Analysis and Design of Raptor Codes Using a Multi-Edge Framework

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 Raptor codes as multi-edge type (MET) low-density parity-check codes. 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 then 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 corresponding to the inner code and the 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. 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 realized rates.