具有低误码平台系统LT码的设计与优化

doi:10.12305/j.issn.1001-506X.2026.10.38

摘要/Abstract

摘要：

卢比变换（Luby transform，LT）码是第一种实用的无速率码，其传输码率值可以根据信道状态自适应地进行调整。然而，LT码固有的误码平台现象限制其在实际传输场景中的应用。为了解决此问题，设计了一种系统无速率编码方案，以提高LT码在较宽范围信噪比（signal-to-noise ratio，SNR）内的误比特率（bit error rate，BER）性能。该方案通过优化编码结构与节点传输模式，实现高SNR区域快速收敛译码、低SNR区域无差错译码。此外，基于外信息传递图法分析了该编码方案在两种传输情况时的收敛性，在所需SNR范围内预设了若干期望值，并以此为核心约束条件优化了校验度分布设计模型；之后，设计了最优参数搜索算法，为度分布设计模型中关键参数的选取提供了经验依据。仿真结果表明，该方案的BER性能优于现有的改进方案，且节省的编码开销可达码长的10%。

关键词: 信道编码, 无速率码, 度分布, 误码平台

Abstract:

Luby transform （LT） codes are the first practical rateless codes whose transmission code rate can be adjusted adaptively according to the channel state. However, the inherent error floor phenomenon of LT code limits its application in practical transmission scenarios. To solve this problem, a systematic rateless coding scheme is designed to improve the bit error rate （BER） performance of LT codes in a wide range of signal-to-noise ratio （SNR）. By optimizing the coding structure and transmission mode of nodes, this scheme realizes fast convergence decoding in high SNR region and error-free decoding in low SNR region. In addition, the convergence of the encoding scheme in two transmission cases is analyzed based on the extrinsic information transfer chart method. Some expected values are preset within the desired SNR range, and the check degree distribution design model is optimized based on these core constraints. Then, the optimal parameter search algorithm is designed, which provides an empirical basis for selecting the key parameters in the degree distribution design model. Simulation results show that the BER performance of the proposed scheme outperforms the existing improved coding schemes, and the coding overhead can be saved up to 10% of the code length.

Key words: channel coding, rateless code, degree distribution, error floor

中图分类号:

TN 911.22

孙伟柏, 倪淑燕, 宋鑫, 雷拓峰. 具有低误码平台系统LT码的设计与优化[J]. 系统工程与电子技术, 2026, 48(10): 3683-3692.

Weibai Sun, Shuyan Ni, Xin Song, Tuofeng Lei. Design and optimization of LT codes with low error floor system[J]. Systems Engineering and Electronics, 2026, 48(10): 3683-3692.

图/表 14

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SNR/dB	${\sigma _n}$	${C_{{\sigma _n}}}$
−2.82	0.9783	0.5000
−1.53	0.8433	0.6005
−0.27	0.7294	0.7004
1,07	0.6252	0.7994
2.73	0.5164	0.9000

${\alpha _1}$	${\alpha _2}$	${\alpha _{{\text{sum}}}}$	${\alpha _1}$	${\alpha _2}$	${\alpha _{{\text{sum}}}}$
10.5	12.1	77.6411	10.8	12.1	79.1411
	12.2	77.8489		12.2	79.3489
	12.3	78.0567		12.3	79.5567
	12.4	78.2644		12.4	79.7644
10.6	12.1	78.1411	10.9	12.1	79.6411
	12.2	78.3489		12.2	79.8489
	12.3	78.5567		12.3	80.0567
	12.4	78.7644		12.4	80.2644
10.7	12.1	78.6411	11.0	12.1	80.1411
	12.2	78.8489		12.2	80.3489
	12.3	79.0567		12.3	80.5567
	12.4	79.2644		12.4	80.7644

$ {\alpha }_{1} $	$ \beta $	校验节点度分布
10.9	36.3333	$ \begin{array}{l} {\varOmega }_{1}\left(x\right)=0.134\;3{x}^{13}+0.806\;0{x}^{14}+0.003\;6{x}^{110}+\\ 0.003\;2{x}^{111}+0.053{x}^{300}\end{array} $
10.9	11.4444	$ \begin{array}{l}{\varOmega}_{2}\left(x\right)=0.062{x}^{4}+0.897\;9{x}^{5}+0.025{x}^{87}+\\ 0.015\;1{x}^{300}\end{array} $
8.9	29.6667	$ \begin{array}{l}{\varOmega }_{1}\left(x\right)=0.617\;4{x}^{14}+0.302\;5{x}^{15}+0.004\;2{x}^{89}+\\ \text{ }0.075\;9{x}^{300}\end{array} $
8.9	11.4444	$ \begin{array}{l}{\varOmega }_{2}\left(x\right)=0.006\;3{x}^{4}+0.953\;1{x}^{5}+0.008{x}^{87}+\\ \text{ }0.017\;9{x}^{88}+0.014\;6{x}^{300}\end{array} $

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