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conference paper

Universal Polar Codes

Hassani, S. Hamed  
•
Urbanke, Ruediger  
2014
2014 Ieee International Symposium On Information Theory (Isit)
IEEE International Symposium on Information Theory (ISIT)

Polar codes, invented by Arikan in 2009, are known to achieve the capacity of any binary-input memoryless outputsymmetric channel. Further, both the encoding and the decoding can be accomplished in O(N log(N)) real operations, where N is the blocklength. One of the few drawbacks of the original polar code construction is that it is not universal. This means that the code has to be tailored to the channel if we want to transmit close to capacity. We present two "polar-like" schemes that are capable of achieving the compound capacity of the whole class of binary-input memoryless symmetric channels with low complexity. Roughly speaking, for the first scheme we stack up N polar blocks of length N on top of each other but shift them with respect to each other so that they form a "staircase." Then by coding across the columns of this staircase with a standard ReedSolomon code, we can achieve the compound capacity using a standard successive decoder to process the rows (the polar codes) and in addition a standard Reed-Solomon erasure decoder to process the columns. Compared to standard polar codes this scheme has essentially the same complexity per bit but a block length which is larger by a factor O(N log(2)(N)/epsilon). Here N is the required blocklength for a standard polar code to achieve an acceptable block error probability for a single channel at a distance of at most ! from capacity. For the second scheme we first show how to construct a true polar code which achieves the compound capacity for a finite number of channels. We achieve this by introducing special " polarization" steps which " align" the good indices for the various channels. We then show how to exploit the compactness of the space of binary-input memoryless output-symmetric channels to reduce the compound capacity problem for this class to a compound capacity problem for a finite set of channels. This scheme is similar in spirit to standard polar codes, but the price for universality is a considerably larger blocklength.

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Type
conference paper
DOI
10.1109/ISIT.2014.6875073
Web of Science ID

WOS:000346496101117

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

2014

Publisher

Ieee

Publisher place

New York

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

978-1-4799-5186-4

Total of pages

5

Series title/Series vol.

IEEE International Symposium on Information Theory

Start page

1451

End page

1455

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

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

Honolulu, HI

JUN 29-JUL 04, 2014

Available on Infoscience
April 13, 2015
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/113067
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