggi, “On the
capacity of additive AVCs with feedback,” in 2022 IEEE International Symposium
on Information Theory, Espoo, Finland, 2022, vol. 2022, pp. 504–509.
ista: 'Joshi P, Purkayastha A, Zhang Y, Budkuley AJ, Jaggi S. 2022. On the capacity
of additive AVCs with feedback. 2022 IEEE International Symposium on Information
Theory. ISIT: Internation Symposium on Information Theory vol. 2022, 504–509.'
mla: Joshi, Pranav, et al. “On the Capacity of Additive AVCs with Feedback.” 2022
IEEE International Symposium on Information Theory, vol. 2022, IEEE, 2022,
pp. 504–09, doi:10.1109/ISIT50566.2022.9834850.
short: P. Joshi, A. Purkayastha, Y. Zhang, A.J. Budkuley, S. Jaggi, in:, 2022 IEEE
International Symposium on Information Theory, IEEE, 2022, pp. 504–509.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:04Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2022-09-05T10:23:35Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834850
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 504-509
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the capacity of additive AVCs with feedback
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12018'
abstract:
- lang: eng
text: We study the problem of characterizing the maximal rates of list decoding
in Euclidean spaces for finite list sizes. For any positive integer L ≥ 2 and
real N > 0, we say that a subset C⊂Rn is an (N,L – 1)-multiple packing or an (N,L–
1)-list decodable code if every Euclidean ball of radius nN−−−√ in ℝ n contains
no more than L − 1 points of C. We study this problem with and without ℓ 2 norm
constraints on C, and derive the best-known lower bounds on the maximal rate for
(N,L−1) multiple packing. Our bounds are obtained via error exponents for list
decoding over Additive White Gaussian Noise (AWGN) channels. We establish a curious
inequality which relates the error exponent, a quantity of average-case nature,
to the list-decoding radius, a quantity of worst-case nature. We derive various
bounds on the error exponent for list decoding in both bounded and unbounded settings
which could be of independent interest beyond multiple packing.
article_processing_charge: No
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. Lower bounds on list decoding capacity using error exponents.
In: 2022 IEEE International Symposium on Information Theory. Vol 2022.
Institute of Electrical and Electronics Engineers; 2022:1324-1329. doi:10.1109/ISIT50566.2022.9834815'
apa: 'Zhang, Y., & Vatedka, S. (2022). Lower bounds on list decoding capacity
using error exponents. In 2022 IEEE International Symposium on Information
Theory (Vol. 2022, pp. 1324–1329). Espoo, Finland: Institute of Electrical
and Electronics Engineers. https://doi.org/10.1109/ISIT50566.2022.9834815'
chicago: Zhang, Yihan, and Shashank Vatedka. “Lower Bounds on List Decoding Capacity
Using Error Exponents.” In 2022 IEEE International Symposium on Information
Theory, 2022:1324–29. Institute of Electrical and Electronics Engineers, 2022.
https://doi.org/10.1109/ISIT50566.2022.9834815.
ieee: Y. Zhang and S. Vatedka, “Lower bounds on list decoding capacity using error
exponents,” in 2022 IEEE International Symposium on Information Theory,
Espoo, Finland, 2022, vol. 2022, pp. 1324–1329.
ista: 'Zhang Y, Vatedka S. 2022. Lower bounds on list decoding capacity using error
exponents. 2022 IEEE International Symposium on Information Theory. ISIT: Internation
Symposium on Information Theory vol. 2022, 1324–1329.'
mla: Zhang, Yihan, and Shashank Vatedka. “Lower Bounds on List Decoding Capacity
Using Error Exponents.” 2022 IEEE International Symposium on Information Theory,
vol. 2022, Institute of Electrical and Electronics Engineers, 2022, pp. 1324–29,
doi:10.1109/ISIT50566.2022.9834815.
short: Y. Zhang, S. Vatedka, in:, 2022 IEEE International Symposium on Information
Theory, Institute of Electrical and Electronics Engineers, 2022, pp. 1324–1329.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:06Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2023-02-13T09:02:06Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834815
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 1324-1329
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower bounds on list decoding capacity using error exponents
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12015'
abstract:
- lang: eng
text: We study the problem of high-dimensional multiple packing in Euclidean space.
