---
_id: '10595'
abstract:
- lang: eng
  text: 'A recent line of work has analyzed the theoretical properties of deep neural
    networks via the Neural Tangent Kernel (NTK). In particular, the smallest eigenvalue
    of the NTK has been related to the memorization capacity, the global convergence
    of gradient descent algorithms and the generalization of deep nets. However, existing
    results either provide bounds in the two-layer setting or assume that the spectrum
    of the NTK matrices is bounded away from 0 for multi-layer networks. In this paper,
    we provide tight bounds on the smallest eigenvalue of NTK matrices for deep ReLU
    nets, both in the limiting case of infinite widths and for finite widths. In the
    finite-width setting, the network architectures we consider are fairly general:
    we require the existence of a wide layer with roughly order of $N$ neurons, $N$
    being the number of data samples; and the scaling of the remaining layer widths
    is arbitrary (up to logarithmic factors). To obtain our results, we analyze various
    quantities of independent interest: we give lower bounds on the smallest singular
    value of hidden feature matrices, and upper bounds on the Lipschitz constant of
    input-output feature maps.'
acknowledgement: "The authors would like to thank the anonymous reviewers for their
  helpful comments. MM was partially supported\r\nby the 2019 Lopez-Loreta Prize.
  QN and GM acknowledge support from the European Research Council (ERC) under\r\nthe
  European Union’s Horizon 2020 research and innovation programme (grant agreement
  no 757983)."
alternative_title:
- Proceedings of Machine Learning Research
article_processing_charge: No
arxiv: 1
author:
- first_name: Quynh
  full_name: Nguyen, Quynh
  last_name: Nguyen
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
- first_name: Guido F
  full_name: Montufar, Guido F
  last_name: Montufar
citation:
  ama: 'Nguyen Q, Mondelli M, Montufar GF. Tight bounds on the smallest eigenvalue
    of the neural tangent kernel for deep ReLU networks. In: Meila M, Zhang T, eds.
    <i>Proceedings of the 38th International Conference on Machine Learning</i>. Vol
    139. ML Research Press; 2021:8119-8129.'
  apa: 'Nguyen, Q., Mondelli, M., &#38; Montufar, G. F. (2021). Tight bounds on the
    smallest eigenvalue of the neural tangent kernel for deep ReLU networks. In M.
    Meila &#38; T. Zhang (Eds.), <i>Proceedings of the 38th International Conference
    on Machine Learning</i> (Vol. 139, pp. 8119–8129). Virtual: ML Research Press.'
  chicago: Nguyen, Quynh, Marco Mondelli, and Guido F Montufar. “Tight Bounds on the
    Smallest Eigenvalue of the Neural Tangent Kernel for Deep ReLU Networks.” In <i>Proceedings
    of the 38th International Conference on Machine Learning</i>, edited by Marina
    Meila and Tong Zhang, 139:8119–29. ML Research Press, 2021.
  ieee: Q. Nguyen, M. Mondelli, and G. F. Montufar, “Tight bounds on the smallest
    eigenvalue of the neural tangent kernel for deep ReLU networks,” in <i>Proceedings
    of the 38th International Conference on Machine Learning</i>, Virtual, 2021, vol.
    139, pp. 8119–8129.
  ista: 'Nguyen Q, Mondelli M, Montufar GF. 2021. Tight bounds on the smallest eigenvalue
    of the neural tangent kernel for deep ReLU networks. Proceedings of the 38th International
    Conference on Machine Learning. ICML: International Conference on Machine Learning,
    Proceedings of Machine Learning Research, vol. 139, 8119–8129.'
  mla: Nguyen, Quynh, et al. “Tight Bounds on the Smallest Eigenvalue of the Neural
    Tangent Kernel for Deep ReLU Networks.” <i>Proceedings of the 38th International
    Conference on Machine Learning</i>, edited by Marina Meila and Tong Zhang, vol.
    139, ML Research Press, 2021, pp. 8119–29.
  short: Q. Nguyen, M. Mondelli, G.F. Montufar, in:, M. Meila, T. Zhang (Eds.), Proceedings
    of the 38th International Conference on Machine Learning, ML Research Press, 2021,
    pp. 8119–8129.
conference:
  end_date: 2021-07-24
  location: Virtual
  name: 'ICML: International Conference on Machine Learning'
  start_date: 2021-07-18
date_created: 2022-01-03T10:57:49Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2024-09-10T13:03:17Z
department:
- _id: MaMo
editor:
- first_name: Marina
  full_name: Meila, Marina
  last_name: Meila
- first_name: Tong
  full_name: Zhang, Tong
  last_name: Zhang
external_id:
  arxiv:
  - '2012.11654'
intvolume: '       139'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://proceedings.mlr.press/v139/nguyen21g.html
oa: 1
oa_version: Published Version
page: 8119-8129
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 38th International Conference on Machine Learning
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
status: public
title: Tight bounds on the smallest eigenvalue of the neural tangent kernel for deep
  ReLU networks
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 139
year: '2021'
...
