Threshold Saturation on BMS Channels via Spatial Coupling

TL;DR

This paper investigates how spatial coupling in code ensembles, especially convolutional LDPC, enhances belief propagation thresholds over BMS channels, supported by empirical evidence and threshold comparisons.

Contribution

It extends the understanding of threshold saturation from erasure channels to general BMS channels through empirical analysis and threshold comparisons.

Findings

Spatial coupling increases BP thresholds over BMS channels.

Empirical evidence supports threshold saturation phenomenon.

Methods to reduce rate-loss in coupled ensembles are discussed.

Abstract

We consider spatially coupled code ensembles. A particular instance are convolutional LDPC ensembles. It was recently shown that, for transmission over the binary erasure channel, this coupling increases the belief propagation threshold of the ensemble to the maximum a-priori threshold of the underlying component ensemble. We report on empirical evidence which suggest that the same phenomenon also occurs when transmission takes place over a general binary memoryless symmetric channel. This is confirmed both by simulations as well as by computing EBP GEXIT curves and by comparing the empirical BP thresholds of coupled ensembles to the empirically determined MAP thresholds of the underlying regular ensembles. We further consider ways of reducing the rate-loss incurred by such constructions.