Multiple packing is a natural generalization of sphere packing and is defined
as follows. Let P, N > 0 and L∈Z≥2. A multiple packing is a set C of points in
Bn(0–,nP−−−√) such that any point in ℝ n lies in the intersection of at most L
– 1 balls of radius nN−−−√ around points in C. 1 In this paper, we derive two
lower bounds on the largest possible density of a multiple packing. These bounds
are obtained through a stronger notion called average-radius multiple packing.
Specifically, we exactly pin down the asymptotics of (expurgated) Gaussian codes
and (expurgated) spherical codes under average-radius multiple packing. To this
end, we apply tools from high-dimensional geometry and large deviation theory.
The bound for spherical codes matches the previous best known bound which was
obtained for the standard (weaker) notion of multiple packing through a curious
connection with error exponents [Bli99], [ZV21]. The bound for Gaussian codes
suggests that they are strictly inferior to spherical codes.
article_processing_charge: No
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. Lower bounds for multiple packing. In: 2022 IEEE International
Symposium on Information Theory. Vol 2022. IEEE; 2022:3085-3090. doi:10.1109/ISIT50566.2022.9834443'
apa: 'Zhang, Y., & Vatedka, S. (2022). Lower bounds for multiple packing. In
2022 IEEE International Symposium on Information Theory (Vol. 2022, pp.
3085–3090). Espoo, Finland: IEEE. https://doi.org/10.1109/ISIT50566.2022.9834443'
chicago: Zhang, Yihan, and Shashank Vatedka. “Lower Bounds for Multiple Packing.”
In 2022 IEEE International Symposium on Information Theory, 2022:3085–90.
IEEE, 2022. https://doi.org/10.1109/ISIT50566.2022.9834443.
ieee: Y. Zhang and S. Vatedka, “Lower bounds for multiple packing,” in 2022 IEEE
International Symposium on Information Theory, Espoo, Finland, 2022, vol.
2022, pp. 3085–3090.
ista: 'Zhang Y, Vatedka S. 2022. Lower bounds for multiple packing. 2022 IEEE International
Symposium on Information Theory. ISIT: Internation Symposium on Information Theory
vol. 2022, 3085–3090.'
mla: Zhang, Yihan, and Shashank Vatedka. “Lower Bounds for Multiple Packing.” 2022
IEEE International Symposium on Information Theory, vol. 2022, IEEE, 2022,
pp. 3085–90, doi:10.1109/ISIT50566.2022.9834443.
short: Y. Zhang, S. Vatedka, in:, 2022 IEEE International Symposium on Information
Theory, IEEE, 2022, pp. 3085–3090.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:05Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2022-09-05T10:39:04Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834443
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 3085-3090
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower bounds for multiple packing
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12014'
abstract:
- lang: eng
text: We study the problem of high-dimensional multiple packing in Euclidean space.
Multiple packing is a natural generalization of sphere packing and is defined
as follows. Let N > 0 and L∈Z≥2. A multiple packing is a set C of points in Rn
such that any point in Rn lies in the intersection of at most L – 1 balls of radius
nN−−−√ around points in C. Given a well-known connection with coding theory, multiple
packings can be viewed as the Euclidean analog of list-decodable codes, which
are well-studied for finite fields. In this paper, we exactly pin down the asymptotic
density of (expurgated) Poisson Point Processes under a stronger notion called
average-radius multiple packing. To this end, we apply tools from high-dimensional
geometry and large deviation theory. This gives rise to the best known lower bound
on the largest multiple packing density. Our result corrects a mistake in a previous
paper by Blinovsky [Bli05].
article_processing_charge: No
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. List-decodability of Poisson Point Processes. In: 2022
IEEE International Symposium on Information Theory. Vol 2022. IEEE; 2022:2559-2564.
doi:10.1109/ISIT50566.2022.9834512'
apa: 'Zhang, Y., & Vatedka, S. (2022). List-decodability of Poisson Point Processes.
