---
_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.'
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'
...