An Alternative Approach Obtaining a Normalization Factor in Normalized Min-Sum Algorithm for Low-Density Parity-Check Code

The min-sum algorithm (MSA) for decoding Low-Density Parity-Check (LDPC) code is an approximation algorithm that can greatly reduce the computational complexity of the belief propagation algorithm (BPA). To reduce the error between MSA and BPA, an improved MSA such as normalized min-sum algorithm (NMSA) that uses the normalization factor when updating the check node is used in many LDPC decoders. When obtaining an optimal normalization factor, density evolution (DE) is usually used. However, not only does the DE method require a large number of calculations, it may not be optimal for obtaining a normalization factor due to the theoretical assumptions that need to be satisfied. This paper proposes a new method obtaining a normalization factor for NMSA. We first examine the relationship between the minimum value of variable node messages’ magnitudes and the magnitudes of check node outputs of BPA using the check node message distribution (CMD) chart. And then, we find a normalization factor that minimizes the error between the magnitudes of check node output of NMSA and BPA. We use the least square method (LSM) to minimize the error. Simulation on ATSC 3.0 LDPC codes demonstrates that the normalization factor obtained by this proposed method shows better decoding performance than the normalization factor obtained by DE.