---
_id: '12233'
abstract:
- lang: eng
  text: A novel recursive list decoding (RLD) algorithm for Reed-Muller (RM) codes
    based on successive permutations (SP) of the codeword is presented. A low-complexity
    SP scheme applied to a subset of the symmetry group of RM codes is first proposed
    to carefully select a good codeword permutation on the fly. Then, the proposed
    SP technique is integrated into an improved RLD algorithm that initializes different
    decoding paths with random codeword permutations, which are sampled from the full
    symmetry group of RM codes. Finally, efficient latency and complexity reduction
    schemes are introduced that virtually preserve the error-correction performance
    of the proposed decoder. Simulation results demonstrate that at the target frame
    error rate of 10−3 for the RM code of length 256 with 163 information bits, the
    proposed decoder reduces 6% of the computational complexity and 22% of the decoding
    latency of the state-of-the-art semi-parallel simplified successive-cancellation
    decoder with fast Hadamard transform (SSC-FHT) that uses 96 permutations from
    the full symmetry group of RM codes, while relatively maintaining the error-correction
    performance and memory consumption of the semi-parallel permuted SSC-FHT decoder.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nghia
  full_name: Doan, Nghia
  last_name: Doan
- 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: Warren J.
  full_name: Gross, Warren J.
  last_name: Gross
citation:
  ama: Doan N, Hashemi SA, Mondelli M, Gross WJ. Decoding Reed-Muller codes with successive
    codeword permutations. <i>IEEE Transactions on Communications</i>. 2022;70(11):7134-7145.
    doi:<a href="https://doi.org/10.1109/tcomm.2022.3211101">10.1109/tcomm.2022.3211101</a>
  apa: Doan, N., Hashemi, S. A., Mondelli, M., &#38; Gross, W. J. (2022). Decoding
    Reed-Muller codes with successive codeword permutations. <i>IEEE Transactions
    on Communications</i>. Institute of Electrical and Electronics Engineers. <a href="https://doi.org/10.1109/tcomm.2022.3211101">https://doi.org/10.1109/tcomm.2022.3211101</a>
  chicago: Doan, Nghia, Seyyed Ali Hashemi, Marco Mondelli, and Warren J. Gross. “Decoding
    Reed-Muller Codes with Successive Codeword Permutations.” <i>IEEE Transactions
    on Communications</i>. Institute of Electrical and Electronics Engineers, 2022.
    <a href="https://doi.org/10.1109/tcomm.2022.3211101">https://doi.org/10.1109/tcomm.2022.3211101</a>.
  ieee: N. Doan, S. A. Hashemi, M. Mondelli, and W. J. Gross, “Decoding Reed-Muller
    codes with successive codeword permutations,” <i>IEEE Transactions on Communications</i>,
    vol. 70, no. 11. Institute of Electrical and Electronics Engineers, pp. 7134–7145,
    2022.
  ista: Doan N, Hashemi SA, Mondelli M, Gross WJ. 2022. Decoding Reed-Muller codes
    with successive codeword permutations. IEEE Transactions on Communications. 70(11),
    7134–7145.
  mla: Doan, Nghia, et al. “Decoding Reed-Muller Codes with Successive Codeword Permutations.”
    <i>IEEE Transactions on Communications</i>, vol. 70, no. 11, Institute of Electrical
    and Electronics Engineers, 2022, pp. 7134–45, doi:<a href="https://doi.org/10.1109/tcomm.2022.3211101">10.1109/tcomm.2022.3211101</a>.
  short: N. Doan, S.A. Hashemi, M. Mondelli, W.J. Gross, IEEE Transactions on Communications
    70 (2022) 7134–7145.
date_created: 2023-01-16T09:50:38Z
date_published: 2022-11-01T00:00:00Z
date_updated: 2023-08-04T09:34:43Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/tcomm.2022.3211101
external_id:
  arxiv:
  - '2109.02122'
  isi:
  - '000937284600006'
intvolume: '        70'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2109.02122'
month: '11'
oa: 1
oa_version: Preprint
page: 7134-7145
publication: IEEE Transactions on Communications
publication_identifier:
  eissn:
  - 1558-0857
  issn:
  - 0090-6778
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Decoding Reed-Muller codes with successive codeword permutations
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 70
year: '2022'
...
---
_id: '6674'
abstract:
- lang: eng
  text: Polar codes represent one of the major recent breakthroughs in coding theory
    and, because of their attractive features, they have been selected for the incoming
    5G standard. As such, a lot of attention has been devoted to the development of
    decoding algorithms with good error performance and efficient hardware implementation.
