---
_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. IEEE Transactions on Communications. 2022;70(11):7134-7145.
doi:10.1109/tcomm.2022.3211101
apa: Doan, N., Hashemi, S. A., Mondelli, M., & Gross, W. J. (2022). Decoding
Reed-Muller codes with successive codeword permutations. IEEE Transactions
on Communications. Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/tcomm.2022.3211101
chicago: Doan, Nghia, Seyyed Ali Hashemi, Marco Mondelli, and Warren J. Gross. “Decoding
Reed-Muller Codes with Successive Codeword Permutations.” IEEE Transactions
on Communications. Institute of Electrical and Electronics Engineers, 2022.
https://doi.org/10.1109/tcomm.2022.3211101.
ieee: N. Doan, S. A. Hashemi, M. Mondelli, and W. J. Gross, “Decoding Reed-Muller
codes with successive codeword permutations,” IEEE Transactions on Communications,
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.”
IEEE Transactions on Communications, vol. 70, no. 11, Institute of Electrical
and Electronics Engineers, 2022, pp. 7134–45, doi:10.1109/tcomm.2022.3211101.
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: '6739'
abstract:
- lang: eng
text: 'We explore the relationship between polar and RM codes and we describe a
coding scheme which improves upon the performance of the standard polar code at
practical block lengths. Our starting point is the experimental observation that
RM codes have a smaller error probability than polar codes under MAP decoding.
This motivates us to introduce a family of codes that “interpolates” between RM
and polar codes, call this family C inter = {C α : α ∈ [0, 1j}, where C α|α=1
is the original polar code, and C α|α=0 is an RM code. Based on numerical observations,
we remark that the error probability under MAP decoding is an increasing function
of α. MAP decoding has in general exponential complexity, but empirically the
performance of polar codes at finite block lengths is boosted by moving along
the family Cinter even under low-complexity decoding schemes such as, for instance,
belief propagation or successive cancellation list decoder. We demonstrate the
performance gain via numerical simulations for transmission over the erasure channel
as well as the Gaussian channel.'
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. From polar to Reed-Muller codes: A technique
to improve the finite-length performance. IEEE Transactions on Communications.
2014;62(9):3084-3091. doi:10.1109/tcomm.2014.2345069'
apa: 'Mondelli, M., Hassani, H., & Urbanke, R. (2014). From polar to Reed-Muller
codes: A technique to improve the finite-length performance. IEEE Transactions
on Communications. IEEE. https://doi.org/10.1109/tcomm.2014.2345069'
chicago: 'Mondelli, Marco, Hamed Hassani, and Rudiger Urbanke. “From Polar to Reed-Muller
Codes: A Technique to Improve the Finite-Length Performance.” IEEE Transactions
on Communications. IEEE, 2014. https://doi.org/10.1109/tcomm.2014.2345069.'
ieee: 'M. Mondelli, H. Hassani, and R. Urbanke, “From polar to Reed-Muller codes:
A technique to improve the finite-length performance,” IEEE Transactions on
Communications, vol. 62, no. 9. IEEE, pp. 3084–3091, 2014.'
ista: 'Mondelli M, Hassani H, Urbanke R. 2014. From polar to Reed-Muller codes:
A technique to improve the finite-length performance. IEEE Transactions on Communications.
62(9), 3084–3091.'
mla: 'Mondelli, Marco, et al. “From Polar to Reed-Muller Codes: A Technique to Improve
the Finite-Length Performance.” IEEE Transactions on Communications, vol.
62, no. 9, IEEE, 2014, pp. 3084–91, doi:10.1109/tcomm.2014.2345069.'
short: M. Mondelli, H. Hassani, R. Urbanke, IEEE Transactions on Communications
62 (2014) 3084–3091.
date_created: 2019-07-31T07:20:21Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2021-01-12T08:08:46Z
day: '01'
doi: 10.1109/tcomm.2014.2345069
extern: '1'
external_id:
arxiv:
- '1401.3127'
intvolume: ' 62'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1401.3127
month: '09'
oa: 1
oa_version: Preprint
page: 3084-3091
publication: IEEE Transactions on Communications
publication_identifier:
issn:
- 0090-6778
publication_status: published
publisher: IEEE
quality_controlled: '1'
status: public
title: 'From polar to Reed-Muller codes: A technique to improve the finite-length
performance'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 62
year: '2014'
...