Design of Bilayer and Multi-layer LDPC Ensembles from Individual Degree Distributions

TL;DR

This paper introduces a novel design method for bilayer and multi-layer LDPC codes using individual degree distributions, enabling efficient, capacity-approaching decoding with scalable complexity and optimized decoding schedules.

Contribution

It presents a new construction approach for multilayer LDPC ensembles that reduces complexity, approaches capacity, and includes an optimal decoding schedule for asymmetric decoding costs.

Findings

Enables low-complexity decoding at high SNR

Provably approaches capacity at low SNR

Scales linearly with the number of layers

Abstract

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.