---
_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
arxiv: 1
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. <i>IEEE
    Transactions on Information Theory</i>. 2023. doi:<a href="https://doi.org/10.1109/TIT.2023.3334032">10.1109/TIT.2023.3334032</a>'
  apa: 'Zhang, Y., &#38; Vatedka, S. (2023). Multiple packing: Lower bounds via error
    exponents. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href="https://doi.org/10.1109/TIT.2023.3334032">https://doi.org/10.1109/TIT.2023.3334032</a>'
  chicago: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via
    Error Exponents.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2023.
    <a href="https://doi.org/10.1109/TIT.2023.3334032">https://doi.org/10.1109/TIT.2023.3334032</a>.'
  ieee: 'Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via error exponents,”
    <i>IEEE Transactions on Information Theory</i>. 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.” <i>IEEE Transactions on Information Theory</i>, IEEE, 2023, doi:<a
    href="https://doi.org/10.1109/TIT.2023.3334032">10.1109/TIT.2023.3334032</a>.'
  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
arxiv: 1
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. <i>IEEE Transactions
    on Information Theory</i>. 2023;69(7):4093-4127. doi:<a href="https://doi.org/10.1109/tit.2023.3257239">10.1109/tit.2023.3257239</a>
  apa: Zhang, Y. (2023). Zero-error communication over adversarial MACs. <i>IEEE Transactions
    on Information Theory</i>. Institute of Electrical and Electronics Engineers.
    <a href="https://doi.org/10.1109/tit.2023.3257239">https://doi.org/10.1109/tit.2023.3257239</a>
  chicago: Zhang, Yihan. “Zero-Error Communication over Adversarial MACs.” <i>IEEE
    Transactions on Information Theory</i>. Institute of Electrical and Electronics
    Engineers, 2023. <a href="https://doi.org/10.1109/tit.2023.3257239">https://doi.org/10.1109/tit.2023.3257239</a>.
  ieee: Y. Zhang, “Zero-error communication over adversarial MACs,” <i>IEEE Transactions
    on Information Theory</i>, 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.” <i>IEEE Transactions
    on Information Theory</i>, vol. 69, no. 7, Institute of Electrical and Electronics
    Engineers, 2023, pp. 4093–127, doi:<a href="https://doi.org/10.1109/tit.2023.3257239">10.1109/tit.2023.3257239</a>.
  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
arxiv: 1
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. <i>IEEE Transactions on Information
    Theory</i>. 2023;69(10):6340-6357. doi:<a href="https://doi.org/10.1109/TIT.2023.3292219">10.1109/TIT.2023.3292219</a>
  apa: Polyanskii, N., &#38; Zhang, Y. (2023). Codes for the Z-channel. <i>IEEE Transactions
    on Information Theory</i>. Institute of Electrical and Electronics Engineers.
    <a href="https://doi.org/10.1109/TIT.2023.3292219">https://doi.org/10.1109/TIT.2023.3292219</a>
  chicago: Polyanskii, Nikita, and Yihan Zhang. “Codes for the Z-Channel.” <i>IEEE
    Transactions on Information Theory</i>. Institute of Electrical and Electronics
    Engineers, 2023. <a href="https://doi.org/10.1109/TIT.2023.3292219">https://doi.org/10.1109/TIT.2023.3292219</a>.
  ieee: N. Polyanskii and Y. Zhang, “Codes for the Z-channel,” <i>IEEE Transactions
    on Information Theory</i>, 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.” <i>IEEE Transactions
    on Information Theory</i>, vol. 69, no. 10, Institute of Electrical and Electronics
    Engineers, 2023, pp. 6340–57, doi:<a href="https://doi.org/10.1109/TIT.2023.3292219">10.1109/TIT.2023.3292219</a>.
  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: '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
arxiv: 1
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.
