Decoding algorithms based on oscillation for low-density parity check codes

In this paper we focus on the decoding error of the Log-Likelihood Ratio Belief Propagation (LLR-BP) decoding algorithm caused by oscillation. The decoding error caused by the oscillation is dominant in high E _b/N₀ region. Oscillation of the LLR of the extrinsic value in the bit node process (ex-LLR) is propagated to the other bits and affects the whole decoding. The Ordered Statistic Decoding (OSD) algorithm is known to improve the error rate performance of the LLR-BP decoding algorithm. The OSD algorithm is performed by deciding the reliability of each bit based on a posteriori probability. In this paper we propose two decoding algorithms based on two types of oscillations of LLR for LDPC codes. One is the oscillation-based OSD algorithm with deciding the reliability of each bit based on oscillation. The other is the oscillation-based LLR-BP decoding algorithm that modifies ex-LLR based on oscillation. In the oscillation-based LLR-BP decoding algorithm, when ex-LLR oscillates, then we reduce the magnitude of this ex-LLR to reduce the effects on the other bits. Both algorithms improve the decoding errors caused by oscillation. From the computer simulations, we show that paying attention to the oscillation, we can improve the error rate performance of the LLR-BP decoding algorithm.