# Memory-Based LT Codes for Efficient 5G Networks and Beyond

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries and Related Work

#### 2.1. LT Encoding Process

Algorithm 1: Encoding Process of LT Codes |

#### 2.2. LT Decoding Process

Algorithm 2: BP Decoding Process of LT Codes |

#### 2.3. Degree Distributions of LT Codes

## 3. Y-Network Using MBLT Algorithm

#### 3.1. Encoding Process of the MBLT on the Y-Network

Algorithm 3: MBLT encoding process at the Y-network. |

#### 3.2. Decoding Process of MBLT Algorithm

## 4. Performance Analysis

#### 4.1. Decoding Success Probability

#### 4.2. Optimization of LT Code Parameters

## 5. Numerical Results

#### 5.1. LT Parameters

#### 5.2. DSP and BER

## 6. Conclusions

## Funding

## Conflicts of Interest

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**Figure 2.**The encoding process of LT codes, where k source symbols (circles) are used to generate n encoded symbols (squares).

**Figure 3.**A toy example of an LT decoding process, where there are 4 source symbols (circles) and 5 encoded symbols (squares). Figures from (

**a**–

**d**) show the decoding steps of the example.

**Figure 4.**Decoding success probability (DSP) versus the overhead ($\u03f5$) for LT codes of $k=128$ at different values of c and $\delta $. (

**a**) $\delta =0.05$. (

**b**) $\delta =0.1$. (

**c**) $\delta =0.2$. (

**d**) $\delta =0.5$.

**Figure 5.**DSP versus the overhead ($\u03f5$) for LT codes of $k=256$ at different values of c. (

**a**) $\delta =0.05$. (

**b**) $\delta =0.1$. (

**c**) $\delta =0.2$. (

**d**) $\delta =0.5$.

**Figure 6.**DSP versus the overhead ($\u03f5$) for different coding schemes at $k=128$ and erasure probabilities of ${\epsilon}_{1}=0$, ${\epsilon}_{2}=0$, and ${\epsilon}_{3}=0$.

**Figure 7.**Bit error rate (BER) versus the overhead ($\u03f5$) for different coding schemes at $k=128$ and erasure probabilities of ${\epsilon}_{1}=0$, ${\epsilon}_{2}=0$, and ${\epsilon}_{3}=0$.

**Figure 8.**DSP versus the overhead ($\u03f5$) for different coding schemes at $k=128$ and erasure probabilities of ${\epsilon}_{1}=0.01$, ${\epsilon}_{2}=0.01$, and ${\epsilon}_{3}=0.1$.

**Figure 9.**BER versus the overhead ($\u03f5$) for different coding schemes at $k=128$ and erasure probabilities of ${\epsilon}_{1}=0.01$, ${\epsilon}_{2}=0.01$, and ${\epsilon}_{3}=0.1$.

**Figure 10.**BER versus the overhead ($\u03f5$) for different coding schemes at $k=256$ and erasure probabilities of ${\epsilon}_{1}=0$, ${\epsilon}_{2}=0$, and ${\epsilon}_{3}=0$.

**Figure 11.**BER versus the overhead ($\u03f5$) for different coding schemes at $k=256$ and erasure probabilities of ${\epsilon}_{1}=0.01$, ${\epsilon}_{2}=0.01$, and ${\epsilon}_{3}=0$.

**Figure 12.**BER versus the overhead ($\u03f5$) for different coding schemes at $k=256$ and erasure probabilities of ${\epsilon}_{1}=0.01$, ${\epsilon}_{2}=0.01$, and ${\epsilon}_{3}=0.01$.

**Figure 13.**BER versus the overhead ($\u03f5$) for different coding schemes at $k=256$ and erasure probabilities of ${\epsilon}_{1}=0.01$, ${\epsilon}_{2}=0.01$, and ${\epsilon}_{3}=0.1$.

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Hayajneh, K.F.
Memory-Based LT Codes for Efficient 5G Networks and Beyond. *Electronics* **2021**, *10*, 3169.
https://doi.org/10.3390/electronics10243169

**AMA Style**

Hayajneh KF.
Memory-Based LT Codes for Efficient 5G Networks and Beyond. *Electronics*. 2021; 10(24):3169.
https://doi.org/10.3390/electronics10243169

**Chicago/Turabian Style**

Hayajneh, Khaled F.
2021. "Memory-Based LT Codes for Efficient 5G Networks and Beyond" *Electronics* 10, no. 24: 3169.
https://doi.org/10.3390/electronics10243169