NDLI: Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation

Content Provider	IEEE Xplore Digital Library
Author	Kudekar, S. Richardson, T. Urbanke, R.L.
Copyright Year	1963
Abstract	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 that fulfills these constraints universally on this class of channels under belief propagation decoding. In fact, most codes in this ensemble have this property. The quantifier universal refers to the single ensemble/code that is good for all channels but 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.
Sponsorship	IEEE Information Theory Society
Starting Page	7761
Ending Page	7813
Page Count	53
File Size	16267271
File Format	PDF
ISSN	00189448
Volume Number	59
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Decoding Parity check codes Couplings Convolutional codes Error probability Encoding Energy states threshold saturation Belief propagation (BP) capacity-achieving codes channel coding convolutional low-density parity-check (LDPC) codes iterative decoding LDPC codes spatial coupling spatially coupled codes
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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