12 problems

Let terminated spatially-coupled low-density parity-check (SC-LDPC) codes be constructed from an underlying LDPC code ensemble, and let their BP threshold and the MAP threshold of…

Consider a smooth family of binary-input memoryless symmetric channels ordered by degradation, with channel parameter $\epsilon$ equal to the channel entropy. Let…

In the setting of quantitative group testing with a non-binary alphabet, let BP denote belief-propagation decoding and let spatial coupling refer to a spatially coupled code or gra…

For spatially-coupled SC-TC with Gray mapping, let the BP threshold be the channel threshold obtained under belief-propagation decoding, and let the MAP threshold be the threshold…

A protograph ensemble is an ensemble of spatially coupled low-density parity-check codes specified by a protograph, and shaping parameters determine the energy levels and their ass…

Let $w$ be the size of the coupling window, let $E_{\rm f}$ be the true error floor, let $\epsilon>0$, and let $\Delta F_{\rm un}$ denote the relevant free-energy gap in the uncoup…

In compressed sensing, consider a Bayesian probabilistic reconstruction approach using the approximate message passing algorithm together with a specially designed spatially couple…

A spatially coupled system is obtained by coupling copies of an uncoupled component system along one spatial dimension; BP decoding denotes belief-propagation decoding, while MAP d…

Let $\tilde{u}_{\mathrm{un}}(x)$ be the non-uniform stationary solution described above for the spatially coupled system. Instability conjecture. We conjecture that…

Extension universality conjecture. For all these extensions, threshold saturation should continue to occur, and spatially coupled codes should achieve near-universal performance.

Spatial-coupling universality conjecture. The principle of spatial coupling is very general, and threshold saturation should apply to a very broad class of graphical models.

Spatial coupling refers to coupling local graphical-model components across spatial positions, and threshold saturation is the phenomenon in which the belief-propagation threshold…