    One of the leading candidates in this regard is represented by successive-cancellation
    list (SCL) decoding. However, its hardware implementation requires a large amount
    of memory. Recently, a partitioned SCL (PSCL) decoder has been proposed to significantly
    reduce the memory consumption. In this paper, we consider the paradigm of PSCL
    decoding from a practical standpoint, and we provide several improvements. First,
    by changing the target signal-to-noise ratio and consequently modifying the construction
    of the code, we are able to improve the performance at no additional computational,
    latency, or memory cost. Second, we bridge the performance gap between SCL and
    PSCL decoding by introducing a generalized PSCL decoder and a layered PSCL decoder.
    In this way, we obtain almost the same performance of the SCL decoder with a significantly
    lower memory requirement, as testified by hardware implementation results. Third,
    we present an optimal scheme to allocate cyclic redundancy checks. Finally, we
    provide a lower bound on the list size that guarantees optimal maximum a posteriori
    performance for the binary erasure channel.
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: S. Hamed
  full_name: Hassani, S. Hamed
  last_name: Hassani
- first_name: Carlo
  full_name: Condo, Carlo
  last_name: Condo
- first_name: Rudiger L.
  full_name: Urbanke, Rudiger L.
  last_name: Urbanke
- first_name: Warren J.
  full_name: Gross, Warren J.
  last_name: Gross
citation:
  ama: 'Hashemi SA, Mondelli M, Hassani SH, Condo C, Urbanke RL, Gross WJ. Decoder
    partitioning: Towards practical list decoding of polar codes. <i>IEEE Transactions
    on Communications</i>. 2018;66(9):3749-3759. doi:<a href="https://doi.org/10.1109/tcomm.2018.2832207">10.1109/tcomm.2018.2832207</a>'
  apa: 'Hashemi, S. A., Mondelli, M., Hassani, S. H., Condo, C., Urbanke, R. L., &#38;
    Gross, W. J. (2018). Decoder partitioning: Towards practical list decoding of
    polar codes. <i>IEEE Transactions on Communications</i>. IEEE. <a href="https://doi.org/10.1109/tcomm.2018.2832207">https://doi.org/10.1109/tcomm.2018.2832207</a>'
  chicago: 'Hashemi, Seyyed Ali, Marco Mondelli, S. Hamed Hassani, Carlo Condo, Rudiger
    L. Urbanke, and Warren J. Gross. “Decoder Partitioning: Towards Practical List
    Decoding of Polar Codes.” <i>IEEE Transactions on Communications</i>. IEEE, 2018.
    <a href="https://doi.org/10.1109/tcomm.2018.2832207">https://doi.org/10.1109/tcomm.2018.2832207</a>.'
  ieee: 'S. A. Hashemi, M. Mondelli, S. H. Hassani, C. Condo, R. L. Urbanke, and W.
    J. Gross, “Decoder partitioning: Towards practical list decoding of polar codes,”
    <i>IEEE Transactions on Communications</i>, vol. 66, no. 9. IEEE, pp. 3749–3759,
    2018.'
  ista: 'Hashemi SA, Mondelli M, Hassani SH, Condo C, Urbanke RL, Gross WJ. 2018.
    Decoder partitioning: Towards practical list decoding of polar codes. IEEE Transactions
    on Communications. 66(9), 3749–3759.'
  mla: 'Hashemi, Seyyed Ali, et al. “Decoder Partitioning: Towards Practical List
    Decoding of Polar Codes.” <i>IEEE Transactions on Communications</i>, vol. 66,
    no. 9, IEEE, 2018, pp. 3749–59, doi:<a href="https://doi.org/10.1109/tcomm.2018.2832207">10.1109/tcomm.2018.2832207</a>.'
  short: S.A. Hashemi, M. Mondelli, S.H. Hassani, C. Condo, R.L. Urbanke, W.J. Gross,
    IEEE Transactions on Communications 66 (2018) 3749–3759.
date_created: 2019-07-24T08:59:41Z
date_published: 2018-09-01T00:00:00Z
date_updated: 2021-01-12T08:08:31Z
day: '01'
doi: 10.1109/tcomm.2018.2832207
extern: '1'
intvolume: '        66'
issue: '9'
language:
- iso: eng
month: '09'
oa_version: None
page: 3749-3759
publication: IEEE Transactions on Communications
publication_identifier:
  eissn:
  - 1558-0857
publication_status: published
publisher: IEEE
quality_controlled: '1'
status: public
title: 'Decoder partitioning: Towards practical list decoding of polar codes'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 66
year: '2018'
...