# A Joint Detection and Decoding Scheme for PC-SCMA System Based on Pruning Iteration

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## Abstract

**:**

## 1. Introduction

#### 1.1. Related Work

#### 1.2. Organization and Notation

## 2. System Model

## 3. Proposed Algorithm for Joint Detection and Decoding

#### 3.1. Joint Detection and Decoding Scheme Based on Pruning Iteration PI-JDD

#### 3.1.1. RNs Update

#### 3.1.2. SCAN Decoding

#### 3.2. Joint Optimization Scheme for Joint Detection and Decoding PIC-JDD

## 4. Computational Complexity

## 5. Numerical Results

#### 5.1. BER Performance Analysis of PI-JDD

#### 5.2. BER Performance Analysis of C-JIDD

#### 5.3. BER Performance Analysis of PIC-JDD

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Algorithm | ADD | MUL | COM |

S-JIDD | $\begin{array}{l}\mathrm{T}\times \mathrm{K}\times \left({d}_{f}\times \left(\left({\mathrm{M}}^{\wedge}{d}_{f}\right)\times \left(2*{d}_{f}-1\right)+2\times \mathrm{M}\right)+{d}_{f}\right)\\ +\mathrm{N}\times \mathrm{log}(\mathrm{N})\times \mathrm{T}\end{array}$ | $\mathrm{T}\times \mathrm{K}\times \left({d}_{f}\times \left({\mathrm{M}}^{\wedge}{d}_{f}\right)\times {\mathrm{d}}_{f}\right)+\mathrm{N}\times \mathrm{log}(\mathrm{N})\times \mathrm{T}$ | $0$ |

PIC-JDD | $\begin{array}{l}\mathrm{K}\times {\mathrm{d}}_{\mathrm{f}}\times \left({\mathrm{M}}^{\wedge}{d}_{f}\right)\times \left(2\times {d}_{f}-1\right)+(\mathrm{T}-1)\times \\ \left\{\mathrm{K}\times {\mathrm{d}}_{f}+\mathrm{K}\times ({d}_{f}-\right.\left.1)\times \left[{\mathrm{M}}^{\wedge}\left({d}_{f}-1\right)\right]\times \left(2*{d}_{f}-1\right)+\mathrm{N}\times \mathrm{log}(\mathrm{N})\right\}\\ +\mathrm{T}\times \left(\mathrm{K}\times {\mathrm{d}}_{f}\times 2\times \mathrm{M}\right.\left.+K\times {d}_{f}\right)\end{array}$ | $\begin{array}{l}\mathrm{K}\times \left[{d}_{f}\times \left({\mathrm{M}}^{\wedge}{d}_{f}\right)\times {\mathrm{d}}_{f}\right]+(\mathrm{T}-1)\times \\ \left\{\left\{{d}_{f}\times \left[M^\left({d}_{f}-1\right)\right]\times \left({d}_{f}-1\right)\right\}+N\times \mathrm{log}\left(N\right)\right\}\end{array}$ | $\left(T-1\right)\times K\times {d}_{f}$ |

Parameter | Value |

Number of users J | 6 |

Size of codebook M | 4 |

Number of resources K | 4 |

System load λ | 150% |

a (N = 256) | 0.6 |

a (N = 1024) | 0.4 |

Code rate R (N = 256) | 0.47 |

Code rate R (N = 1024) | 0.32 |

Channel model | AWGN |

Construction mode of polar code | Gaussian approximate |

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**MDPI and ACS Style**

Zhang, Y.; Ge, W.; Zhang, P.; Gao, M.; Zhang, G.
A Joint Detection and Decoding Scheme for PC-SCMA System Based on Pruning Iteration. *Symmetry* **2020**, *12*, 1624.
https://doi.org/10.3390/sym12101624

**AMA Style**

Zhang Y, Ge W, Zhang P, Gao M, Zhang G.
A Joint Detection and Decoding Scheme for PC-SCMA System Based on Pruning Iteration. *Symmetry*. 2020; 12(10):1624.
https://doi.org/10.3390/sym12101624

**Chicago/Turabian Style**

Zhang, Yongxing, Wenping Ge, Pengju Zhang, Mengyao Gao, and Gecheng Zhang.
2020. "A Joint Detection and Decoding Scheme for PC-SCMA System Based on Pruning Iteration" *Symmetry* 12, no. 10: 1624.
https://doi.org/10.3390/sym12101624