    <i>IEEE Transactions on Information Theory</i>. 2023;69(7):4513-4527. doi:<a href="https://doi.org/10.1109/TIT.2023.3260950">10.1109/TIT.2023.3260950</a>'
  apa: 'Zhang, Y., &#38; Vatedka, S. (2023). Multiple packing: Lower bounds via infinite
    constellations. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href="https://doi.org/10.1109/TIT.2023.3260950">https://doi.org/10.1109/TIT.2023.3260950</a>'
  chicago: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via
    Infinite Constellations.” <i>IEEE Transactions on Information Theory</i>. IEEE,
    2023. <a href="https://doi.org/10.1109/TIT.2023.3260950">https://doi.org/10.1109/TIT.2023.3260950</a>.'
  ieee: 'Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via infinite constellations,”
    <i>IEEE Transactions on Information Theory</i>, 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.” <i>IEEE Transactions on Information Theory</i>, vol. 69, no.
    7, IEEE, 2023, pp. 4513–27, doi:<a href="https://doi.org/10.1109/TIT.2023.3260950">10.1109/TIT.2023.3260950</a>.'
  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: '10775'
abstract:
- lang: eng
  text: List-decodability of Reed–Solomon codes has received a lot of attention, but
    the best-possible dependence between the parameters is still not well-understood.
    In this work, we focus on the case where the list-decoding radius is of the form
    r = 1-ε for ε tending to zero. Our main result states that there exist Reed–Solomon
    codes with rate Ω(ε) which are (1 - ε, O(1/ε))-list-decodable, meaning that any
    Hamming ball of radius 1-ε contains at most O(1/ε) codewords. This trade-off between
    rate and list-decoding radius is best-possible for any code with list size less
    than exponential in the block length. By achieving this trade-off between rate
    and list-decoding radius we improve a recent result of Guo, Li, Shangguan, Tamo,
    and Wootters, and resolve the main motivating question of their work. Moreover,
    while their result requires the field to be exponentially large in the block length,
    we only need the field size to be polynomially large (and in fact, almost-linear
    suffices). We deduce our main result from a more general theorem, in which we
    prove good list-decodability properties of random puncturings of any given code
    with very large distance.
acknowledgement: Research supported by NSF Award DMS-1953990.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Asaf
  full_name: Ferber, Asaf
  last_name: Ferber
- first_name: Matthew Alan
  full_name: Kwan, Matthew Alan
  id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
  last_name: Kwan
  orcid: 0000-0002-4003-7567
- first_name: Lisa
  full_name: Sauermann, Lisa
  last_name: Sauermann
citation:
  ama: Ferber A, Kwan MA, Sauermann L. List-decodability with large radius for Reed-Solomon
    codes. <i>IEEE Transactions on Information Theory</i>. 2022;68(6):3823-3828. doi:<a
    href="https://doi.org/10.1109/TIT.2022.3148779">10.1109/TIT.2022.3148779</a>
  apa: Ferber, A., Kwan, M. A., &#38; Sauermann, L. (2022). List-decodability with
    large radius for Reed-Solomon codes. <i>IEEE Transactions on Information Theory</i>.
    IEEE. <a href="https://doi.org/10.1109/TIT.2022.3148779">https://doi.org/10.1109/TIT.2022.3148779</a>
  chicago: Ferber, Asaf, Matthew Alan Kwan, and Lisa Sauermann. “List-Decodability
    with Large Radius for Reed-Solomon Codes.” <i>IEEE Transactions on Information
    Theory</i>. IEEE, 2022. <a href="https://doi.org/10.1109/TIT.2022.3148779">https://doi.org/10.1109/TIT.2022.3148779</a>.
  ieee: A. Ferber, M. A. Kwan, and L. Sauermann, “List-decodability with large radius
    for Reed-Solomon codes,” <i>IEEE Transactions on Information Theory</i>, vol.
