Abstract
Polar codes were proposed by Erdal Arikan in 2007. He showed that the error correction capability can achieve the Shannon limit when the code length achieves to infinity. Today the polar decoding algorithm can be roughly divided into two classes, i.e., the successive cancellation algorithm and the belief propagation algorithm. Owing to the sequential of the successive cancellation algorithm its hardware complexity is low. When the code length becomes longer, the throughput becomes lower. In order to mitigate this problem, the belief propagation algorithm was proposed. The belief propagation algorithm can mitigate this problem by using the concept of iteration and parallel processing; However its error correction capability is slightly worse than the successive cancellation algorithm. In the thesis, we proposed a modify belief propagation algorithm by using the inversion function. Simulation results show that the throughput of the proposed algorithm loses $3.32\%$ and the hardware area increases $4.8\%$, but the frame error rate is $20$ times better than the original belief propagation algorithm when the signal to noise ratio is $4.5$ dB.