Analysis and design of Raptor codes using a multi-edge framework

TL;DR

This paper presents a novel multi-edge framework for analyzing and designing Raptor codes, enabling improved performance and stability analysis over traditional methods, with optimized code designs that outperform existing solutions.

Contribution

The paper introduces a multi-edge framework for Raptor code analysis and design, including a new density evolution method and stability expression, leading to better-performing codes.

Findings

Designed Raptor codes outperform existing codes in realized rate.

The multi-edge framework provides a unified analysis tool.

Optimized codes show improved performance in simulations.

Abstract

The focus of this paper is on the analysis and design of Raptor codes using a multi-edge framework. In this regard, we first represent the Raptor code as a multi-edge type low-density parity-check (METLDPC) code. This MET representation gives a general framework to analyze and design Raptor codes over a binary input additive white Gaussian noise channel using MET density evolution (MET-DE). We consider a joint decoding scheme based on the belief propagation (BP) decoding for Raptor codes in the multi-edge framework, and analyze the convergence behavior of the BP decoder using MET-DE. In joint decoding of Raptor codes, the component codes correspond to inner code and precode are decoded in parallel and provide information to each other. We also derive an exact expression for the stability of Raptor codes with joint decoding. We then propose an efficient Raptor code design method using the multi-edge framework, where we simultaneously optimize the inner code and the precode. Finally we consider performance-complexity trade-offs of Raptor codes using the multi-edge framework. Through density evolution analysis we show that the designed Raptor codes using the multi-edge framework outperform the existing Raptor codes in literature in terms of the realized rate.