    68, no. 6. IEEE, pp. 3823–3828, 2022.
  ista: Ferber A, Kwan MA, Sauermann L. 2022. List-decodability with large radius
    for Reed-Solomon codes. IEEE Transactions on Information Theory. 68(6), 3823–3828.
  mla: Ferber, Asaf, et al. “List-Decodability with Large Radius for Reed-Solomon
    Codes.” <i>IEEE Transactions on Information Theory</i>, vol. 68, no. 6, IEEE,
    2022, pp. 3823–28, doi:<a href="https://doi.org/10.1109/TIT.2022.3148779">10.1109/TIT.2022.3148779</a>.
  short: A. Ferber, M.A. Kwan, L. Sauermann, IEEE Transactions on Information Theory
    68 (2022) 3823–3828.
date_created: 2022-02-20T23:01:34Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2023-08-03T06:57:01Z
day: '01'
department:
- _id: MaKw
doi: 10.1109/TIT.2022.3148779
external_id:
  arxiv:
  - '2012.10584'
  isi:
  - '000799622500022'
intvolume: '        68'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2012.10584
month: '06'
oa: 1
oa_version: Preprint
page: 3823-3828
publication: IEEE Transactions on Information Theory
publication_identifier:
  eissn:
  - 1557-9654
  issn:
  - 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
  record:
  - id: '11145'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: List-decodability with large radius for Reed-Solomon codes
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 68
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
arxiv: 1
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.
    <i>IEEE Transactions on Information Theory</i>. 2022;68(12):7753-7786. doi:<a
    href="https://doi.org/10.1109/TIT.2022.3189542">10.1109/TIT.2022.3189542</a>
  apa: Zhang, Y., &#38; Vatedka, S. (2022). List decoding random Euclidean codes and
    Infinite constellations. <i>IEEE Transactions on Information Theory</i>. IEEE.
    <a href="https://doi.org/10.1109/TIT.2022.3189542">https://doi.org/10.1109/TIT.2022.3189542</a>
  chicago: Zhang, Yihan, and Shashank Vatedka. “List Decoding Random Euclidean Codes
    and Infinite Constellations.” <i>IEEE Transactions on Information Theory</i>.
    IEEE, 2022. <a href="https://doi.org/10.1109/TIT.2022.3189542">https://doi.org/10.1109/TIT.2022.3189542</a>.
  ieee: Y. Zhang and S. Vatedka, “List decoding random Euclidean codes and Infinite
    constellations,” <i>IEEE Transactions on Information Theory</i>, 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.” <i>IEEE Transactions on Information Theory</i>, vol.
    68, no. 12, IEEE, 2022, pp. 7753–86, doi:<a href="https://doi.org/10.1109/TIT.2022.3189542">10.1109/TIT.2022.3189542</a>.
  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
arxiv: 1
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. <i>IEEE Transactions on Information Theory</i>. 2022;68(8):4901-4948.
    doi:<a href="https://doi.org/10.1109/tit.2022.3167554">10.1109/tit.2022.3167554</a>
  apa: Zhang, Y., Vatedka, S., Jaggi, S., &#38; Sarwate, A. D. (2022). Quadratically
    constrained myopic adversarial channels. <i>IEEE Transactions on Information Theory</i>.
    Institute of Electrical and Electronics Engineers. <a href="https://doi.org/10.1109/tit.2022.3167554">https://doi.org/10.1109/tit.2022.3167554</a>
  chicago: Zhang, Yihan, Shashank Vatedka, Sidharth Jaggi, and Anand D. Sarwate. “Quadratically
    Constrained Myopic Adversarial Channels.” <i>IEEE Transactions on Information
    Theory</i>. Institute of Electrical and Electronics Engineers, 2022. <a href="https://doi.org/10.1109/tit.2022.3167554">https://doi.org/10.1109/tit.2022.3167554</a>.
  ieee: Y. Zhang, S. Vatedka, S. Jaggi, and A. D. Sarwate, “Quadratically constrained
    myopic adversarial channels,” <i>IEEE Transactions on Information Theory</i>,
    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.”