In 2022 IEEE International Symposium on Information Theory (Vol. 2022,
pp. 2559–2564). Espoo, Finland: IEEE. https://doi.org/10.1109/ISIT50566.2022.9834512'
chicago: Zhang, Yihan, and Shashank Vatedka. “List-Decodability of Poisson Point
Processes.” In 2022 IEEE International Symposium on Information Theory,
2022:2559–64. IEEE, 2022. https://doi.org/10.1109/ISIT50566.2022.9834512.
ieee: Y. Zhang and S. Vatedka, “List-decodability of Poisson Point Processes,” in
2022 IEEE International Symposium on Information Theory, Espoo, Finland,
2022, vol. 2022, pp. 2559–2564.
ista: 'Zhang Y, Vatedka S. 2022. List-decodability of Poisson Point Processes. 2022
IEEE International Symposium on Information Theory. ISIT: Internation Symposium
on Information Theory vol. 2022, 2559–2564.'
mla: Zhang, Yihan, and Shashank Vatedka. “List-Decodability of Poisson Point Processes.”
2022 IEEE International Symposium on Information Theory, vol. 2022, IEEE,
2022, pp. 2559–64, doi:10.1109/ISIT50566.2022.9834512.
short: Y. Zhang, S. Vatedka, in:, 2022 IEEE International Symposium on Information
Theory, IEEE, 2022, pp. 2559–2564.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:04Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2022-09-05T09:23:04Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834512
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 2559-2564
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: List-decodability of Poisson Point Processes
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12019'
abstract:
- lang: eng
text: This paper studies combinatorial properties of codes for the Z-channel. A
Z-channel with error fraction τ takes as input a length-n binary codeword and
injects in an adversarial manner up to nτ asymmetric errors, i.e., errors that
only zero out bits but do not flip 0’s to 1’s. It is known that the largest (L
− 1)-list-decodable code for the Z-channel with error fraction τ has exponential
(in n) size if τ is less than a critical value that we call the Plotkin point
and has constant size if τ is larger than the threshold. The (L−1)-list-decoding
Plotkin point is known to be L−1L−1−L−LL−1. In this paper, we show that the largest
(L−1)-list-decodable code ε-above the Plotkin point has size Θ L (ε −3/2 ) for
any L − 1 ≥ 1.
article_processing_charge: No
author:
- first_name: Nikita
full_name: Polyanskii, Nikita
last_name: Polyanskii
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
citation:
ama: 'Polyanskii N, Zhang Y. List-decodable zero-rate codes for the Z-channel. In:
2022 IEEE International Symposium on Information Theory. Vol 2022. Institute
of Electrical and Electronics Engineers; 2022:2553-2558. doi:10.1109/ISIT50566.2022.9834829'
apa: 'Polyanskii, N., & Zhang, Y. (2022). List-decodable zero-rate codes for
the Z-channel. In 2022 IEEE International Symposium on Information Theory
(Vol. 2022, pp. 2553–2558). Espoo, Finland: Institute of Electrical and Electronics
Engineers. https://doi.org/10.1109/ISIT50566.2022.9834829'
chicago: Polyanskii, Nikita, and Yihan Zhang. “List-Decodable Zero-Rate Codes for
the Z-Channel.” In 2022 IEEE International Symposium on Information Theory,
2022:2553–58. Institute of Electrical and Electronics Engineers, 2022. https://doi.org/10.1109/ISIT50566.2022.9834829.
ieee: N. Polyanskii and Y. Zhang, “List-decodable zero-rate codes for the Z-channel,”
in 2022 IEEE International Symposium on Information Theory, Espoo, Finland,
2022, vol. 2022, pp. 2553–2558.
ista: 'Polyanskii N, Zhang Y. 2022. List-decodable zero-rate codes for the Z-channel.
