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In this letter, we consider the design of Raptor codes for a wide signal-to-noise ratio (SNR) range using a multi-edge framework. The main idea is to change the degree distribution in a way to optimize the rate efficiency when more output bits are sent out. The proposed code shows near capacity performance in the designed SNR range, and achieves higher efficiencies compared with the reference Raptor codes from the literature. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

This paper considers density evolution for low-density parity-check (LDPC) and multi-edge type LDPC (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three single-parameter Gaussian approximations for density evolution and discuss their accuracy under several conditions, namely, at low rates, with punctured and degree-one variable nodes. We observe that the assumption of symmetric Gaussian distribution for the density-evolution messages is not accurate in the early decoding iterations, particularly at low rates and with punctured variable nodes. Thus, single-parameter Gaussian approximation methods produce very poor results in these cases. Based on these observations, we then introduce a new density evolution approximation algorithm for LDPC and MET-LDPC codes. Our method is a combination of full density evolution and a single-parameter Gaussian approximation, where we assume a symmetric Gaussian distribution only after density-evolution messages closely follow a symmetric Gaussian distribution. Our method significantly improves the accuracy of the code threshold estimation. Additionally, the proposed method significantly reduces the computational time of evaluating the code threshold compared with full density evolution thereby making it more suitable for code design. [ABSTRACT FROM PUBLISHER]