    <i>IEEE Transactions on Information Theory</i>, vol. 68, no. 8, Institute of Electrical
    and Electronics Engineers, 2022, pp. 4901–48, doi:<a href="https://doi.org/10.1109/tit.2022.3167554">10.1109/tit.2022.3167554</a>.
  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'
...
---
_id: '9002'
abstract:
- lang: eng
  text: ' We prove that, for the binary erasure channel (BEC), the polar-coding paradigm
    gives rise to codes that not only approach the Shannon limit but do so under the
    best possible scaling of their block length as a function of the gap to capacity.
    This result exhibits the first known family of binary codes that attain both optimal
    scaling and quasi-linear complexity of encoding and decoding. Our proof is based
    on the construction and analysis of binary polar codes with large kernels. When
    communicating reliably at rates within ε>0 of capacity, the code length n often
    scales as O(1/εμ), where the constant μ is called the scaling exponent. It is
    known that the optimal scaling exponent is μ=2, and it is achieved by random linear
    codes. The scaling exponent of conventional polar codes (based on the 2×2 kernel)
    on the BEC is μ=3.63. This falls far short of the optimal scaling guaranteed by
    random codes. Our main contribution is a rigorous proof of the following result:
    for the BEC, there exist ℓ×ℓ binary kernels, such that polar codes constructed
    from these kernels achieve scaling exponent μ(ℓ) that tends to the optimal value
    of 2 as ℓ grows. We furthermore characterize precisely how large ℓ needs to be
    as a function of the gap between μ(ℓ) and 2. The resulting binary codes maintain
    the recursive structure of conventional polar codes, and thereby achieve construction
    complexity O(n) and encoding/decoding complexity O(nlogn).'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Arman
  full_name: Fazeli, Arman
  last_name: Fazeli
- first_name: Hamed
  full_name: Hassani, Hamed
  last_name: Hassani
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
- first_name: Alexander
  full_name: Vardy, Alexander
  last_name: Vardy
citation:
  ama: 'Fazeli A, Hassani H, Mondelli M, Vardy A. Binary linear codes with optimal
    scaling: Polar codes with large kernels. <i>IEEE Transactions on Information Theory</i>.
    2021;67(9):5693-5710. doi:<a href="https://doi.org/10.1109/TIT.2020.3038806">10.1109/TIT.2020.3038806</a>'
  apa: 'Fazeli, A., Hassani, H., Mondelli, M., &#38; Vardy, A. (2021). Binary linear
    codes with optimal scaling: Polar codes with large kernels. <i>IEEE Transactions
    on Information Theory</i>. IEEE. <a href="https://doi.org/10.1109/TIT.2020.3038806">https://doi.org/10.1109/TIT.2020.3038806</a>'
  chicago: 'Fazeli, Arman, Hamed Hassani, Marco Mondelli, and Alexander Vardy. “Binary
    Linear Codes with Optimal Scaling: Polar Codes with Large Kernels.” <i>IEEE Transactions
    on Information Theory</i>. IEEE, 2021. <a href="https://doi.org/10.1109/TIT.2020.3038806">https://doi.org/10.1109/TIT.2020.3038806</a>.'
  ieee: 'A. Fazeli, H. Hassani, M. Mondelli, and A. Vardy, “Binary linear codes with
    optimal scaling: Polar codes with large kernels,” <i>IEEE Transactions on Information
    Theory</i>, vol. 67, no. 9. IEEE, pp. 5693–5710, 2021.'
  ista: 'Fazeli A, Hassani H, Mondelli M, Vardy A. 2021. Binary linear codes with
    optimal scaling: Polar codes with large kernels. IEEE Transactions on Information
    Theory. 67(9), 5693–5710.'
  mla: 'Fazeli, Arman, et al. “Binary Linear Codes with Optimal Scaling: Polar Codes
    with Large Kernels.” <i>IEEE Transactions on Information Theory</i>, vol. 67,
    no. 9, IEEE, 2021, pp. 5693–710, doi:<a href="https://doi.org/10.1109/TIT.2020.3038806">10.1109/TIT.2020.3038806</a>.'
