Phase modulated holographic storage offers superior storage capacity and a longer life span compared with other storage technologies. However, its application is limited by its high raw bit error rate. We aimed to introduce low-density parity-check (LDPC) codes for data protection in phase modulated holographic storage systems. However, traditional LDPC codes can not fully exploit data error characteristics, causing inaccurate initial log-likelihood ratio (LLR) information, which degrades decoding performance, thus limiting the improvement degree of data reliability in phase modulated holographic storage. Therefore, we propose a reliable bit aware LDPC optimization method (RaLDPC) that analyzes and employs phase demodulation characteristics to obtain reliable bits. More accurate initial LLR weights are assigned to these reliable bits. Hence, the optimized initial LLR can reflect the reliability of the demodulated data more accurately. Experimental results show that RaLDPC can reduce the bit error rate by an average of 38.89% compared with the traditional LDPC code, improving the data reliability of phase modulated holographic storage.