2022 IEEE International Symposium on Information Theory. ISIT: Internation Symposium
on Information Theory vol. 2022, 2553–2558.'
mla: Polyanskii, Nikita, and Yihan Zhang. “List-Decodable Zero-Rate Codes for the
Z-Channel.” 2022 IEEE International Symposium on Information Theory, vol.
2022, Institute of Electrical and Electronics Engineers, 2022, pp. 2553–58, doi:10.1109/ISIT50566.2022.9834829.
short: N. Polyanskii, Y. Zhang, in:, 2022 IEEE International Symposium on Information
Theory, Institute of Electrical and Electronics Engineers, 2022, pp. 2553–2558.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:07Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2023-02-13T09:02:18Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834829
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 2553-2558
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: List-decodable zero-rate codes for the Z-channel
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '11639'
abstract:
- lang: eng
text: We study the list decodability of different ensembles of codes over the real
alphabet under the assumption of an omniscient adversary. It is a well-known result
that when the source and the adversary have power constraints P and N respectively,
the list decoding capacity is equal to 1/2logP/N. Random spherical codes achieve
constant list sizes, and the goal of the present paper is to obtain a better understanding
of the smallest achievable list size as a function of the gap to capacity. We
show a reduction from arbitrary codes to spherical codes, and derive a lower bound
on the list size of typical random spherical codes. We also give an upper bound
on the list size achievable using nested Construction-A lattices and infinite
Construction-A lattices. We then define and study a class of infinite constellations
that generalize Construction-A lattices and prove upper and lower bounds for the
same. Other goodness properties such as packing goodness and AWGN goodness of
infinite constellations are proved along the way. Finally, we consider random
lattices sampled from the Haar distribution and show that if a certain conjecture
that originates in analytic number theory is true, then the list size grows as
a polynomial function of the gap-to-capacity.
acknowledgement: "This work was done when Shashank Vatedka was at the Chinese University
of Hong Kong, where he was supported in part by CUHK Direct Grants 4055039 and 4055077.
He would like to acknowledge funding from a seed grant offered by IIT Hyderabad
and the Start-up Research Grant (SRG/2020/000910) from the Science and Engineering
Board, India. Yihan Zhang has received funding from the European Union’s Horizon
2020 research and innovation programme\r\nunder grant agreement No 682203-ERC-[Inf-Speed-Tradeoff]."
article_processing_charge: No
article_type: original
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: Zhang Y, Vatedka S. List decoding random Euclidean codes and Infinite constellations.
IEEE Transactions on Information Theory. 2022;68(12):7753-7786. doi:10.1109/TIT.2022.3189542
apa: Zhang, Y., & Vatedka, S. (2022). List decoding random Euclidean codes and
Infinite constellations. IEEE Transactions on Information Theory. IEEE.
https://doi.org/10.1109/TIT.2022.3189542
chicago: Zhang, Yihan, and Shashank Vatedka. “List Decoding Random Euclidean Codes
and Infinite Constellations.” IEEE Transactions on Information Theory.
IEEE, 2022. https://doi.org/10.1109/TIT.2022.3189542.
ieee: Y. Zhang and S. Vatedka, “List decoding random Euclidean codes and Infinite
constellations,” IEEE Transactions on Information Theory, vol. 68, no.
12. IEEE, pp. 7753–7786, 2022.
ista: Zhang Y, Vatedka S. 2022. List decoding random Euclidean codes and Infinite
constellations. IEEE Transactions on Information Theory. 68(12), 7753–7786.
mla: Zhang, Yihan, and Shashank Vatedka. “List Decoding Random Euclidean Codes and
Infinite Constellations.” IEEE Transactions on Information Theory, vol.
