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research article

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

Mondelli, Marco  
•
Hassani, S. Hamed  
•
Urbanke, Ruediger L.
2014
Ieee Transactions On Communications

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-alpha : alpha is an element of [0, 1]}, where C-alpha vertical bar(alpha=1) is the original polar code, and C-alpha vertical bar(alpha=0) is an RM code. Based on numerical observations, we remark that the error probability under MAP decoding is an increasing function of a. 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 C-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
research article
DOI
10.1109/Tcomm.2014.2345069
Web of Science ID

WOS:000344524600004

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

2014

Publisher

Ieee-Inst Electrical Electronics Engineers Inc

Published in
Ieee Transactions On Communications
Volume

62

Issue

9

Start page

3084

End page

3091

Subjects

Polar codes

•

RM codes

•

MAP decoding

•

SC decoding

•

list decoding

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
ISC  
Available on Infoscience
December 30, 2014
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/109863
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