  short: A. Fazeli, H. Hassani, M. Mondelli, A. Vardy, IEEE Transactions on Information
    Theory 67 (2021) 5693–5710.
date_created: 2021-01-10T23:01:18Z
date_published: 2021-09-01T00:00:00Z
date_updated: 2024-03-07T12:18:50Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/TIT.2020.3038806
external_id:
  arxiv:
  - '1711.01339'
intvolume: '        67'
issue: '9'
language:
- iso: eng
month: '09'
oa_version: Preprint
page: 5693-5710
publication: IEEE Transactions on Information Theory
publication_identifier:
  eissn:
  - 1557-9654
  issn:
  - 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
  record:
  - id: '6665'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: 'Binary linear codes with optimal scaling: Polar codes with large kernels'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 67
year: '2021'
...
---
_id: '6678'
abstract:
- lang: eng
  text: We survey coding techniques that enable reliable transmission at rates that
    approach the capacity of an arbitrary discrete memoryless channel. In particular,
    we take the point of view of modern coding theory and discuss how recent advances
    in coding for symmetric channels help provide more efficient solutions for the
    asymmetric case. We consider, in more detail, three basic coding paradigms. The
    first one is Gallager's scheme that consists of concatenating a linear code with
    a non-linear mapping so that the input distribution can be appropriately shaped.
    We explicitly show that both polar codes and spatially coupled codes can be employed
    in this scenario. Furthermore, we derive a scaling law between the gap to capacity,
    the cardinality of the input and output alphabets, and the required size of the
    mapper. The second one is an integrated scheme in which the code is used both
    for source coding, in order to create codewords distributed according to the capacity-achieving
    input distribution, and for channel coding, in order to provide error protection.
    Such a technique has been recently introduced by Honda and Yamamoto in the context
    of polar codes, and we show how to apply it also to the design of sparse graph
    codes. The third paradigm is based on an idea of Böcherer and Mathar, and separates
    the two tasks of source coding and channel coding by a chaining construction that
    binds together several codewords. We present conditions for the source code and
    the channel code, and we describe how to combine any source code with any channel
    code that fulfill those conditions, in order to provide capacity-achieving schemes
    for asymmetric channels. In particular, we show that polar codes, spatially coupled
    codes, and homophonic codes are suitable as basic building blocks of the proposed
    coding strategy. Rather than focusing on the exact details of the schemes, the
    purpose of this tutorial is to present different coding techniques that can then
    be implemented with many variants. There is no absolute winner and, in order to
    understand the most suitable technique for a specific application scenario, we
    provide a detailed comparison that takes into account several performance metrics.
article_type: original
arxiv: 1
author:
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
- first_name: Hamed
  full_name: Hassani, Hamed
  last_name: Hassani
- first_name: 'Rudiger '
  full_name: 'Urbanke, Rudiger '
  last_name: Urbanke
citation:
  ama: Mondelli M, Hassani H, Urbanke R. How to achieve the capacity of asymmetric
    channels. <i>IEEE Transactions on Information Theory</i>. 2018;64(5):3371-3393.
    doi:<a href="https://doi.org/10.1109/tit.2018.2789885">10.1109/tit.2018.2789885</a>
  apa: Mondelli, M., Hassani, H., &#38; Urbanke, R. (2018). How to achieve the capacity
    of asymmetric channels. <i>IEEE Transactions on Information Theory</i>. IEEE.
    <a href="https://doi.org/10.1109/tit.2018.2789885">https://doi.org/10.1109/tit.2018.2789885</a>
  chicago: Mondelli, Marco, Hamed Hassani, and Rudiger  Urbanke. “How to Achieve the
    Capacity of Asymmetric Channels.” <i>IEEE Transactions on Information Theory</i>.
