For a recording system that has a run-length-limited 1 (RLL) constraint, this approach imposes the hard error by 2 flipping bits before recording. A high error coding rate limits 3 the correcting capability of the RLL bit error. Since iterative 4 decoding does not include the estimation technique, it has the 5 potential capability of solving the hard error bits within several 6 iterations compared to an LDPC coded system. In this letter, 7 we implement density evolution and the differential evolution 8 approach to provide a performance evaluation of unequal error 9 protection LDPC code to investigate the optimal LDPC code 10 distribution for an RLL flipped system. 11 Index Terms-Parity check codes, iterative decoding, partial 12 response channels, error correction codes. 13 been applied for timing recovery as well as for alleviating 16 inter-symbol interference (ISI). To achieve a high code rate 17 a recording system can be improved by alleviating the RLL 18 encoder that causes the rate loss within the system. Therefore, 19 the idea is to deliberately flip [3], [4] some bits of the 20 LDPC codeword to meet the RLL constraint on the write 21 side, and than use the error-correcting capability of the LDPC 22 code to remove the flipped bits on the read side. However, 23 the reading side of the recording system simultaneously suffers 24 from AWGN noise and flipping errors from the RLL insertion. 25 Chou et al. [5] provide an interesting approach to detecting the 26 location of the RLL flipping bit. This approach relies on the 27 proposed detection technique to correct any flipping errors, but 28 the decoding complexity of the system is increased though the 29 need to check each code bits. Rather than expanding on the 30 detection approach in [5], Chou et al. [6] have followed the 31 unequal error protection (UEP) design criterions to propose a 32 decoding scheme, where they have exploited the UEP LDPC 33 code by means of regular interleaver to confine the occurrence 34 of flipping errors to a section of the codeword. Well-design 35 LDPC codes and with higher code rate were compared to 36 demonstrate the merit of the proposed system. However, 37 the authors did not investigate a clear method of determining 38 the optimum LDPC code for the proposed system. Density 39 evolution [7] (DE) is a general method for determining the 40 capacity of LDPC codes. This method refers to the evolution 41 of the probability density functions (pdfs) of the messages 42