# Controversial Variable Node Selection-Based Adaptive Belief Propagation Decoding Algorithm Using Bit Flipping Check for JSCC Systems

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## Abstract

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## 1. Introduction

- (1)
- A novel joint coding matrix is constructed through which the source compression and channel coding can be realized simultaneously to improve the coding efficiency.
- (2)
- A bit flipping check (BFC) algorithm is proposed to check and correct the errors of the compressed source block. The unreliable bits of each source block are selected by using the channel soft information to flip. If the reconstruction results of partial and all the source information are the same, the verification is successful.
- (3)
- A controversial variable node selection-based ABP (CVNS-ABP) algorithm is presented for JSC decoding. The proposed CVNS-ABP algorithm reduces the influence of error bits on decoding by selecting error variable nodes (VNs) from controversial VNs and adding them to the sparsity of the parity-check matrix. Based on the BFC algorithm and CVNS-ABP algorithm, several JSC decoding algorithms are proposed. By making full use of the redundancy of the source, the performance of JSC decoding is greatly improved.

## 2. System Description

#### 2.1. JSC Encoding

#### 2.2. Bit Flipping Check Algorithm

Algorithm 1: The Bit Flipping Check Algorithm |

#### 2.3. Controversial Variable Node Selection Based Adaptive Belief Propagation Decoding Algorithm

Algorithm 2: The CVNS-ABP Algorithm |

Initialize: Set damping factor $\alpha $, the maximum iteration number ${i}_{max}$, the LLR of the i-th iteration ${L}^{\left(i\right)}$.Step 1. BFC for each source blockCalculate the ${\mathbf{x}}_{A}$ and ${\mathbf{x}}_{B}$ for each source block. if${\mathbf{x}}_{A}$ = ${\mathbf{x}}_{B}$then$\phantom{(}$else$\phantom{(}$Step 2. Unreliable VN selectionSort the bit sequence according to ${L}^{\left(i\right)}$ and select $\rho $ unreliable VNs with the smallest absolute value. Step 3. Controversial VN selectionSelect the remaining $\theta $ controversial VNs from the unreliable source blocks, where $\rho $ + $\theta $ = $m\times (n-k)$. Step 4. Parity-check matrix updateImplement Gaussian elimination to unitize the $\rho +\theta $ unreliable positions selected in the parity-check matrix. Step 5. Extrinsic information generationCalculate the extrinsic LLR vector ${L}_{\mathrm{ext}}^{\left(i\right)}$ ${L}_{\mathrm{ext}}^{\left(i\right)}\left({v}_{n}\right)={\sum}_{{c}_{m}\in \mathcal{M}\left({v}_{n}\right)}2{tanh}^{-1}$
$$\left({\prod}_{{v}_{j}\in \mathcal{N}\left({c}_{m}\right)\setminus {v}_{n}}tanh\left(\frac{{L}^{\left(i\right)}\left({v}_{j}\right)}{2}\right)\right)$$
Step 6. Bit-level reliabilities update${L}^{(i+1)}={L}^{\left(i\right)}+\alpha {L}_{ext}^{\left(i\right)}$, where $0<\alpha \le 1$. Step 7. Hard decisionMake a hard decision on the value of VNs ${\widehat{c}}_{j}=\left\{\begin{array}{cc}0,\hfill & {L}^{(i+1)}\left({c}_{j}\right)>0\hfill \\ 1,\hfill & {L}^{(i+1)}\left({c}_{j}\right)<0\hfill \end{array}\right.$ Step 8. Termination criterionif${S}_{j}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0,$$j\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1,2,\cdots ,2t$then$\phantom{(}$else if$i={i}_{max}$then$\phantom{(}$else$\phantom{(}$Step 1. |

#### 2.4. High-Performance JSC Decoding Scheme

## 3. Simulation Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Frame error rate (FER) versus Eb/No of the proposed JSC decoding algorithms compared with other algorithms.

**Figure 6.**Frame error rate (FER) versus Eb/No of the proposed JSC decoding algorithm for different source sparsity.

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**MDPI and ACS Style**

Wang, H.; Zhang, W.; Jing, Y.; Chang, Y.; Liu, Y.
Controversial Variable Node Selection-Based Adaptive Belief Propagation Decoding Algorithm Using Bit Flipping Check for JSCC Systems. *Entropy* **2022**, *24*, 427.
https://doi.org/10.3390/e24030427

**AMA Style**

Wang H, Zhang W, Jing Y, Chang Y, Liu Y.
Controversial Variable Node Selection-Based Adaptive Belief Propagation Decoding Algorithm Using Bit Flipping Check for JSCC Systems. *Entropy*. 2022; 24(3):427.
https://doi.org/10.3390/e24030427

**Chicago/Turabian Style**

Wang, Hao, Wei Zhang, Yizhe Jing, Yanyan Chang, and Yanyan Liu.
2022. "Controversial Variable Node Selection-Based Adaptive Belief Propagation Decoding Algorithm Using Bit Flipping Check for JSCC Systems" *Entropy* 24, no. 3: 427.
https://doi.org/10.3390/e24030427