---
_id: '10597'
abstract:
- lang: eng
  text: We thank Emmanuel Abbe and Min Ye for providing us the implementation of RPA
    decoding. D. Fathollahi and M. Mondelli are partially supported by the 2019 Lopez-Loreta
    Prize. N. Farsad is supported by Discovery Grant from the Natural Sciences and
    Engineering Research Council of Canada (NSERC) and Canada Foundation for Innovation
    (CFI), John R. Evans Leader Fund. S. A. Hashemi is supported by a Postdoctoral
    Fellowship from NSERC.
article_processing_charge: No
arxiv: 1
author:
- first_name: Dorsa
  full_name: Fathollahi, Dorsa
  last_name: Fathollahi
- first_name: Nariman
  full_name: Farsad, Nariman
  last_name: Farsad
- first_name: Seyyed Ali
  full_name: Hashemi, Seyyed Ali
  last_name: Hashemi
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
citation:
  ama: 'Fathollahi D, Farsad N, Hashemi SA, Mondelli M. Sparse multi-decoder recursive
    projection aggregation for Reed-Muller codes. In: <i>2021 IEEE International Symposium
    on Information Theory</i>. Institute of Electrical and Electronics Engineers;
    2021:1082-1087. doi:<a href="https://doi.org/10.1109/isit45174.2021.9517887">10.1109/isit45174.2021.9517887</a>'
  apa: 'Fathollahi, D., Farsad, N., Hashemi, S. A., &#38; Mondelli, M. (2021). Sparse
    multi-decoder recursive projection aggregation for Reed-Muller codes. In <i>2021
    IEEE International Symposium on Information Theory</i> (pp. 1082–1087). Virtual,
    Melbourne, Australia: Institute of Electrical and Electronics Engineers. <a href="https://doi.org/10.1109/isit45174.2021.9517887">https://doi.org/10.1109/isit45174.2021.9517887</a>'
  chicago: Fathollahi, Dorsa, Nariman Farsad, Seyyed Ali Hashemi, and Marco Mondelli.
    “Sparse Multi-Decoder Recursive Projection Aggregation for Reed-Muller Codes.”
    In <i>2021 IEEE International Symposium on Information Theory</i>, 1082–87. Institute
    of Electrical and Electronics Engineers, 2021. <a href="https://doi.org/10.1109/isit45174.2021.9517887">https://doi.org/10.1109/isit45174.2021.9517887</a>.
  ieee: D. Fathollahi, N. Farsad, S. A. Hashemi, and M. Mondelli, “Sparse multi-decoder
    recursive projection aggregation for Reed-Muller codes,” in <i>2021 IEEE International
    Symposium on Information Theory</i>, Virtual, Melbourne, Australia, 2021, pp.
    1082–1087.
  ista: 'Fathollahi D, Farsad N, Hashemi SA, Mondelli M. 2021. Sparse multi-decoder
    recursive projection aggregation for Reed-Muller codes. 2021 IEEE International
    Symposium on Information Theory. ISIT: International Symposium on Information
    Theory, 1082–1087.'
  mla: Fathollahi, Dorsa, et al. “Sparse Multi-Decoder Recursive Projection Aggregation
    for Reed-Muller Codes.” <i>2021 IEEE International Symposium on Information Theory</i>,
    Institute of Electrical and Electronics Engineers, 2021, pp. 1082–87, doi:<a href="https://doi.org/10.1109/isit45174.2021.9517887">10.1109/isit45174.2021.9517887</a>.
  short: D. Fathollahi, N. Farsad, S.A. Hashemi, M. Mondelli, in:, 2021 IEEE International
    Symposium on Information Theory, Institute of Electrical and Electronics Engineers,
    2021, pp. 1082–1087.
conference:
  end_date: 2021-07-20
  location: Virtual, Melbourne, Australia
  name: 'ISIT: International Symposium on Information Theory'
  start_date: 2021-07-12
date_created: 2022-01-03T11:31:26Z
date_published: 2021-09-01T00:00:00Z
date_updated: 2024-09-10T13:03:18Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/isit45174.2021.9517887
external_id:
  arxiv:
  - '2011.12882'
  isi:
  - '000701502201029'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2011.12882
month: '09'
oa: 1
oa_version: Preprint
page: 1082-1087
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 2021 IEEE International Symposium on Information Theory
publication_identifier:
  eisbn:
  - 978-1-5386-8209-8
  isbn:
  - 978-1-5386-8210-4
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sparse multi-decoder recursive projection aggregation for Reed-Muller codes
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '10598'
abstract:
- lang: eng
  text: ' We consider the problem of estimating a signal from measurements obtained
    via a generalized linear model. We focus on estimators based on approximate message
    passing (AMP), a family of iterative algorithms with many appealing features:
    the performance of AMP in the high-dimensional limit can be succinctly characterized
    under suitable model assumptions; AMP can also be tailored to the empirical distribution
    of the signal entries, and for a wide class of estimation problems, AMP is conjectured
    to be optimal among all polynomial-time algorithms. However, a major issue of
    AMP is that in many models (such as phase retrieval), it requires an initialization
    correlated with the ground-truth signal and independent from the measurement matrix.
    Assuming that such an initialization is available is typically not realistic.
    In this paper, we solve this problem by proposing an AMP algorithm initialized
    with a spectral estimator. With such an initialization, the standard AMP analysis
    fails since the spectral estimator depends in a complicated way on the design
    matrix. Our main contribution is a rigorous characterization of the performance
    of AMP with spectral initialization in the high-dimensional limit. The key technical
    idea is to define and analyze a two-phase artificial AMP algorithm that first
    produces the spectral estimator, and then closely approximates the iterates of
    the true AMP. We also provide numerical results that demonstrate the validity
    of the proposed approach. '
acknowledgement: The authors would like to thank Andrea Montanari for helpful discussions.
  M. Mondelli was partially supported by the 2019 Lopez-Loreta Prize. R. Venkataramanan
  was partially supported by the Alan Turing Institute under the EPSRC grant EP/N510129/1.
alternative_title:
- Proceedings of Machine Learning Research
article_processing_charge: Yes (via OA deal)
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: Ramji
  full_name: Venkataramanan, Ramji
  last_name: Venkataramanan
citation:
  ama: 'Mondelli M, Venkataramanan R. Approximate message passing with spectral initialization
    for generalized linear models. In: Banerjee A, Fukumizu K, eds. <i>Proceedings
    of The 24th International Conference on Artificial Intelligence and Statistics</i>.
