A RM-Polar Codes

Introduction: Polar codes are a major breakthrough in coding theory [1]. They can achieve Shannon capacity with a simple encoder and a simple successive cancellation (SC) decoder, both with low complexity of the order of ( ) N N log O , where N is the code block size. But for short and moderate lengths, the error rate performance of polar codes with the SC decoding is not as good as LDPC or turbo codes. A new SC-list decoding algorithm was proposed for polar codes recently [2], which performs much better than the simple SC decoder and performs almost the same as the optimal ML (maximum likelihood) decoding at high SNR. In [3], we analyzed the minimum Hamming distance of the Polar codes, obtained a union bound on its frame error rate, and found that the performance of the Polar codes is dominated by its minimum Hamming distance. Although Polar codes can achieve the ML performance by the SC-List decoding, it still performs worse than turbo or LDPC codes due to its poor minimum Hamming distance. In this letter, we propose a hybrid codes called “RM-Polar” codes. This code is constructed by combining the code constructions of Reed-Muller codes and Polar codes. It not only has a larger minimum Hamming distance than the Polar codes, but also can be decoded as Polar codes by the SC decoder and the SC-List decoder. The simulations show that this RM-Polar code has much better error-rate performance than Polar codes.