# Analysis of peeling decoder for MET ensembles

## TL;DR

This paper generalizes the peeling decoder analysis for multi-edge type (MET) LDPC ensembles, deriving differential equations to better understand their decoding behavior and set the stage for finite-length performance studies.

## Contribution

It extends the peeling decoder framework to MET ensembles, providing new differential equations and solutions for analyzing their decoding process.

## Key findings

- Derived differential equations for MET ensemble decoding
- Introduced a new change of variables for analysis
- Facilitated future finite-length behavior investigation

## Abstract

The peeling decoder introduced by Luby, et al. allows analysis of LDPC decoding for the binary erasure channel (BEC). For irregular ensembles, they analyze the decoder state as a Markov process and present a solution to the differential equations describing the process mean. Multi-edge type (MET) ensembles allow greater precision through specifying graph connectivity. We generalize the the peeling decoder for MET ensembles and derive analogous differential equations. We offer a new change of variables and solution to the node fraction evolutions in the general (MET) case. This result is preparatory to investigating finite-length ensemble behavior.