Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation

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 Felstrom 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.

Published in:
Ieee Transactions On Information Theory, 59, 12, 7761-7813
Piscataway, Institute of Electrical and Electronics Engineers

 Record created 2014-01-09, last modified 2018-09-13

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