    Vol 130. ML Research Press; 2021:397-405.'
  apa: 'Mondelli, M., &#38; Venkataramanan, R. (2021). Approximate message passing
    with spectral initialization for generalized linear models. In A. Banerjee &#38;
    K. Fukumizu (Eds.), <i>Proceedings of The 24th International Conference on Artificial
    Intelligence and Statistics</i> (Vol. 130, pp. 397–405). Virtual, San Diego, CA,
    United States: ML Research Press.'
  chicago: Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing
    with Spectral Initialization for Generalized Linear Models.” In <i>Proceedings
    of The 24th International Conference on Artificial Intelligence and Statistics</i>,
    edited by Arindam Banerjee and Kenji Fukumizu, 130:397–405. ML Research Press,
    2021.
  ieee: M. Mondelli and R. Venkataramanan, “Approximate message passing with spectral
    initialization for generalized linear models,” in <i>Proceedings of The 24th International
    Conference on Artificial Intelligence and Statistics</i>, Virtual, San Diego,
    CA, United States, 2021, vol. 130, pp. 397–405.
  ista: 'Mondelli M, Venkataramanan R. 2021. Approximate message passing with spectral
    initialization for generalized linear models. Proceedings of The 24th International
    Conference on Artificial Intelligence and Statistics. AISTATS: Artificial Intelligence
    and Statistics, Proceedings of Machine Learning Research, vol. 130, 397–405.'
  mla: Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing with
    Spectral Initialization for Generalized Linear Models.” <i>Proceedings of The
    24th International Conference on Artificial Intelligence and Statistics</i>, edited
    by Arindam Banerjee and Kenji Fukumizu, vol. 130, ML Research Press, 2021, pp.
    397–405.
  short: M. Mondelli, R. Venkataramanan, in:, A. Banerjee, K. Fukumizu (Eds.), Proceedings
    of The 24th International Conference on Artificial Intelligence and Statistics,
    ML Research Press, 2021, pp. 397–405.
conference:
  end_date: 2021-04-15
  location: Virtual, San Diego, CA, United States
  name: 'AISTATS: Artificial Intelligence and Statistics'
  start_date: 2021-04-13
date_created: 2022-01-03T11:34:22Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2024-03-07T10:36:53Z
day: '01'
department:
- _id: MaMo
editor:
- first_name: Arindam
  full_name: Banerjee, Arindam
  last_name: Banerjee
- first_name: Kenji
  full_name: Fukumizu, Kenji
  last_name: Fukumizu
external_id:
  arxiv:
  - '2010.03460'
intvolume: '       130'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://proceedings.mlr.press/v130/mondelli21a.html
month: '04'
oa: 1
oa_version: Preprint
page: 397-405
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of The 24th International Conference on Artificial Intelligence
  and Statistics
publication_identifier:
  issn:
  - 2640-3498
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
related_material:
  record:
  - id: '12480'
    relation: later_version
    status: public
scopus_import: '1'
status: public
title: Approximate message passing with spectral initialization for generalized linear
  models
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 130
year: '2021'
...
---
_id: '10599'
abstract:
- lang: eng
  text: A two-part successive syndrome-check decoding of polar codes is proposed with
    the first part successively refining the received codeword and the second part
    checking its syndrome. A new formulation of the successive-cancellation (SC) decoding
    algorithm is presented that allows for successively refining the received codeword
    by comparing the log-likelihood ratio value of a frozen bit with its predefined
    value. The syndrome of the refined received codeword is then checked for possible
    errors. In case there are no errors, the decoding process is terminated. Otherwise,
    the decoder continues to refine the received codeword. The proposed method is
    extended to the case of SC list (SCL) decoding by terminating the decoding process
    when the syndrome of the best candidate in the list indicates no errors. Simulation
    results show that the proposed method reduces the time-complexity of SC and SCL
    decoders and their fast variants, especially at high signal-to-noise ratios.
acknowledgement: This work is supported in part by ONR grant N00014-18-1-2191. S.
  A. Hashemi was supported by a Postdoctoral Fellowship from the Natural Sciences
  and Engineering Research Council of Canada (NSERC) and by Huawei. M. Mondelli was
  partially supported by the 2019 Lopez-Loreta Prize.
article_processing_charge: No
arxiv: 1
author:
- first_name: Seyyed Ali
  full_name: Hashemi, Seyyed Ali
  last_name: Hashemi
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
- first_name: John
  full_name: Cioffi, John
  last_name: Cioffi
- first_name: Andrea
  full_name: Goldsmith, Andrea
  last_name: Goldsmith
citation:
  ama: 'Hashemi SA, Mondelli M, Cioffi J, Goldsmith A. Successive syndrome-check decoding
    of polar codes. In: <i>Proceedings of the 55th Asilomar Conference on Signals,
    Systems, and Computers</i>. Vol 2021-October. Institute of Electrical and Electronics
    Engineers; 2021:943-947. doi:<a href="https://doi.org/10.1109/IEEECONF53345.2021.9723394">10.1109/IEEECONF53345.2021.9723394</a>'
  apa: 'Hashemi, S. A., Mondelli, M., Cioffi, J., &#38; Goldsmith, A. (2021). Successive
    syndrome-check decoding of polar codes. In <i>Proceedings of the 55th Asilomar
    Conference on Signals, Systems, and Computers</i> (Vol. 2021–October, pp. 943–947).
    Virtual, Pacific Grove, CA, United States: Institute of Electrical and Electronics
    Engineers. <a href="https://doi.org/10.1109/IEEECONF53345.2021.9723394">https://doi.org/10.1109/IEEECONF53345.2021.9723394</a>'
  chicago: Hashemi, Seyyed Ali, Marco Mondelli, John Cioffi, and Andrea Goldsmith.
