SCIENCE CHINA Information Sciences, Volume 61, Issue 2: 022309(2018) https://doi.org/10.1007/s11432-017-9128-x

## A complexity-reduced fast successive cancellation list decoder for polar codes

• AcceptedApr 25, 2017
• PublishedNov 20, 2017
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### Abstract

A multi-bit decision for polar codes based on a simplified successive cancellation (SSC) decoding algorithm can improve the throughput of polar decoding. A list algorithm is used to improve the error-correcting performance. However, list decoders are highly complex compared with decoders without a list algorithm. In this paper, a low-complexity list decoder is proposed, where path-splitting operations for a multi-bit decision can be avoided, if the decoding reliability exceeds a threshold. The threshold is determined based on the reliability of subchannels and positions of decoding nodes. Path splitting rules are designed for multi-bit decision processes, and a complexity-reduced list decoder is proposed based on this. Results show that the number of survival paths can be greatly reduced at the cost of negligible deterioration in block error performance. Thus, the computational complexity can be significantly reduced, especially for a high signal-to-noise ratio (SNR) region.

### Acknowledgment

This work was partially supported by National Major Project (Grant No. 2016ZX030010- 11005), National Natural Science Foundation Project (Grant No. 61521061), and Intel Corporation.

### References

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• Figure 1

(Color online) Decoding tree of an (8, 4) polar code.

• Figure 2

(Color online) Delivery of LLR messages in decoding tree for N=8.

• Figure 3

(Color online) BLER performance of different $\rho$ for N=1024, L=32.

• Figure 4

(Color online) Average complexity of different $\rho$ for N=1024, L=32.

• Figure 5

(Color online) BLER performance for L=8, N=256, 1024 and 4096.

• Figure 6

(Color online) Average complexity for L=8, N=256, 1024 and 4096.

• Figure 7

(Color online) Average complexity for N=1024, L=8, 16, 32.

• Figure 8

(Color online) BLER performance for N=1024, L=8, 16, 32.

•

Algorithm 1 Complexity reduced fast SSC list decoder

Decoding starts from the root node by setting ${\alpha~_v}[i]~=~\log~\left(~{\frac{{\Pr~({y_i}|{x_i}~=~0)}}{{\Pr~({y_i}|{x_i}~=~1)}}}~\right),{\rm{~for~}}~1~\le~i~\le~N$.

if current node $v~\in~\left\{~{{\rm{Rate~-~0,~Rate~-~1,~REP}},{\rm{~SPC}}}~\right\}$ then

for each source path l

Calculate ${{\boldsymbol{\beta~}}_v}$ according to Subsection 2.3;

if $|{\alpha~_v}[\min~]|~>~{\rm~TL}_{N}^j$ then

Do not split new paths;

else

Generate new path according to Subsection 3.3;

end if

end for

Prune paths if path number exceeds the specific list size L;

else

Calculate ${{\boldsymbol{\alpha~}}_l}$ of each path: ${\alpha~_l}[i]~=~{{F}}\left(~{{\alpha~_v}[2i~-~1],{\alpha~_v}[2i]}~\right)$;

go to the left child node;

Calculate ${{\boldsymbol{\alpha~}}_r}$ of each path: ${\alpha~_r}[i]~=~{\mathop{~G}\nolimits}~\left(~{{\alpha~_v}[2i~-~1],{\alpha~_v}[2i],{\beta~_l}[i]}~\right)$;

go to the right child node;

Calculate ${{\boldsymbol{\beta~}}_v}$ of each path: $\left\{~{{\beta~_v}[2i~-~1],{\beta~_v}[2i]}~\right\}~=~\left\{~{{\beta~_l}[i]~\oplus~{\beta~_r}[i],{\beta~_r}[i]}~\right\}$;

end if

When the decoding returns from the root node, select the final output that satisfies the CRC constraint.

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