Novel Fast Iterative Decoding Threshold Estimation for Protograph-Based LDPC Convolutional Codes

The iterative decoding threshold (IDT) estimation for LDPC convolutional codes (LDPC-CCs) may become difficult over additive white Gaussian noise channels, especially when the termination length L gets very large or even approaches infinity. In this paper, we devise a novel fast IDT estimation scheme using the protograph-based extrinsic information transfer (PEXIT) analysis for protograph-based LDPC-CCs. Based on our new analysis, we propose a PEXIT-fast algorithm in which only the mutual information (MI) of a posteriori probability (APP) of the first variable node will be monitored to determine whether the current E_b/N_0 (signal-energy-per-information-bit to noise-power- spectral-density ratio) in evaluation is an upper bound or a lower bound of the IDT. Hence, it is no longer necessary to get through the whole MI evolution and the computational complexity can be greatly reduced thereby. We also design an efficient approach to determine the IDT for an LDPC-CC with an arbitrary large termination length L which can also be allowed to be infinity. The closeness between the known IDTs and the estimated IDTs using our proposed new method for several LDPC-CCs in simulation confirms the effectiveness of our scheme.