    “Successive Syndrome-Check Decoding of Polar Codes.” In <i>Proceedings of the
    55th Asilomar Conference on Signals, Systems, and Computers</i>, 2021–October:943–47.
    Institute of Electrical and Electronics Engineers, 2021. <a href="https://doi.org/10.1109/IEEECONF53345.2021.9723394">https://doi.org/10.1109/IEEECONF53345.2021.9723394</a>.
  ieee: S. A. Hashemi, M. Mondelli, J. Cioffi, and A. Goldsmith, “Successive syndrome-check
    decoding of polar codes,” in <i>Proceedings of the 55th Asilomar Conference on
    Signals, Systems, and Computers</i>, Virtual, Pacific Grove, CA, United States,
    2021, vol. 2021–October, pp. 943–947.
  ista: 'Hashemi SA, Mondelli M, Cioffi J, Goldsmith A. 2021. Successive syndrome-check
    decoding of polar codes. Proceedings of the 55th Asilomar Conference on Signals,
    Systems, and Computers. ACSSC: Asilomar Conference on Signals, Systems, and Computers
    vol. 2021–October, 943–947.'
  mla: Hashemi, Seyyed Ali, et al. “Successive Syndrome-Check Decoding of Polar Codes.”
    <i>Proceedings of the 55th Asilomar Conference on Signals, Systems, and Computers</i>,
    vol. 2021–October, Institute of Electrical and Electronics Engineers, 2021, pp.
    943–47, doi:<a href="https://doi.org/10.1109/IEEECONF53345.2021.9723394">10.1109/IEEECONF53345.2021.9723394</a>.
  short: S.A. Hashemi, M. Mondelli, J. Cioffi, A. Goldsmith, in:, Proceedings of the
    55th Asilomar Conference on Signals, Systems, and Computers, Institute of Electrical
    and Electronics Engineers, 2021, pp. 943–947.
conference:
  end_date: 2021-11-03
  location: Virtual, Pacific Grove, CA, United States
  name: 'ACSSC: Asilomar Conference on Signals, Systems, and Computers'
  start_date: 2021-10-31
date_created: 2022-01-03T11:39:51Z
date_published: 2021-11-01T00:00:00Z
date_updated: 2024-09-10T13:03:17Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/IEEECONF53345.2021.9723394
external_id:
  arxiv:
  - '2112.00057'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2112.00057'
month: '11'
oa: 1
oa_version: Preprint
page: 943-947
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 55th Asilomar Conference on Signals, Systems, and
  Computers
publication_identifier:
  isbn:
  - '9781665458283'
  issn:
  - 1058-6393
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Successive syndrome-check decoding of polar codes
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2021-October
year: '2021'
...
---
_id: '8536'
abstract:
- lang: eng
  text: This work analyzes the latency of the simplified successive cancellation (SSC)
    decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It
    is shown that, unlike conventional successive cancellation decoding, where latency
    is linear in the block length, the latency of SSC decoding is sublinear. More
    specifically, the latency of SSC decoding is O(N 1−1/µ ), where N is the block
    length and µ is the scaling exponent of the channel, which captures the speed
    of convergence of the rate to capacity. Numerical results demonstrate the tightness
    of the bound and show that most of the latency reduction arises from the parallel
    decoding of subcodes of rate 0 and 1.
acknowledgement: M. Mondelli was partially supported by grants NSF DMS-1613091, CCF-1714305,
  IIS-1741162 and ONR N00014-18-1-2729. S. A. Hashemi is supported by a Postdoctoral
  Fellowship from the Natural Sciences and Engineering Research Council of Canada
  (NSERC) and by Huawei.
article_number: 401-406
article_processing_charge: No
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: Seyyed Ali
  full_name: Hashemi, Seyyed Ali
  last_name: Hashemi
- first_name: John
  full_name: Cioffi, John
  last_name: Cioffi
- first_name: Andrea
  full_name: Goldsmith, Andrea
  last_name: Goldsmith
citation:
  ama: 'Mondelli M, Hashemi SA, Cioffi J, Goldsmith A. Simplified successive cancellation
    decoding of polar codes has sublinear latency. In: <i>IEEE International Symposium
    on Information Theory - Proceedings</i>. Vol 2020-June. IEEE; 2020. doi:<a href="https://doi.org/10.1109/ISIT44484.2020.9174141">10.1109/ISIT44484.2020.9174141</a>'
  apa: 'Mondelli, M., Hashemi, S. A., Cioffi, J., &#38; Goldsmith, A. (2020). Simplified
    successive cancellation decoding of polar codes has sublinear latency. In <i>IEEE
    International Symposium on Information Theory - Proceedings</i> (Vol. 2020–June).
    Los Angeles, CA, United States: IEEE. <a href="https://doi.org/10.1109/ISIT44484.2020.9174141">https://doi.org/10.1109/ISIT44484.2020.9174141</a>'
  chicago: Mondelli, Marco, Seyyed Ali Hashemi, John Cioffi, and Andrea Goldsmith.
    “Simplified Successive Cancellation Decoding of Polar Codes Has Sublinear Latency.”
    In <i>IEEE International Symposium on Information Theory - Proceedings</i>, Vol.