    IEEE, 2018. <a href="https://doi.org/10.1109/tit.2018.2789885">https://doi.org/10.1109/tit.2018.2789885</a>.
  ieee: M. Mondelli, H. Hassani, and R. Urbanke, “How to achieve the capacity of asymmetric
    channels,” <i>IEEE Transactions on Information Theory</i>, vol. 64, no. 5. IEEE,
    pp. 3371–3393, 2018.
  ista: Mondelli M, Hassani H, Urbanke R. 2018. How to achieve the capacity of asymmetric
    channels. IEEE Transactions on Information Theory. 64(5), 3371–3393.
  mla: Mondelli, Marco, et al. “How to Achieve the Capacity of Asymmetric Channels.”
    <i>IEEE Transactions on Information Theory</i>, vol. 64, no. 5, IEEE, 2018, pp.
    3371–93, doi:<a href="https://doi.org/10.1109/tit.2018.2789885">10.1109/tit.2018.2789885</a>.
  short: M. Mondelli, H. Hassani, R. Urbanke, IEEE Transactions on Information Theory
    64 (2018) 3371–3393.
date_created: 2019-07-24T12:38:49Z
date_published: 2018-05-01T00:00:00Z
date_updated: 2023-02-23T12:50:46Z
day: '01'
doi: 10.1109/tit.2018.2789885
extern: '1'
external_id:
  arxiv:
  - '1406.7373'
intvolume: '        64'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1406.7373
month: '05'
oa: 1
oa_version: Preprint
page: 3371-3393
publication: IEEE Transactions on Information Theory
publication_identifier:
  issn:
  - 0018-9448
  - 1557-9654
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
  record:
  - id: '6740'
    relation: earlier_version
    status: public
status: public
title: How to achieve the capacity of asymmetric channels
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 64
year: '2018'
...
---
_id: '6730'
abstract:
- lang: eng
  text: We introduce a new approach to proving that a sequence of deterministic linear
    codes achieves capacity on an erasure channel under maximum a posteriori decoding.
    Rather than relying on the precise structure of the codes, our method exploits
    code symmetry. In particular, the technique applies to any sequence of linear
    codes where the blocklengths are strictly increasing, the code rates converge,
    and the permutation group of each code is doubly transitive. In other words, we
    show that symmetry alone implies near-optimal performance. An important consequence
    of this result is that a sequence of Reed-Muller codes with increasing block length
    and converging rate achieves capacity. This possibility has been suggested previously
    in the literature but it has only been proven for cases where the limiting code
    rate is 0 or 1. Moreover, these results extend naturally to all affine-invariant
    codes and, thus, to extended primitive narrow-sense BCH codes. This also resolves,
    in the affirmative, the existence question for capacity-achieving sequences of
    binary cyclic codes. The primary tools used in the proof are the sharp threshold
    property for symmetric monotone Boolean functions and the area theorem for extrinsic
    information transfer functions.
arxiv: 1
author:
- first_name: Shrinivas
  full_name: Kudekar, Shrinivas
  last_name: Kudekar
- first_name: Santhosh
  full_name: Kumar, Santhosh
  last_name: Kumar
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
- first_name: Henry D.
  full_name: Pfister, Henry D.
  last_name: Pfister
- first_name: Eren
  full_name: Sasoglu, Eren
  last_name: Sasoglu
- first_name: Ridiger L.
  full_name: Urbanke, Ridiger L.
