The decoding algorithm of low-density parity-check (LDPC) codes in quaternary phase shift keying (QPSK) modulation is in-depth studied. The specific method of the maximum average mutual information quantization is analyzed and deduced. With this method to quantify the initial message, each iteration of the variable messages and check messages becomes integer, then the min-sum decoding algorithm ... [Show full abstract] based on integer arithmetic is implemented. Simulation results show that the performance of the min-sum decoding algorithm with maximum average mutual information quantization is about 0.39 dB worse than the performance of high-precision floating-point sum-product decoding algorithm. At the same time all the variables in the algorithm are fixed-length integers, so it is easy to implement in hardware. Although the decoding performance is slightly worse than sum-product decoding performance, the decoding time is greatly reduced.