具有逆向边增长结构LT码的设计与分析

宋鑫; 程乃平; 廖育荣; 倪淑燕; 雷拓峰

doi:10.12263/DZXB.20210595

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具有逆向边增长结构LT码的设计与分析

学术论文 | 更新时间：2025-12-08

- 具有逆向边增长结构LT码的设计与分析
- Design and Analysis of LT Code with Reverse Edge Growth Framework
- 电子学报 2022年50卷第5期页码：1201-1210
- 作者机构：
  
  1.航天工程大学研究生院, 北京 101416
  2.航天工程大学电子与光学工程系，北京 101416
- 作者简介：
  
  [ "宋鑫男,1995年出生于山西省临汾市.现为航天工程大学博士研究生.主要研究方向为信道编码,信道均衡,稀疏码分多址技术等. E‑mail: singlersx@163.com" ]
  [ "程乃平男,1962年出生于陕西省宝鸡市.现为航天工程大学研究员.主要研究方向为卫星信号处理,正交频分复用技术,信道编码等. E‑mail: cheng_np@163.com" ]
  [ "廖育荣男,1972年出生于四川省德阳市.现为航天工程大学研究员.主要研究方向为航天测控技术,卫星信号处理技术等.E‑mail: 406573420@qq.com" ]
  [ "倪淑燕女,1981年出生于河北省邢台市.现为航天工程大学副教授.主要研究方向为阵列信号处理,正交频分复用技术等.E⁃mail: daninini@163.com" ]
  [ "雷拓峰男,1998年出生于陕西省西安市.现为航天工程大学博士研究生.主要研究方向为正交频分复用技术,稀疏码分多址技术,信道编码等.E‑mail: tuofenglei@163.com" ]
- 基金信息：
  
  国家自然科学青年基金(61805283);军内科研项目(1700050400)
- DOI：10.12263/DZXB.20210595
  中图分类号： TN911.22
- 收稿：2021-05-10，
  
  修回：2021-12-19，
  
  纸质出版：2022-05-25
- 稿件说明：
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宋鑫,程乃平,廖育荣等.具有逆向边增长结构LT码的设计与分析[J].电子学报,2022,50(05):1201-1210.

SONG Xin,CHENG Nai-ping,LIAO Yu-rong,et al.Design and Analysis of LT Code with Reverse Edge Growth Framework[J].ACTA ELECTRONICA SINICA,2022,50(05):1201-1210.
宋鑫,程乃平,廖育荣等.具有逆向边增长结构LT码的设计与分析[J].电子学报,2022,50(05):1201-1210. DOI： 10.12263/DZXB.20210595.

SONG Xin,CHENG Nai-ping,LIAO Yu-rong,et al.Design and Analysis of LT Code with Reverse Edge Growth Framework[J].ACTA ELECTRONICA SINICA,2022,50(05):1201-1210. DOI： 10.12263/DZXB.20210595.

摘要

为了解决传统卢比变换（Luby Transform，LT）码在加性高斯白噪声（Additive White Gaussian Noise，AWGN）信道中存在高误码平台的问题，提出了一种具有逆向边增长（Reverse Edge Growth，REG）结构的LT码.REG-LT码会标记度数值相对较小的信息节点，并使其逆向精准地选取足够数量的校验节点，从而获得不低于期望目标的度数值.首先，设计了REG-LT码的编码算法，分析了校验节点和信息节点的选取原则.其次，推导了REG-LT码的信息节点度分布和校验节点度分布的数学表达式，分析了REG-LT码的收敛性.最后，引入增益损失比（Gain Loss Ratio，GLR）以衡量参数

对收敛性的影响，将最大化GLR作为求解最优

值的设计原则.仿真结果表明，与传统LT码相比，本文的REG-LT码可将误码平台降低3至5个数量级，且至少可获得2dB的编码增益；此外，REG-LT码也能够实现优于现有LT码的误比特率（Bit Error Rate，BER）性能.

Abstract

To solve the problem of high error floor for the conventional Luby transform(LT) codes in additive white gaussian noise(AWGN) channels

the LT code with reverse edge growth(REG) framework is proposed. For the REG-LT code

those information nodes with relatively small degrees will be marked

and these nodes will accurately select enough check nodes in reverse to obtain a degree that is not lower than the desired target. The coding scheme of the REG-LT code is designed

and the selection principle of check node and information node is analyzed. The mathematical expressions of the information degree distribution and check degree distribution of the REG-LT code are derived

and the convergence behavior of the REG-LT code is analyzed. The parameter gain loss ratio(GLR) is designed to measure the impact of the parameter

on convergence behavior

and maximize the GLR is used as a design principle to solve the optimal

. The simulation results show that compared with the conventional LT code

the REG-LT code in this paper can reduce the error platform by 3 to 5 orders of magnitude

and at least 2dB of coding gain can be obtained. Besides

the designed LT code outperforms the existing LT codes in terms of bit error rate(BER) performance.

关键词

Keywords

references

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