  last_name: Urbanke
citation:
  ama: Kudekar S, Kumar S, Mondelli M, Pfister HD, Sasoglu E, Urbanke RL. Reed–Muller
    codes achieve capacity on erasure channels. <i>IEEE Transactions on Information
    Theory</i>. 2017;63(7):4298-4316. doi:<a href="https://doi.org/10.1109/tit.2017.2673829">10.1109/tit.2017.2673829</a>
  apa: Kudekar, S., Kumar, S., Mondelli, M., Pfister, H. D., Sasoglu, E., &#38; Urbanke,
    R. L. (2017). Reed–Muller codes achieve capacity on erasure channels. <i>IEEE
    Transactions on Information Theory</i>. IEEE. <a href="https://doi.org/10.1109/tit.2017.2673829">https://doi.org/10.1109/tit.2017.2673829</a>
  chicago: Kudekar, Shrinivas, Santhosh Kumar, Marco Mondelli, Henry D. Pfister, Eren
    Sasoglu, and Ridiger L. Urbanke. “Reed–Muller Codes Achieve Capacity on Erasure
    Channels.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2017. <a href="https://doi.org/10.1109/tit.2017.2673829">https://doi.org/10.1109/tit.2017.2673829</a>.
  ieee: S. Kudekar, S. Kumar, M. Mondelli, H. D. Pfister, E. Sasoglu, and R. L. Urbanke,
    “Reed–Muller codes achieve capacity on erasure channels,” <i>IEEE Transactions
    on Information Theory</i>, vol. 63, no. 7. IEEE, pp. 4298–4316, 2017.
  ista: Kudekar S, Kumar S, Mondelli M, Pfister HD, Sasoglu E, Urbanke RL. 2017. Reed–Muller
    codes achieve capacity on erasure channels. IEEE Transactions on Information Theory.
    63(7), 4298–4316.
  mla: Kudekar, Shrinivas, et al. “Reed–Muller Codes Achieve Capacity on Erasure Channels.”
    <i>IEEE Transactions on Information Theory</i>, vol. 63, no. 7, IEEE, 2017, pp.
    4298–316, doi:<a href="https://doi.org/10.1109/tit.2017.2673829">10.1109/tit.2017.2673829</a>.
  short: S. Kudekar, S. Kumar, M. Mondelli, H.D. Pfister, E. Sasoglu, R.L. Urbanke,
    IEEE Transactions on Information Theory 63 (2017) 4298–4316.
date_created: 2019-07-30T07:18:11Z
date_published: 2017-07-01T00:00:00Z
date_updated: 2021-01-12T08:08:43Z
day: '01'
doi: 10.1109/tit.2017.2673829
extern: '1'
external_id:
  arxiv:
  - '1601.04689'
intvolume: '        63'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1601.04689
month: '07'
oa: 1
oa_version: Preprint
page: 4298-4316
publication: IEEE Transactions on Information Theory
publication_identifier:
  eissn:
  - 1557-9654
  issn:
  - 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
status: public
title: Reed–Muller codes achieve capacity on erasure channels
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 63
year: '2017'
...
---
_id: '6732'
abstract:
- lang: eng
  text: Consider the transmission of a polar code of block length N and rate R over
    a binary memoryless symmetric channel W and let P e be the block error probability
    under successive cancellation decoding. In this paper, we develop new bounds that
    characterize the relationship of the parameters R, N, P e , and the quality of
    the channel W quantified by its capacity I(W) and its Bhattacharyya parameter
    Z(W). In previous work, two main regimes were studied. In the error exponent regime,
    the channel W and the rate R <; I(W) are fixed, and it was proved that the error
    probability Pe scales roughly as 2 -√N . In the scaling exponent approach, the
    channel W and the error probability Pe are fixed and it was proved that the gap
    to capacity I(W) - R scales as N -1/μ . Here, μ is called scaling exponent and
    this scaling exponent depends on the channel W. A heuristic computation for the
    binary erasure channel (BEC) gives μ = 3.627 and it was shown that, for any channel
    W, 3.579 ≤ μ ≤ 5.702. Our contributions are as follows. First, we provide the
    tighter upper bound μ <;≤ 4.714 valid for any W. With the same technique, we obtain
    the upper bound μ ≤ 3.639 for the case of the BEC; this upper bound approaches
    very closely the heuristically derived value for the scaling exponent of the erasure
    channel. Second, we develop a trade-off between the gap to capacity I(W)- R and
    the error probability Pe as the functions of the block length N. In other words,
    we neither fix the gap to capacity (error exponent regime) nor the error probability
    (scaling exponent regime), but we do consider a moderate deviations regime in
    which we study how fast both quantities, as the functions of the block length
    N, simultaneously go to 0. Third, we prove that polar codes are not affected by
    error floors. To do so, we fix a polar code of block length N and rate R. Then,
    we vary the channel W and study the impact of this variation on the error probability.
