Spatially coupled ensembles universally achieve capacity under belief propagation

By Shrinivas Kudekar, T. Richardson, Rüdiger L. Urbanke. IEEE International Symposium on Information Theory. Proceedings, 2012

437 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/f8a109be16720b748067b16d4eb91c6e0b8301fc

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In Computer Networks and Communications

1. Jinwoo Shin
2. A. Alvarado
3. Yung Yi
4. Yunhun Jang
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Citations in the corpus

• Replacing the Soft-Decision FEC Limit Paradigm in the Design of Optical Communication Systems (2015, background): “, [39] and [40], and recently for spatially-coupled LDPC codes in [41].”
• Efficient Learning for Crowdsourced Regression (2017, background): “In this paper, we formally define a crowdsourced regression problem and study these fundamental questions.”