Wireless channels introduce different levels of fading and distortion caused by their multipath nature. Noise and interference from other systems can also be considered as other reasons for channel errors. Forward Error Correction (FEC) codes are usually used to reduce transmission errors in wireless systems. This thesis provides an investigation on the suitability of different forward error correction techniques for wireless systems. The codes covered here are Trellis Coded Modulation (TCM), Low Density Parity Check (LDPC) codes, Turbo codes and finally the newly invented with the encouraging performance, and relatively lowest cost, the polar coding technique. The work uses computer simulation tests to measure bit error rate (BER) performance, and investigates the required complexity and bandwidth efficiency for the studied coding schemes. Three channel models are used in tests. These are additive white Gaussian noise (AWGN), single tap flat fading, and multipath fading channels. Simulation results have shown that polar codes give the best tradeoff between performance and complexity over all channels tested with useful coding gain on the expense of low coding rate (low bandwidth efficiency). At least 20% reduction in complexity (mathematical operations) of polar code is achieved over all other codes tested in the work. Further, a coding gain as large as 11 dB was achieved over other codes. For other low rate codes; irregular LDPC code showed poor performance at relatively high signal to noise ratio (SNR), while turbo codes provide improved performance. Finally, TCM codes are the best codes studied in terms of bandwidth efficiency with moderate performance. Thus for wireless fading channels, the polar and turbo codes seem to be promising schemes if the rate is not important (large bandwidth available) otherwise TCM could be used.