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

作　　者：宋鑫 程乃平 廖育荣 倪淑燕 雷拓峰 SONG Xin;CHENG Nai-ping;LIAO Yu-rong;NI Shu-yan;LEI Tuo-feng(Department of Graduate Management,Space Engineering University,Beijing 101416,China;Department of Electronic and Optical Engineering,Space Engineering University,Beijing 101416,China)

机构地区：[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

出　　处：《电子学报》2022年第5期1201-1210,共10页Acta Electronica Sinica

基　　金：国家自然科学青年基金(No.61805283);军内科研项目(No.1700050400)。

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T;对收敛性的影响,将最大化GLR作为求解最优T;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2 dB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.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 T;on convergence behavior,and maximize the GLR is used as a design principle to solve the optimal T;.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：喷泉码 LT码 高斯信道 误比特率 度分布 编码算法 外信息传递图 

分 类 号：TN911.22[电子电信—通信与信息系统]