On the Non-Approximate Successive Cancellation Decoding of Binary Polar Codes With Medium Kernels
Polar codes constructed by large kernels can attain better finite length performance than those originating from Arıkan’s <inline-formula> <tex-math notation="LaTeX">$2\times 2$ </tex-math></inline-formula> kernel. However, the successive cance...
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10214576/ |
| _version_ | 1797739772054077440 |
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| author | Zhiliang Huang Zongsheng Jiang Shuihong Zhou Xiaoyan Zhang |
| author_facet | Zhiliang Huang Zongsheng Jiang Shuihong Zhou Xiaoyan Zhang |
| author_sort | Zhiliang Huang |
| collection | DOAJ |
| description | Polar codes constructed by large kernels can attain better finite length performance than those originating from Arıkan’s <inline-formula> <tex-math notation="LaTeX">$2\times 2$ </tex-math></inline-formula> kernel. However, the successive cancellation (SC) decoding for these polar codes is impractical even for relatively small kernel size of <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> because complexity of the kernel computation grows exponentially with <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula>. This research shows when <inline-formula> <tex-math notation="LaTeX">$m>2$ </tex-math></inline-formula>, there exists a large amount of like terms in the kernel computation which yields a ground for facilitating the decoding. By transferring the kernel computation from the probability domain to the likelihood ratio domain (<inline-formula> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula>-domain), the so- called <inline-formula> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula>-formula method provides an efficient way to combine the like terms in the kernel computation for kernels up to size 11. However, the <inline-formula> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula>-formula method becomes intractable for kernel size beyond 11. To further reduce the computational complexity, this paper proposes a <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-formula method which transforms the kernel computation into the probability pair domain (<inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-domain). Advanced from the <inline-formula> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula>-domain, the numerator and denominator of the likelihood ratio are considered separately, which eases the restrictions of combining like terms. The <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-formula method can combine much more like terms resulting in a significant reduction on the number of sub-formulas for medium kernels (<inline-formula> <tex-math notation="LaTeX">$m\leq 16$ </tex-math></inline-formula>). Furthermore, in the <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-domain, sub-formulas become regular and there exist many common sub-formulas whose computations can be shared. Being able to handle kernels of size up to 16, we show that the <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-formula based SC decoding achieves a significant complexity reduction over the existing non-approximate SC decoding (the <inline-formula> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula>-formula based SC decoding). |
| first_indexed | 2024-03-12T14:02:57Z |
| format | Article |
| id | doaj.art-a0ea8107292d4754b4a921e1c22d6add |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-12T14:02:57Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
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| series | IEEE Access |
| spelling | doaj.art-a0ea8107292d4754b4a921e1c22d6add2023-08-21T23:00:42ZengIEEEIEEE Access2169-35362023-01-0111875058751910.1109/ACCESS.2023.330432910214576On the Non-Approximate Successive Cancellation Decoding of Binary Polar Codes With Medium KernelsZhiliang Huang0https://orcid.org/0000-0003-0876-063XZongsheng Jiang1Shuihong Zhou2Xiaoyan Zhang3School of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, ChinaSchool of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, ChinaSchool of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, ChinaSchool of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, ChinaPolar codes constructed by large kernels can attain better finite length performance than those originating from Arıkan’s <inline-formula> <tex-math notation="LaTeX">$2\times 2$ </tex-math></inline-formula> kernel. However, the successive cancellation (SC) decoding for these polar codes is impractical even for relatively small kernel size of <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> because complexity of the kernel computation grows exponentially with <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula>. This research shows when <inline-formula> <tex-math notation="LaTeX">$m>2$ </tex-math></inline-formula>, there exists a large amount of like terms in the kernel computation which yields a ground for facilitating the decoding. By transferring the kernel computation from the probability domain to the likelihood ratio domain (<inline-formula> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula>-domain), the so- called <inline-formula> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula>-formula method provides an efficient way to combine the like terms in the kernel computation for kernels up to size 11. However, the <inline-formula> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula>-formula method becomes intractable for kernel size beyond 11. To further reduce the computational complexity, this paper proposes a <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-formula method which transforms the kernel computation into the probability pair domain (<inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-domain). Advanced from the <inline-formula> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula>-domain, the numerator and denominator of the likelihood ratio are considered separately, which eases the restrictions of combining like terms. The <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-formula method can combine much more like terms resulting in a significant reduction on the number of sub-formulas for medium kernels (<inline-formula> <tex-math notation="LaTeX">$m\leq 16$ </tex-math></inline-formula>). Furthermore, in the <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-domain, sub-formulas become regular and there exist many common sub-formulas whose computations can be shared. Being able to handle kernels of size up to 16, we show that the <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-formula based SC decoding achieves a significant complexity reduction over the existing non-approximate SC decoding (the <inline-formula> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula>-formula based SC decoding).https://ieeexplore.ieee.org/document/10214576/Large kernelmedium kernelpolar codesSC decodingW-formula |
| spellingShingle | Zhiliang Huang Zongsheng Jiang Shuihong Zhou Xiaoyan Zhang On the Non-Approximate Successive Cancellation Decoding of Binary Polar Codes With Medium Kernels IEEE Access Large kernel medium kernel polar codes SC decoding W-formula |
| title | On the Non-Approximate Successive Cancellation Decoding of Binary Polar Codes With Medium Kernels |
| title_full | On the Non-Approximate Successive Cancellation Decoding of Binary Polar Codes With Medium Kernels |
| title_fullStr | On the Non-Approximate Successive Cancellation Decoding of Binary Polar Codes With Medium Kernels |
| title_full_unstemmed | On the Non-Approximate Successive Cancellation Decoding of Binary Polar Codes With Medium Kernels |
| title_short | On the Non-Approximate Successive Cancellation Decoding of Binary Polar Codes With Medium Kernels |
| title_sort | on the non approximate successive cancellation decoding of binary polar codes with medium kernels |
| topic | Large kernel medium kernel polar codes SC decoding W-formula |
| url | https://ieeexplore.ieee.org/document/10214576/ |
| work_keys_str_mv | AT zhilianghuang onthenonapproximatesuccessivecancellationdecodingofbinarypolarcodeswithmediumkernels AT zongshengjiang onthenonapproximatesuccessivecancellationdecodingofbinarypolarcodeswithmediumkernels AT shuihongzhou onthenonapproximatesuccessivecancellationdecodingofbinarypolarcodeswithmediumkernels AT xiaoyanzhang onthenonapproximatesuccessivecancellationdecodingofbinarypolarcodeswithmediumkernels |