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  4. Spatially coupled ensembles universally achieve capacity under belief propagation
 
conference paper not in proceedings

Spatially coupled ensembles universally achieve capacity under belief propagation

Urbanke, Rüdiger  
•
Kudekar, Shrinivas  
•
Richardson, T.
2012
Internationel Symposium on Information Theory ISIT2012

We investigate spatially coupled code ensembles. For transmission over the binary erasure channel, it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a-priori threshold of the underlying component ensemble. This explains why convolutional LDPC ensembles, originally introduced by Felström and Zigangirov, perform so well over this channel. We show that the equivalent result holds true for transmission over general binary-input memoryless output-symmetric channels. More precisely, given a desired error probability and a gap to capacity, we can construct a spatially coupled ensemble which fulfills these constraints universally on this class of channels under belief propagation decoding. In fact, most codes in that ensemble have that property. The quantifier universal refers to the single ensemble/code which is good for all channels if we assume that the channel is known at the receiver. The key technical result is a proof that under belief propagation decoding spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble. We conclude by discussing some interesting open problems.

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Type
conference paper not in proceedings
DOI
10.1109/ISIT.2012.6284229
Author(s)
Urbanke, Rüdiger  
Kudekar, Shrinivas  
Richardson, T.
Date Issued

2012

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
LTHC  
Event nameEvent placeEvent date
Internationel Symposium on Information Theory ISIT2012

Boston, Massachusetts, USA

1-6 July, 2012

Available on Infoscience
September 25, 2012
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/85674
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