    2020–June. IEEE, 2020. <a href="https://doi.org/10.1109/ISIT44484.2020.9174141">https://doi.org/10.1109/ISIT44484.2020.9174141</a>.
  ieee: M. Mondelli, S. A. Hashemi, J. Cioffi, and A. Goldsmith, “Simplified successive
    cancellation decoding of polar codes has sublinear latency,” in <i>IEEE International
    Symposium on Information Theory - Proceedings</i>, Los Angeles, CA, United States,
    2020, vol. 2020–June.
  ista: 'Mondelli M, Hashemi SA, Cioffi J, Goldsmith A. 2020. Simplified successive
    cancellation decoding of polar codes has sublinear latency. IEEE International
    Symposium on Information Theory - Proceedings. ISIT: Internation Symposium on
    Information Theory vol. 2020–June, 401–406.'
  mla: Mondelli, Marco, et al. “Simplified Successive Cancellation Decoding of Polar
    Codes Has Sublinear Latency.” <i>IEEE International Symposium on Information Theory
    - Proceedings</i>, vol. 2020–June, 401–406, IEEE, 2020, doi:<a href="https://doi.org/10.1109/ISIT44484.2020.9174141">10.1109/ISIT44484.2020.9174141</a>.
  short: M. Mondelli, S.A. Hashemi, J. Cioffi, A. Goldsmith, in:, IEEE International
    Symposium on Information Theory - Proceedings, IEEE, 2020.
conference:
  end_date: 2020-06-26
  location: Los Angeles, CA, United States
  name: 'ISIT: Internation Symposium on Information Theory'
  start_date: 2020-06-21
date_created: 2020-09-20T22:01:37Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-08-07T13:36:24Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/ISIT44484.2020.9174141
external_id:
  arxiv:
  - '1909.04892'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1909.04892
month: '06'
oa: 1
oa_version: Preprint
publication: IEEE International Symposium on Information Theory - Proceedings
publication_identifier:
  isbn:
  - '9781728164328'
  issn:
  - '21578095'
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
  record:
  - id: '9047'
    relation: later_version
    status: public
scopus_import: '1'
status: public
title: Simplified successive cancellation decoding of polar codes has sublinear latency
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2020-June
year: '2020'
...
---
_id: '6748'
abstract:
- lang: eng
  text: "Fitting a function by using linear combinations of a large number N of `simple'
    components is one of the most fruitful ideas in statistical learning. This idea
    lies at the core of a variety of methods, from two-layer neural networks to kernel
    regression, to boosting. In general, the resulting risk minimization problem is
    non-convex and is solved by gradient descent or its variants. Unfortunately, little
    is known about global convergence properties of these approaches.\r\nHere we consider
    the problem of learning a concave function f on a compact convex domain Ω⊆ℝd,
    using linear combinations of `bump-like' components (neurons). The parameters
    to be fitted are the centers of N bumps, and the resulting empirical risk minimization
    problem is highly non-convex. We prove that, in the limit in which the number
    of neurons diverges, the evolution of gradient descent converges to a Wasserstein
    gradient flow in the space of probability distributions over Ω. Further, when
    the bump width δ tends to 0, this gradient flow has a limit which is a viscous
    porous medium equation. Remarkably, the cost function optimized by this gradient
    flow exhibits a special property known as displacement convexity, which implies
    exponential convergence rates for N→∞, δ→0. Surprisingly, this asymptotic theory
    appears to capture well the behavior for moderate values of δ,N. Explaining this
    phenomenon, and understanding the dependence on δ,N in a quantitative manner remains
    an outstanding challenge."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Adel
  full_name: Javanmard, Adel
  last_name: Javanmard
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
- first_name: Andrea
  full_name: Montanari, Andrea
  last_name: Montanari
citation:
  ama: Javanmard A, Mondelli M, Montanari A. Analysis of a two-layer neural network
    via displacement convexity. <i>Annals of Statistics</i>. 2020;48(6):3619-3642.
    doi:<a href="https://doi.org/10.1214/20-AOS1945">10.1214/20-AOS1945</a>
  apa: Javanmard, A., Mondelli, M., &#38; Montanari, A. (2020). Analysis of a two-layer
    neural network via displacement convexity. <i>Annals of Statistics</i>. Institute
    of Mathematical Statistics. <a href="https://doi.org/10.1214/20-AOS1945">https://doi.org/10.1214/20-AOS1945</a>
  chicago: Javanmard, Adel, Marco Mondelli, and Andrea Montanari. “Analysis of a Two-Layer
    Neural Network via Displacement Convexity.” <i>Annals of Statistics</i>. Institute
    of Mathematical Statistics, 2020. <a href="https://doi.org/10.1214/20-AOS1945">https://doi.org/10.1214/20-AOS1945</a>.
  ieee: A. Javanmard, M. Mondelli, and A. Montanari, “Analysis of a two-layer neural
    network via displacement convexity,” <i>Annals of Statistics</i>, vol. 48, no.
    6. Institute of Mathematical Statistics, pp. 3619–3642, 2020.
  ista: Javanmard A, Mondelli M, Montanari A. 2020. Analysis of a two-layer neural
    network via displacement convexity. Annals of Statistics. 48(6), 3619–3642.
  mla: Javanmard, Adel, et al. “Analysis of a Two-Layer Neural Network via Displacement
    Convexity.” <i>Annals of Statistics</i>, vol. 48, no. 6, Institute of Mathematical
    Statistics, 2020, pp. 3619–42, doi:<a href="https://doi.org/10.1214/20-AOS1945">10.1214/20-AOS1945</a>.
  short: A. Javanmard, M. Mondelli, A. Montanari, Annals of Statistics 48 (2020) 3619–3642.
date_created: 2019-07-31T09:39:42Z
date_published: 2020-12-11T00:00:00Z
date_updated: 2024-03-06T08:28:50Z
day: '11'
department:
- _id: MaMo
doi: 10.1214/20-AOS1945
external_id:
  arxiv:
  - '1901.01375'
  isi:
  - '000598369200021'
intvolume: '        48'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1901.01375
month: '12'
oa: 1
oa_version: Preprint
page: 3619-3642
publication: Annals of Statistics
publication_identifier:
  eissn:
  - 1941-7330
  issn:
  - 1932-6157
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
status: public
title: Analysis of a two-layer neural network via displacement convexity
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2020'
...
