SCIENCE CHINA Information Sciences, Volume 62, Issue 8: 080303(2019) https://doi.org/10.1007/s11432-019-9905-7

Partial CRC-aided decoding of 5G-NR short codes using reliability information

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  • ReceivedMar 5, 2019
  • AcceptedMay 23, 2019
  • PublishedJul 11, 2019


In this paper, we focus on how to further enhance the performance of the channel codes in order to meet the more stringent reliability requirements of future networks (5G and beyond). A general decoder with the aid of partial cyclic redundancy check (CRC) bits is proposed for the polar codes and short low-density parity-check (LDPC) codes in 5G systems.The decoder based on ordered statistic decoding (OSD) method can effectively improve the error-correction performance on the condition that extra CRC bits are used to assist in decoding. Meanwhile, the remaining part of CRC keeps its capability of error-detection to guarantee the undetected error rate low enough.This paper gives the detailed implementation schemes of the partial CRC-aided OSD process and its combination with the conventional decodings of the LDPC/polar codes in 5G systems. The simulation results show our proposed decoding scheme achieves a promising trade-off between the performance gain and the error-detection capabilities.


This work was supported in part by National Natural Science Foundation of China (Grant No. 61771133) and in part by National Science Technology Projects of China (Grant No. 2018ZX03001002).


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  • Figure 1

    (Color online) The systematic structure of CRC-LDPC/polar codes. (a) CRC-LDPC codes; (b) CRC-polar codes.

  • Table 1   Complexity comparison of different algorithms for polar codes
    AlgorithmEquivalent addition numbers
    CASCL $\zeta_{s}=~L\cdot~N\cdot~\log_{2}{N}~+~K\cdot~L\cdot~\log_{2}{2L}~$
    Proposed $\zeta_{p}=\zeta_{s}+R_{f}\cdot~\zeta_{o}~$

    Algorithm 1 OSD algorithm with partial CRC aided

    Require:reliability information $~{\boldsymbol{R}}~$, input data of receiver $~{\boldsymbol{Y}}~$, union generator matrix $~{{\hat{\boldsymbol~G}}}_{I}~$;

    Output: optimal codeword ${\boldsymbol{C}}_{\rm~op}$, CRC decision;

    Sort the absolute value of $~{\boldsymbol{R}}~$ in descending order, get $~\pi_{1}({\boldsymbol{R}})~$;

    Swap the corresponding column of $~{{\hat{\boldsymbol~G}}}_{I}~$, get $\pi_{1}({{\hat{\boldsymbol~G}}}_{I})$;

    Do Gaussian elimination (GE) on $\pi_{1}({{\hat{\boldsymbol~G}}}_{I})$, make additional column swaps $\pi_{2}$ when there is all-zero column, get systematic matrix ${{\tilde{\boldsymbol~G}}}_{I}={\rm{GE}}(\pi_{2}(\pi_{1}({{\hat{\boldsymbol~G}}}_{I})))$;

    Do hard decision on $~{\boldsymbol{R}}~$, get codeword ${\boldsymbol{C}}$;

    Make corresponding two swaps on ${\boldsymbol{C}}$, get $\tilde{\boldsymbol{C}}=\pi_{2}(\pi_{1}(\boldsymbol{C}))$;

    Do order-$i$ flipping on the basis of $\tilde{\boldsymbol{C}}$, get a code set ${\mathcal{C}_{f}}=\{{\boldsymbol{C}}_{f,j},~j=1,2,\ldots,\binom{\hat{A}}{i}\}$;

    for $j=1,2,\ldots,\binom{\hat{A}}{i}$


    Calculate Euclidean distance between $~{\boldsymbol{Y}}_{f,j}~$ and $~{\boldsymbol{Y}}~$;

    end for

    Find $~{\boldsymbol{Y}}_{f,j}~$ with minimum Euclidean distance and the corresponding codeword $~{\boldsymbol{C}}_{f,j}~=~{\tilde{\boldsymbol{C}}}_{\rm~op}~$;

    Recover the codeword in original sequence ${\boldsymbol{C}}_{\rm~op}=\pi_{1}^{-1}(\pi_{2}^{-1}({\tilde{\boldsymbol{C}}}_{\rm~op}))~$;

    Do CRC testing on ${\boldsymbol{C}}_{\rm~op}$ and make a final decision if ${\boldsymbol{C}}_{\rm~op}$ is a correct codeword.

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