Performances analysis of polar codes decoding algorithms over variant binary-input channels

In this paper, the performance of state of the art decoding methods of polar codes, such as the SC (Successive Cancellation), BP (belief propagation), LP (Linear Programming), LSC(List Successive Cancellation) and ML(Maximum Likelihood) decoding, over different binary-input discrete memoryless channels (B-DMCs) are presented. Simulation results indicate that decoding algorithms of polar codes have the performances of the estimated bit error rate (BER) below the order of 10^-5. In addition, we came to the conclusion that BP algorithm outperforms SC at the cost of computational complexity. The performance of LP decoder is better than BP and the complexity is less than BP scheme, however, it can only be used in binary erasure channels (BECs). ML decoder has the best performance, but its high complexity makes it act as a reference to reveal the gap between ML and other algorithms. In order to remedy the performance deficiencies without any significant increase in decoding complexity, we further study the concatenated polar codes - the polar-LDPC(Low Density Parity Check) concatenation scheme, which is substantially outperforms ML decoding. What's more, the concatenated Polar-LDPC codes can remedy the error floor of LDPC codes. We firmly believed that the concatenated scheme of polar-LDPC would be a prominent technique in 5G (5th-generation) to support the more reliable transmission demand.