Filter Bank Multicarrier with offset QAM (OQAM) is a suitable multicarrier waveform technique for 5 G and future wireless networks and standards. Being a multicarrier technique, it suffers from high peak-to-average-power ratio (PAPR) problem. In this paper we have used some non-linear companding transforms such as μ-law, A-law, rooting, tangent rooting, and logarithmic rooting to overcome the PAPR problem. Since non-linear companding techniques degrade bit-error-rate (BER) performance of a system. Hence, some channel coding techniques such as convolutional codes and turbo codes are employed to enhance the BER performance of non-linearly companded FBMC-OQAM system. It was observed that the combination of convolutional coding with logarithmic rooting companding provides PAPR reduction gain of about 4.896 dB and coding gain of about 2 dB as compared to conventional FBMC-OQAM system and is an appropriate choice for applications requiring reduced system complexity. It was observed that the combination of turbo coding with logarithmic rooting companding provides PAPR reduction gain of about 4.922 dB and a sufficiently high coding gain of about 7 dB as compared to conventional FBMC-OQAM system and is suitable for applications requiring improved data reliability at the expense of increased system complexity and latency.