The two-dimensional (2D) interference is one of the major impairments in bit-patterned media recording (BPMR) systems due to small bit and track pitches, especially at high recording densities. To alleviate this problem, we introduced a rate-4/5 constructive inter-track interference (CITI) coding scheme to prevent the destructive data patterns to be written onto a magnetic medium for an uncoded BPMR system, i.e., without error-correction codes. Because the CITI code produces only the hard decision, it cannot be employed in a coded BPMR system that uses a low-density parity-check (LDPC) code. To utilize it in an iterative decoding scheme, we propose a soft CITI coding scheme based on the log-likelihood ratio algebra implementation in Boolean logic mappings in order that the soft CITI coding scheme together with a modified 2D soft-output Viterbi algorithm (SOVA) detector and a LDPC decoder will jointly perform iterative decoding. Simulation results show that the proposed scheme provides a significant performance improvement, in particular when an areal density (AD) is high and/or the position jitter is large. Specifically, at a bit-error rate of 10-4 and no position jitter, the proposed system can provide approximately 1.8 and 3.5 dB gain over the conventional coded system without using the CITI code at the ADs of 2.5 and 3.0 Tera-bit per square inch (Tb/in2), respectively.