Density Evolution Based on Two-Type Degree Distribution Framework of Raptor-Like LDPC

Abstract

The traditional degree distribution framework is a useful tool to analyze irregular low density parity check (LDPC) code. However, it cannot be used to analyze raptor-like LDPC code as it cannot describe the most important structural feature of raptor-like LDPC code, which is that any check node is connected to at most one degree-one variable node. In this paper, we propose a two-type degree distribution framework for raptor-like LDPC code. The proposed framework can describe the special structural feature of raptor-like LDPC code by dividing the check nodes into two different sets. One is the set of check nodes connected to those degree-one variable nodes, the other is the set of check nodes unconnected to those degree-one variable nodes. Furthermore, we propose a two-type discrete density evolution algorithm and a two-type Gaussian approximation density evolution algorithm based on the proposed two-type degree distribution framework to estimate the threshold of raptor-like LDPC code. During the decoding analysis, the proposed algorithms treat the check nodes belonging the two separate sets differently. Compared with the traditional multi-edge type (MET) algorithm, the proposed algorithms allow us to calculate the threshold more quickly without much sacrifice in accuracy. For some raptor-like LDPC codes adopted by the Advanced Television Systems Committee 3.0 (ATSC3.0) standard, the thresholds estimated by the proposed algorithms can be very close to the thresholds estimated by the traditional MET algorithm. The deviations are less than 0.07 dB. Meanwhile, the proposed algorithms can tremendously reduce the computation complexity because of the two-type degree distribution framework and the Gaussian approximation.