---
_id: '9198'
abstract:
- lang: eng
  text: "The optimization of multilayer neural networks typically leads to a solution\r\nwith
    zero training error, yet the landscape can exhibit spurious local minima\r\nand
    the minima can be disconnected. In this paper, we shed light on this\r\nphenomenon:
    we show that the combination of stochastic gradient descent (SGD)\r\nand over-parameterization
    makes the landscape of multilayer neural networks\r\napproximately connected and
    thus more favorable to optimization. More\r\nspecifically, we prove that SGD solutions
    are connected via a piecewise linear\r\npath, and the increase in loss along this
    path vanishes as the number of\r\nneurons grows large. This result is a consequence
    of the fact that the\r\nparameters found by SGD are increasingly dropout stable
    as the network becomes\r\nwider. We show that, if we remove part of the neurons
    (and suitably rescale the\r\nremaining ones), the change in loss is independent
    of the total number of\r\nneurons, and it depends only on how many neurons are
    left. Our results exhibit\r\na mild dependence on the input dimension: they are
    dimension-free for two-layer\r\nnetworks and depend linearly on the dimension
    for multilayer networks. We\r\nvalidate our theoretical findings with numerical
    experiments for different\r\narchitectures and classification tasks."
acknowledgement: M. Mondelli was partially supported by the 2019 LopezLoreta Prize.
  The authors thank Phan-Minh Nguyen for helpful discussions and the IST Distributed
  Algorithms and Systems Lab for providing computational resources.
article_processing_charge: No
arxiv: 1
author:
- first_name: Alexander
  full_name: Shevchenko, Alexander
  last_name: Shevchenko
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
citation:
  ama: 'Shevchenko A, Mondelli M. Landscape connectivity and dropout stability of
    SGD solutions for over-parameterized neural networks. In: <i>Proceedings of the
    37th International Conference on Machine Learning</i>. Vol 119. ML Research Press;
    2020:8773-8784.'
  apa: Shevchenko, A., &#38; Mondelli, M. (2020). Landscape connectivity and dropout
    stability of SGD solutions for over-parameterized neural networks. In <i>Proceedings
    of the 37th International Conference on Machine Learning</i> (Vol. 119, pp. 8773–8784).
    ML Research Press.
  chicago: Shevchenko, Alexander, and Marco Mondelli. “Landscape Connectivity and
    Dropout Stability of SGD Solutions for Over-Parameterized Neural Networks.” In
    <i>Proceedings of the 37th International Conference on Machine Learning</i>, 119:8773–84.
    ML Research Press, 2020.
  ieee: A. Shevchenko and M. Mondelli, “Landscape connectivity and dropout stability
    of SGD solutions for over-parameterized neural networks,” in <i>Proceedings of
    the 37th International Conference on Machine Learning</i>, 2020, vol. 119, pp.
    8773–8784.
  ista: Shevchenko A, Mondelli M. 2020. Landscape connectivity and dropout stability
    of SGD solutions for over-parameterized neural networks. Proceedings of the 37th
    International Conference on Machine Learning. vol. 119, 8773–8784.
  mla: Shevchenko, Alexander, and Marco Mondelli. “Landscape Connectivity and Dropout
    Stability of SGD Solutions for Over-Parameterized Neural Networks.” <i>Proceedings
    of the 37th International Conference on Machine Learning</i>, vol. 119, ML Research
    Press, 2020, pp. 8773–84.
  short: A. Shevchenko, M. Mondelli, in:, Proceedings of the 37th International Conference
    on Machine Learning, ML Research Press, 2020, pp. 8773–8784.
date_created: 2021-02-25T09:36:22Z
date_published: 2020-07-13T00:00:00Z
date_updated: 2024-09-10T13:03:19Z
day: '13'
ddc:
- '000'
department:
- _id: MaMo
external_id:
  arxiv:
  - '1912.10095'
file:
- access_level: open_access
  checksum: f042c8d4316bd87c6361aa76f1fbdbbe
  content_type: application/pdf
  creator: dernst
  date_created: 2021-03-02T15:38:14Z
  date_updated: 2021-03-02T15:38:14Z
  file_id: '9217'
  file_name: 2020_PMLR_Shevchenko.pdf
  file_size: 5336380
  relation: main_file
  success: 1
file_date_updated: 2021-03-02T15:38:14Z
has_accepted_license: '1'
intvolume: '       119'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 8773-8784
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 37th International Conference on Machine Learning
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
status: public
title: Landscape connectivity and dropout stability of SGD solutions for over-parameterized
  neural networks
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 119
year: '2020'
...
---
_id: '9221'
abstract:
- lang: eng
  text: "Recent works have shown that gradient descent can find a global minimum for
    over-parameterized neural networks where the widths of all the hidden layers scale
    polynomially with N (N being the number of training samples). In this paper, we
    prove that, for deep networks, a single layer of width N following the input layer
    suffices to ensure a similar guarantee. In particular, all the remaining layers
    are allowed to have constant widths, and form a pyramidal topology. We show an
    application of our result to the widely used LeCun’s initialization and obtain
    an over-parameterization requirement for the single wide layer of order N2.\r\n"
acknowledgement: The authors would like to thank Jan Maas, Mahdi Soltanolkotabi, and
  Daniel Soudry for the helpful discussions, Marius Kloft, Matthias Hein and Quoc
  Dinh Tran for proofreading portions of a prior version of this paper, and James
  Martens for a clarification concerning LeCun’s initialization. M. Mondelli was partially
  supported by the 2019 Lopez-Loreta Prize. Q. Nguyen was partially supported by the
  German Research Foundation (DFG) award KL 2698/2-1.
