A joint decoding scheme was proposed by Li and Qu to recover low-density parity-check (LDPC) codeword and partial transmit sequence (PTS) phase factors, for OFDM systems with a low peak-to-average power ratio (PAPR). However, the error-correcting performance of the joint decoding scheme heavily relies on how the OFDM subcarriers are partitioned into groups in the PTS scheme. With a pseudorandom partition, the joint decoding scheme provides satisfactory error-correcting performance only when the number of PTS groups is very small. In this paper, we formulate an optimization problem to improve the joint decoding performance by optimizing the partition. Furthermore, two greedy-based algorithms are proposed to solve the problem. Simulation results show that the joint decoding scheme with the proposed partition algorithms provides satisfactory error-correcting performance for a larger number of PTS groups than it does with the pseudorandom partition. With the improved performance, better PAPR performance can be supported.