  A new approach for designing bilayer and multi-layer LDPC codes is proposed
and studied in the asymptotic regime. The ensembles are defined through
individual uni-variate degree distributions, one for each layer. We present a
construction that: 1) enables low-complexity decoding for high-SNR channel
instances, 2) provably approaches capacity for low-SNR instances, 3) scales
linearly (in terms of design complexity) in the number of layers. For the setup
where decoding the second layer is significantly more costly than the first
layer, we propose an optimal-cost decoding schedule and study the trade-off
between code rate and decoding cost.