article_processing_charge: No
arxiv: 1
author:
- first_name: Quynh
  full_name: Nguyen, Quynh
  last_name: Nguyen
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
citation:
  ama: 'Nguyen Q, Mondelli M. Global convergence of deep networks with one wide layer
    followed by pyramidal topology. In: <i>34th Conference on Neural Information Processing
    Systems</i>. Vol 33. Curran Associates; 2020:11961–11972.'
  apa: 'Nguyen, Q., &#38; Mondelli, M. (2020). Global convergence of deep networks
    with one wide layer followed by pyramidal topology. In <i>34th Conference on Neural
    Information Processing Systems</i> (Vol. 33, pp. 11961–11972). Vancouver, Canada:
    Curran Associates.'
  chicago: Nguyen, Quynh, and Marco Mondelli. “Global Convergence of Deep Networks
    with One Wide Layer Followed by Pyramidal Topology.” In <i>34th Conference on
    Neural Information Processing Systems</i>, 33:11961–11972. Curran Associates,
    2020.
  ieee: Q. Nguyen and M. Mondelli, “Global convergence of deep networks with one wide
    layer followed by pyramidal topology,” in <i>34th Conference on Neural Information
    Processing Systems</i>, Vancouver, Canada, 2020, vol. 33, pp. 11961–11972.
  ista: 'Nguyen Q, Mondelli M. 2020. Global convergence of deep networks with one
    wide layer followed by pyramidal topology. 34th Conference on Neural Information
    Processing Systems. NeurIPS: Neural Information Processing Systems vol. 33, 11961–11972.'
  mla: Nguyen, Quynh, and Marco Mondelli. “Global Convergence of Deep Networks with
    One Wide Layer Followed by Pyramidal Topology.” <i>34th Conference on Neural Information
    Processing Systems</i>, vol. 33, Curran Associates, 2020, pp. 11961–11972.
  short: Q. Nguyen, M. Mondelli, in:, 34th Conference on Neural Information Processing
    Systems, Curran Associates, 2020, pp. 11961–11972.
conference:
  end_date: 2020-12-12
  location: Vancouver, Canada
  name: 'NeurIPS: Neural Information Processing Systems'
  start_date: 2020-12-06
date_created: 2021-03-03T12:06:02Z
date_published: 2020-07-07T00:00:00Z
date_updated: 2024-09-10T13:03:17Z
day: '07'
department:
- _id: MaMo
external_id:
  arxiv:
  - '2002.07867'
intvolume: '        33'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2002.07867
month: '07'
oa: 1
oa_version: Preprint
page: 11961–11972
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 34th Conference on Neural Information Processing Systems
publication_status: published
publisher: Curran Associates
quality_controlled: '1'
status: public
title: Global convergence of deep networks with one wide layer followed by pyramidal
  topology
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 33
year: '2020'
...
---
_id: '6750'
abstract:
- lang: eng
  text: 'Polar codes have gained extensive attention during the past few years and
    recently they have been selected for the next generation of wireless communications
    standards (5G). Successive-cancellation-based (SC-based) decoders, such as SC
    list (SCL) and SC flip (SCF), provide a reasonable error performance for polar
    codes at the cost of low decoding speed. Fast SC-based decoders, such as Fast-SSC,
    Fast-SSCL, and Fast-SSCF, identify the special constituent codes in a polar code
    graph off-line, produce a list of operations, store the list in memory, and feed
    the list to the decoder to decode the constituent codes in order efficiently,
    thus increasing the decoding speed. However, the list of operations is dependent
    on the code rate and as the rate changes, a new list is produced, making fast
    SC-based decoders not rate-flexible. In this paper, we propose a completely rate-flexible
    fast SC-based decoder by creating the list of operations directly in hardware,
    with low implementation complexity. We further propose a hardware architecture
    implementing the proposed method and show that the area occupation of the rate-flexible
    fast SC-based decoder in this paper is only 38% of the total area of the memory-based
    base-line decoder when 5G code rates are supported. '
article_number: '8854897'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Seyyed Ali
  full_name: Hashemi, Seyyed Ali
  last_name: Hashemi
- first_name: Carlo
  full_name: Condo, Carlo
  last_name: Condo
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
- first_name: Warren J
  full_name: Gross, Warren J
  last_name: Gross
citation:
  ama: Hashemi SA, Condo C, Mondelli M, Gross WJ. Rate-flexible fast polar decoders.
    <i>IEEE Transactions on Signal Processing</i>. 2019;67(22). doi:<a href="https://doi.org/10.1109/TSP.2019.2944738">10.1109/TSP.2019.2944738</a>
  apa: Hashemi, S. A., Condo, C., Mondelli, M., &#38; Gross, W. J. (2019). Rate-flexible
    fast polar decoders. <i>IEEE Transactions on Signal Processing</i>. IEEE. <a href="https://doi.org/10.1109/TSP.2019.2944738">https://doi.org/10.1109/TSP.2019.2944738</a>
  chicago: Hashemi, Seyyed Ali, Carlo Condo, Marco Mondelli, and Warren J Gross. “Rate-Flexible
    Fast Polar Decoders.” <i>IEEE Transactions on Signal Processing</i>. IEEE, 2019.
    <a href="https://doi.org/10.1109/TSP.2019.2944738">https://doi.org/10.1109/TSP.2019.2944738</a>.
  ieee: S. A. Hashemi, C. Condo, M. Mondelli, and W. J. Gross, “Rate-flexible fast
    polar decoders,” <i>IEEE Transactions on Signal Processing</i>, vol. 67, no. 22.
