10 problems

Capacity-achieving conjecture. GSC-PCC ensembles with any convolutional component codes should be capable of achieving the binary erasure channel capacity.

Let GD codes and GD-TC codes be the code ensembles defined in the paper, with GD-TC codes using tailored pseudo-memories and coupling patterns to approximate GD ensembles. GD-TC ve…

For a spatially coupled Low-Density Parity-Check code, consider the profile of “error probabilities” along the spatial direction. Decoding-wave profile conjecture. After a short tr…

Let $L$ be the chain length and $M$ the coupling length or block-size parameter of a spatially-coupled low-density parity-check code ensemble. The effect that the ensemble has a va…

For the non-binary spatially-coupled low-density parity-check code ensembles considered on the binary-input additive white Gaussian noise channel (BIAWGNC), let $m$ denote the fiel…

Let $\hat{c}_1(\tau)$ denote the normalized expected number of degree-one check nodes at scaled iteration time $\tau$. The steady-state phase is the regime in which the mean evolut…

Let $Q(x)$ denote the error function associated with the density-evolution analysis, and let the trial entropy be the function obtained by integrating the BP EXIT function…

BEC speed upper-bound conjecture. The upper bound of the speed on the BEC is also an upper bound of the speed on the other channels with the same channel entropy.

Let an ensemble of spatially-coupled low-density parity-check (LDPC) codes be used over different bit-interleaved coded-modulation (BICM) schemes, and consider ensembles with large…

LP-threshold conjecture. The LP threshold of a spatially coupled ensemble on the BSC is the same as that of the base ensemble.