# Low-Complexity Multi-Size Circular-Shift Network for 5G New Radio LDPC Decoders

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## Abstract

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## 1. Introduction

## 2. Multi-Size Circular-Shift Network for 5G NR LDPC Decoder

#### 2.1. 5G NR LDPC Characteristics

#### 2.2. Multi-Size Circular-Shift Network

## 3. Proposed Low-Complexity Multi-Size Circular-Shift Network for 5G New Radio LDPC Decoder

#### 3.1. Modified Lifting Size Table for 5G New Radio LDPC Codes

#### 3.2. Structure of Forward Routing Network

#### 3.3. Fine-Coarse Structure for Circular-Shift Network

- Step 1. Pre-rotator: Each sub-block of ${Z}_{p}$ input data are processed by a pre-rotator subnetwork to generate the pre-circular shift by performing ${c}_{p}$ shift operation.
- Step 2. Main rotator: The k-th ouput datum of each pre-rotator network is distributed into the k-th main rotator subnetwork, where $0\le k<{Z}_{p}$. The main circular shift is generated by performing ${c}_{m}$ shift operation on each main rotator subnetwork. To overcome the inside-group rotation at the pre-rotator network, the cross-group movement is performed by the ${c}_{m}+1$ circular shift at the k-th main rotator subnetwork where $k+{c}_{p}\ge {Z}_{p}$.

#### 3.4. Proposed Low-Complexity Multi-Size Circular-Shift Network

## 4. Implementation Results and Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Benes network $2\times 2$ switch; (

**b**) Benes network when P = 8; (

**c**) Banyan network when $P=8$.

**Figure 7.**Proposed MSCS network structure for 5G NR LDPC decoders: (

**a**) MSCS controller; (

**b**) Two stages of the sub-MSCS network.

Components | Resource Consumption | |
---|---|---|

Adders/Subtractors | Adders | 445,970 |

Subtractors | 526,286 | |

Comparators | Lessequal Comparators | 2070 |

Greater Comparators | 481,022 | |

Multiplexers | 732,228 | |

Logic Shifters | 482,448 |

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**MDPI and ACS Style**

Nguyen, T.T.; Nguyen, T.T.B.; Lee, H.
Low-Complexity Multi-Size Circular-Shift Network for 5G New Radio LDPC Decoders. *Sensors* **2022**, *22*, 1792.
https://doi.org/10.3390/s22051792

**AMA Style**

Nguyen TT, Nguyen TTB, Lee H.
Low-Complexity Multi-Size Circular-Shift Network for 5G New Radio LDPC Decoders. *Sensors*. 2022; 22(5):1792.
https://doi.org/10.3390/s22051792

**Chicago/Turabian Style**

Nguyen, Tuy Tan, Tram Thi Bao Nguyen, and Hanho Lee.
2022. "Low-Complexity Multi-Size Circular-Shift Network for 5G New Radio LDPC Decoders" *Sensors* 22, no. 5: 1792.
https://doi.org/10.3390/s22051792