    IEEE, 2019.
  ista: Hashemi SA, Condo C, Mondelli M, Gross WJ. 2019. Rate-flexible fast polar
    decoders. IEEE Transactions on Signal Processing. 67(22), 8854897.
  mla: Hashemi, Seyyed Ali, et al. “Rate-Flexible Fast Polar Decoders.” <i>IEEE Transactions
    on Signal Processing</i>, vol. 67, no. 22, 8854897, IEEE, 2019, doi:<a href="https://doi.org/10.1109/TSP.2019.2944738">10.1109/TSP.2019.2944738</a>.
  short: S.A. Hashemi, C. Condo, M. Mondelli, W.J. Gross, IEEE Transactions on Signal
    Processing 67 (2019).
date_created: 2019-07-31T09:51:14Z
date_published: 2019-11-15T00:00:00Z
date_updated: 2021-01-12T08:08:51Z
day: '15'
department:
- _id: MaMo
doi: 10.1109/TSP.2019.2944738
external_id:
  arxiv:
  - '1903.09203'
intvolume: '        67'
issue: '22'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1903.09203
month: '11'
oa: 1
oa_version: Preprint
publication: IEEE Transactions on Signal Processing
publication_identifier:
  issn:
  - 1053587X
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: 1
status: public
title: Rate-flexible fast polar decoders
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 67
year: '2019'
...
---
_id: '7007'
abstract:
- lang: eng
  text: 'We consider the primitive relay channel, where the source sends a message
    to the relay and to the destination, and the relay helps the communication by
    transmitting an additional message to the destination via a separate channel.
    Two well-known coding techniques have been introduced for this setting: decode-and-forward
    and compress-and-forward. In decode-and-forward, the relay completely decodes
    the message and sends some information to the destination; in compress-and-forward,
    the relay does not decode, and it sends a compressed version of the received signal
    to the destination using Wyner–Ziv coding. In this paper, we present a novel coding
    paradigm that provides an improved achievable rate for the primitive relay channel.
    The idea is to combine compress-and-forward and decode-and-forward via a chaining
    construction. We transmit over pairs of blocks: in the first block, we use compress-and-forward;
    and, in the second block, we use decode-and-forward. More specifically, in the
    first block, the relay does not decode, it compresses the received signal via
    Wyner–Ziv, and it sends only part of the compression to the destination. In the
    second block, the relay completely decodes the message, it sends some information
    to the destination, and it also sends the remaining part of the compression coming
    from the first block. By doing so, we are able to strictly outperform both compress-and-forward
    and decode-and-forward. Note that the proposed coding scheme can be implemented
    with polar codes. As such, it has the typical attractive properties of polar coding
    schemes, namely, quasi-linear encoding and decoding complexity, and error probability
    that decays at super-polynomial speed. As a running example, we take into account
    the special case of the erasure relay channel, and we provide a comparison between
    the rates achievable by our proposed scheme and the existing upper and lower bounds.'
article_number: '218'
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: Rüdiger
  full_name: Urbanke, Rüdiger
  last_name: Urbanke
citation:
  ama: Mondelli M, Hassani SH, Urbanke R. A new coding paradigm for the primitive
    relay channel. <i>Algorithms</i>. 2019;12(10). doi:<a href="https://doi.org/10.3390/a12100218">10.3390/a12100218</a>
  apa: Mondelli, M., Hassani, S. H., &#38; Urbanke, R. (2019). A new coding paradigm
    for the primitive relay channel. <i>Algorithms</i>. MDPI. <a href="https://doi.org/10.3390/a12100218">https://doi.org/10.3390/a12100218</a>
  chicago: Mondelli, Marco, S. Hamed Hassani, and Rüdiger Urbanke. “A New Coding Paradigm
    for the Primitive Relay Channel.” <i>Algorithms</i>. MDPI, 2019. <a href="https://doi.org/10.3390/a12100218">https://doi.org/10.3390/a12100218</a>.
  ieee: M. Mondelli, S. H. Hassani, and R. Urbanke, “A new coding paradigm for the
    primitive relay channel,” <i>Algorithms</i>, vol. 12, no. 10. MDPI, 2019.
  ista: Mondelli M, Hassani SH, Urbanke R. 2019. A new coding paradigm for the primitive
    relay channel. Algorithms. 12(10), 218.
  mla: Mondelli, Marco, et al. “A New Coding Paradigm for the Primitive Relay Channel.”
    <i>Algorithms</i>, vol. 12, no. 10, 218, MDPI, 2019, doi:<a href="https://doi.org/10.3390/a12100218">10.3390/a12100218</a>.
  short: M. Mondelli, S.H. Hassani, R. Urbanke, Algorithms 12 (2019).
date_created: 2019-11-12T14:46:19Z
date_published: 2019-10-18T00:00:00Z
date_updated: 2023-02-23T12:49:28Z
day: '18'
ddc:
- '510'
department:
- _id: MaMo
doi: 10.3390/a12100218
external_id:
  arxiv:
  - '1801.03153'
file:
- access_level: open_access
  checksum: 267756d8f9db572f496cd1663c89d59a
  content_type: application/pdf
  creator: dernst
  date_created: 2019-11-12T14:48:45Z
  date_updated: 2020-07-14T12:47:47Z
  file_id: '7008'
  file_name: 2019_Algorithms_Mondelli.pdf
  file_size: 696791
  relation: main_file
file_date_updated: 2020-07-14T12:47:47Z
has_accepted_license: '1'
intvolume: '        12'
issue: '10'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
publication: Algorithms
publication_identifier:
  issn:
  - 1999-4893
publication_status: published
publisher: MDPI
quality_controlled: '1'
related_material:
  record:
  - id: '6675'
    relation: earlier_version
    status: public
scopus_import: 1
status: public
title: A new coding paradigm for the primitive relay channel
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: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12
year: '2019'
...