In the orthogonal frequency division multiplexing (OFDM) communications, bit flipping can be used for the reduction of peak-to-average-power ratio (PAPR). Error-correction coding can be used to relieve the degradation of bit-error rates (BER) resultant from the bit-flipping. We propose designs which appropriately integrate deliberate bit flipping and error-correcting codes with unequal error protection. A modified density evolution method is used for obtaining appropriate code degree distributions to our bit-flipping system. Another error-correcting codes, i.e. Raptor code also can be adopted to mitigate the BER degradation causing of the flipped bits. Simulation results show that our proposed designs can obtain effective PAPR reduction with very minor BER degradation in many cases.