During past few years, OFDM has gained lots of attention as a multicarrier modulation technique and it has been very well known in high data rate transmission due to its various potentials, like as its ability to combat multipath fading and intersymbol interference, high bandwidth efficiency and finally its simplicity of implementation. Also it has been accepted as a convenient modulation method based on many standards, for examples DAB, DVB(DVB-T, DVB-T2) and WLAN(802.11x, HyperLAN2).
Even though these systems show lots of advantages, one of their main disadvantages is high PAPR that could result in the OFDM from HPA which will affect the amplitude of the transmitted signals. That also will lead to increase bit error rate and spectral spreading, finally it will cause the malfunction of the whole system performance.
Up to now there have been several suggested methods to decrease PAPR in OFDM systems. In this thesis, there have been several reported new methods to decrease PAPR in SISO and MIMO systems based on the fast Reed--Solomon codes over $\mbox{GF}(257)$ and $\mbox{GF}(65537)$. In these methods some different candidates blocks with the same information compare to the main block have been produced. Among those, one or some blocks with the smaller PAPR have been selected.
The length of the code's blocks on the mentioned prime fields are similar to the power of two of those of OFDM blocks, hence in order to implement its coding and decoding, it is possible to use the fast fourier transnsform algorithms. On the other hand, addition and multiplication operations can be done modular on these fields hence have less complications. Any small changes in the symbol's data of these codes will result in the new codes that will be suitable to produce independent block's candidate. Knowing the fact that these codes have capability of error correction and are MDS, they can be used for both error correction and decreasing PA