    We show that the error probability Pe scales as the Bhattacharyya parameter Z(W)
    raised to a power that scales roughly like VN. This agrees with the scaling in
    the error exponent regime.
article_type: original
arxiv: 1
author:
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
- first_name: S. Hamed
  full_name: Hassani, S. Hamed
  last_name: Hassani
- first_name: Rudiger L.
  full_name: Urbanke, Rudiger L.
  last_name: Urbanke
citation:
  ama: 'Mondelli M, Hassani SH, Urbanke RL. Unified scaling of polar codes: Error
    exponent, scaling exponent, moderate deviations, and error floors. <i>IEEE Transactions
    on Information Theory</i>. 2016;62(12):6698-6712. doi:<a href="https://doi.org/10.1109/tit.2016.2616117">10.1109/tit.2016.2616117</a>'
  apa: 'Mondelli, M., Hassani, S. H., &#38; Urbanke, R. L. (2016). Unified scaling
    of polar codes: Error exponent, scaling exponent, moderate deviations, and error
    floors. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href="https://doi.org/10.1109/tit.2016.2616117">https://doi.org/10.1109/tit.2016.2616117</a>'
  chicago: 'Mondelli, Marco, S. Hamed Hassani, and Rudiger L. Urbanke. “Unified Scaling
    of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error
    Floors.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2016. <a href="https://doi.org/10.1109/tit.2016.2616117">https://doi.org/10.1109/tit.2016.2616117</a>.'
  ieee: 'M. Mondelli, S. H. Hassani, and R. L. Urbanke, “Unified scaling of polar
    codes: Error exponent, scaling exponent, moderate deviations, and error floors,”
    <i>IEEE Transactions on Information Theory</i>, vol. 62, no. 12. IEEE, pp. 6698–6712,
    2016.'
  ista: 'Mondelli M, Hassani SH, Urbanke RL. 2016. Unified scaling of polar codes:
    Error exponent, scaling exponent, moderate deviations, and error floors. IEEE
    Transactions on Information Theory. 62(12), 6698–6712.'
  mla: 'Mondelli, Marco, et al. “Unified Scaling of Polar Codes: Error Exponent, Scaling
    Exponent, Moderate Deviations, and Error Floors.” <i>IEEE Transactions on Information
    Theory</i>, vol. 62, no. 12, IEEE, 2016, pp. 6698–712, doi:<a href="https://doi.org/10.1109/tit.2016.2616117">10.1109/tit.2016.2616117</a>.'
  short: M. Mondelli, S.H. Hassani, R.L. Urbanke, IEEE Transactions on Information
    Theory 62 (2016) 6698–6712.
date_created: 2019-07-31T06:03:49Z
date_published: 2016-12-01T00:00:00Z
date_updated: 2021-01-12T08:08:44Z
day: '01'
doi: 10.1109/tit.2016.2616117
extern: '1'
external_id:
  arxiv:
  - '1501.02444'
intvolume: '        62'
issue: '12'
language:
- iso: eng
main_file_link:
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  url: https://arxiv.org/abs/1501.02444
month: '12'
oa: 1
oa_version: Preprint
page: 6698-6712
publication: IEEE Transactions on Information Theory
publication_identifier:
  eissn:
  - 1557-9654
  issn:
  - 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
status: public
title: 'Unified scaling of polar codes: Error exponent, scaling exponent, moderate
  deviations, and error floors'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 62
year: '2016'
...