# Bit-Level Construction for Multiplicative-Repetition-Based Non-Binary Polar Codes +
## 3 Bit-Level Construction for Non-Binary Polar Codes
### Capacity-Based Bit-Level Construction
For practical implementation, MC-based bit-level construction is additionally proposed to reduce computational complexity. The simulation results showed that the proposed construction scheme outperformed binary polar codes and conventional non-binary polar codes with BPSK under both SC and CA-SCL decoding algorithms. Furthermore, we incorporate probabilistic shaping within our bit-level construction framework to address shaping loss in high-order modulation systems. The simulation results demonstrated that the proposed architecture achieved substantial shaping gains for high coding rates, while maintaining notable coding gains at lower coding rates. Conceptualization, R.X., P.C. and B.B. ; methodology, R.X. and L.L. ; software, R.X. and P.C. ; validation, R.X., M.Z. and B.B. ; formal analysis, R.X. and L.L. ; writing--original draft preparation, R.X. ; writing--review and editing, R.X., P.C., L.L., M.Z. and B.B. ; funding acquisition, M.Z. and B.B. All authors have read and agreed to the published version of the manuscript. \[P_{b}(s)=\frac{P_{e,i+1}(j)-P_{e,i}(j)}{1-P_{e,i}(j)} \tag{29}\]1 Performance comparison between the BICM and hybrid MLC-BICM with 64-QAM over the AWGN channel. * [1] [PERSON] Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. _IEEE Trans. Inform. Theory_**2009**, _55_, 3051-3073. * [2] [PERSON]; [PERSON] List decoding of polar codes. _IEEE Trans. Inform. Theory_**2015**, _61_, 2213-2226. * [3] [PERSON]; [PERSON] CRC-aided decoding of polar codes. _IEEE Commun. Lett._**2012**, _16_, 1668-1671. [CrossRef]
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