68, no. 12, IEEE, 2022, pp. 7753–86, doi:10.1109/TIT.2022.3189542.
short: Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory 68 (2022) 7753–7786.
date_created: 2022-07-24T22:01:42Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-03T12:12:19Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/TIT.2022.3189542
external_id:
arxiv:
- '1901.03790'
isi:
- '000891796100007'
intvolume: ' 68'
isi: 1
issue: '12'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1901.03790
month: '12'
oa: 1
oa_version: Preprint
page: 7753-7786
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: List decoding random Euclidean codes and Infinite constellations
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 68
year: '2022'
...
---
_id: '12273'
abstract:
- lang: eng
text: We study communication in the presence of a jamming adversary where quadratic
power constraints are imposed on the transmitter and the jammer. The jamming signal
is allowed to be a function of the codebook, and a noncausal but noisy observation
of the transmitted codeword. For a certain range of the noise-to-signal ratios
(NSRs) of the transmitter and the jammer, we are able to characterize the capacity
of this channel under deterministic encoding or stochastic encoding, i.e., with
no common randomness between the encoder/decoder pair. For the remaining NSR regimes,
we determine the capacity under the assumption of a small amount of common randomness
(at most 2log(n) bits in one sub-regime, and at most Ω(n) bits in the other sub-regime)
available to the encoder-decoder pair. Our proof techniques involve a novel myopic
list-decoding result for achievability, and a Plotkin-type push attack for the
converse in a subregion of the NSRs, both of which may be of independent interest.
We also give bounds on the strong secrecy capacity of this channel assuming that
the jammer is simultaneously eavesdropping.
article_processing_charge: No
article_type: original
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
- first_name: Sidharth
full_name: Jaggi, Sidharth
last_name: Jaggi
- first_name: Anand D.
full_name: Sarwate, Anand D.
last_name: Sarwate
citation:
ama: Zhang Y, Vatedka S, Jaggi S, Sarwate AD. Quadratically constrained myopic adversarial
channels. IEEE Transactions on Information Theory. 2022;68(8):4901-4948.
doi:10.1109/tit.2022.3167554
apa: Zhang, Y., Vatedka, S., Jaggi, S., & Sarwate, A. D. (2022). Quadratically
constrained myopic adversarial channels. IEEE Transactions on Information Theory.
Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/tit.2022.3167554
chicago: Zhang, Yihan, Shashank Vatedka, Sidharth Jaggi, and Anand D. Sarwate. “Quadratically
Constrained Myopic Adversarial Channels.” IEEE Transactions on Information
Theory. Institute of Electrical and Electronics Engineers, 2022. https://doi.org/10.1109/tit.2022.3167554.
ieee: Y. Zhang, S. Vatedka, S. Jaggi, and A. D. Sarwate, “Quadratically constrained
myopic adversarial channels,” IEEE Transactions on Information Theory,
vol. 68, no. 8. Institute of Electrical and Electronics Engineers, pp. 4901–4948,
2022.
ista: Zhang Y, Vatedka S, Jaggi S, Sarwate AD. 2022. Quadratically constrained myopic
adversarial channels. IEEE Transactions on Information Theory. 68(8), 4901–4948.
mla: Zhang, Yihan, et al. “Quadratically Constrained Myopic Adversarial Channels.”
IEEE Transactions on Information Theory, vol. 68, no. 8, Institute of Electrical
and Electronics Engineers, 2022, pp. 4901–48, doi:10.1109/tit.2022.3167554.
short: Y. Zhang, S. Vatedka, S. Jaggi, A.D. Sarwate, IEEE Transactions on Information
Theory 68 (2022) 4901–4948.
date_created: 2023-01-16T10:01:19Z
date_published: 2022-08-01T00:00:00Z
date_updated: 2023-08-04T10:08:49Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/tit.2022.3167554
external_id:
arxiv:
- '1801.05951'
isi:
- '000838527100004'
intvolume: ' 68'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1801.05951
month: '08'
oa: 1
oa_version: Preprint
page: 4901-4948
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quadratically constrained myopic adversarial channels
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 68
year: '2022'
...