Non-binary polar codes with channel symbol permutations.

Inaba Akinori, Hideki Yagi

Ian F. Blake

Rongchi Xu, Peiyao Chen, Ling Liu +2 more

Conventional construction of non-binary polar codes divides the synthesized channels into the frozen channels and information channels. Each information channel carries one symbol i.e.$q$bits. However, there are many middle channels with insufficient polarization, which can not carry one symbol of$q$bits but only$i$bits,$1 \leq i<q, i \in \mathbb{Z}$, at finite block lengths. In this paper, we consider the bit-level construction for multiplicative repetition (MR) based non-binary polar codes and propose bitlevel improved construction for channel degradation method and Monte-Carlo method. Simulation results show that the proposed construction can significantly improve the decoding performance compared with the conventional construction scheme.

Rongchi Xu, Peiyao Chen, Ling Liu +2 more

In this paper, we discuss non-binary polar codes using a 2×2 matrix over a Galois field GF(2q) as the kernel. Conventional construction of non-binary polar codes divides the synthesized channels into frozen channels and information channels. Each information channel carries one symbol, i.e., q bits. However, there are many middle channels with insufficient polarization, which cannot carry one symbol of q bits but only i bits, 1≤i<q,i∈Z, at finite block length. In this paper, we consider bit-level construction for multiplicative repetition (MR)-based non-binary polar codes and propose a bit-level construction based on the two following methods. We first calculate the error probability and channel capacity lower bound of each synthesized channel based on the channel degradation method, and then determine both the number and index of the carried bits for each synthesized channel according to the symbol error probability and capacity. To reduce complexity, we also introduce a Monte-Carlo method. We compute the error probability of each synthesized channel carrying i information bits and select the optimal construction that can minimize the union bound of the error probability. Finally, an improved construction-based probabilistic shaping method for MR-based non-binary polar codes is considered. Simulation results show that the proposed construction significantly improved the decoding performance compared with the conventional construction scheme.

Mongkol Kupimai

In this paper, the new structure of high rate non-binary QC-LDPC codes based on the circulant permutation matrices is proposed. The construction of parity-check matrix of the proposed codes is obtained from (2, L) regular QC-LDPC codes. The parity-check matrix of the proposed codes has girth greater than 8. Simulation results over PR channels with the high order Galois Field show that the bit error rate and the symbol error rate performance of the proposed codes is better than those of the random non-binary LDPC codes, both in PR2 channel and EPR2 channel.

Peihong Yuan, Zhe Chen, Wu Yongpeng +1 more