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  4. From Polar to Reed-Muller Codes: a Technique to Improve the Finite-Length Performance
 
conference paper

From Polar to Reed-Muller Codes: a Technique to Improve the Finite-Length Performance

Mondelli, Marco  
•
Hassani, S. Hamed  
•
Urbanke, Rudiger  
2014
2014 Ieee International Symposium On Information Theory (Isit)
IEEE International Symposium on Information Theory (ISIT'14)

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 ${\mathcal C}{\rm inter} = {C{\alpha} : \alpha \in [0, 1]}$, where $C_{\alpha} \big |{\alpha = 1}$ is the original polar code, and $C{\alpha} \big |{\alpha = 0}$ is an RM code. Based on numerical observations, we remark that the error probability under MAP decoding is an increasing function of $\alpha$. 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 ${\mathcal C}{\rm inter}$ 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.

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Type
conference paper
DOI
10.1109/ISIT.2014.6874809
Web of Science ID

WOS:000346496100026

Author(s)
Mondelli, Marco  
Hassani, S. Hamed  
Urbanke, Rudiger  
Date Issued

2014

Published in
2014 Ieee International Symposium On Information Theory (Isit)
ISBN of the book

978-1-4799-5186-4

Start page

131

End page

135

Subjects

Polar codes

•

RM codes

•

MAP decoding

•

SC decoding

•

list decoding.

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LTHC  
Event nameEvent placeEvent date
IEEE International Symposium on Information Theory (ISIT'14)

Honolulu, HI

JUN 29-JUL 04, 2014

Available on Infoscience
January 14, 2014
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/99522
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