A Transformation for Polar Code BP Decoding

Yi‐Ru Chen, Huang–Chang Lee, Mao‐Chao Lin

A transformation technique has been designed, where the encoding result of the polar code can be transferred to an low-density parity-check (LDPC) code. The belief-propagation decoding can be applied to the received sequence according to the parity-check matrix of the LDPC code. The transferred polar code can provide the same error-rate of the LDPC code, and its performance can be further improved if the success-cancellation decoding is available.

Akira Yamada, Tomoaki Otsuki Ohtsuki

Marvin Geiselhart, Ahmed Elkelesh, Jannis Clausius +1 more

Permutation decoding gained recent interest as it can exploit the symmetries of a code in a parallel fashion. Moreover, it has been shown that by viewing permuted polar codes as polar subcodes, the set of usable permutations in permutation decoding can be increased. We extend this idea to pre-transformed polar codes, such as cyclic redundancy check (CRC)-aided polar codes, which previously could not be decoded using permutations due to their lack of automorphisms. Using belief propagation (BP)-based subdecoders, we showcase a performance close to CRC-aided SCL (CA-SCL) decoding. The proposed algorithm outperforms the previously best performing iterative CRC-aided belief propagation list (CA-BPL) decoder both in error-rate performance and decoding latency.

Dongsheng Wu, Qingshuang Zhang, Yingxian Zhang

Gou Hosoya, Hiroyuki Yashima

Baoping Feng, Rongke Liu, Kairui Tian

For polar codes, the statistical breakdown of belief propagation (BP) decoding errors is firstly proposed by Sunet al.The errors are classified into three categories: unconverged errors, false converged errors and oscillation errors, which are corrected by three different post-processing methods. As for the BP List (BPL) decoding, we discover that one type of error can be transformed to another type by different factor graphs in the failed BP decoding. Besides, false converged error is usually easier to be detected and modified. Therefore, we only target false converged error to detect and correct. In this work, we propose a two-level detection rule for false converged errors and its corresponding post-processing algorithm to modify these errors in order to improve the performance of the BPL decoding. Numerical results show that the error-correction performance of the proposed decoder is more than 0.85dB better than that of the permuted BPL (PBPL) decoder with slight extra computation complexity at the frame error rate (FER) of$10^{-5}$for 5G (1024,512) polar code.