基于共轭梯度求解代价函数的卷积码参数识别算法

doi:10.12305/j.issn.1001-506X.2022.10.29

系统工程与电子技术 ›› 2022, Vol. 44 ›› Issue (10): 3235-3242.doi: 10.12305/j.issn.1001-506X.2022.10.29

基于共轭梯度求解代价函数的卷积码参数识别算法

陈增茂^1,², 陆丽¹, 孙志国^1,*, 孙溶辰¹

1. 哈尔滨工程大学信息与通信工程学院, 黑龙江哈尔滨 150001
2. 哈尔滨工程大学工业和信息化部先进船舶通信与信息技术重点实验室, 黑龙江哈尔滨 150001

收稿日期:2021-07-13 出版日期:2022-09-20 发布日期:2022-10-24
通讯作者: 孙志国
作者简介:陈增茂 (1981—), 男, 副教授, 博士, 主要研究方向为认知无线电、干扰建模、通信对抗|陆丽 (1996—), 女, 硕士研究生, 主要研究方向为纠错编码参数识别|孙志国 (1977—), 男, 教授, 博士, 主要研究方向为认知通信电子战|孙溶辰 (1988—), 男, 副教授, 博士, 主要研究方向为信道测量与建模
基金资助:
国家自然科学基金(62001139)

Parameter estimation algorithm of convolutional codes with solving cost function based on conjugate gradient

Zengmao CHEN^1,², Li LU¹, Zhiguo SUN^1,*, Rongchen SUN¹

1. School of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China
2. Key Laboratory of Advanced Marine Communication and Information Technology, Ministry of Industry and Information Technology, Harbin 150001, China

Received:2021-07-13 Online:2022-09-20 Published:2022-10-24
Contact: Zhiguo SUN

摘要/Abstract

摘要：

卷积码常作为级联码、Turbo码等高性能编码的子码, 正确识别出卷积码的参数是级联码、Turbo码参数识别的基础, 这要求卷积码参数识别算法具有较强的抗噪能力。利用解调软判决序列可以有效提高识别算法的抗噪能力。根据递归系统卷积码编码码元间的线性约束关系构造了一个基于指数函数的代价函数模型, 将生成矩阵的识别问题转化成求解代价函数极小值的最优化问题, 并采用共轭梯度法不断逼近极小点。仿真结果显示, 与现有算法相比, 所提方法显著提高了抗噪能力, 且适用性强、收敛速度快。

关键词: 卷积码参数识别, 递归系统卷积码, 解调软判决, 最优化方法, 共轭梯度法

Abstract:

Convolutional codes are often used as sub-codes of high performance codes such as concatenated codes and turbo codes. Correct parameter estimation of convolutional codes is the basis of recognition of concatenated codes and turbo codes, which requires that the estimation algorithms of convolutional codes should have strong robustness against channel noise. The key to such purpose is to make use of the soft-decesion demodulation received sequence. In this paper, a cost function model based on exponential function is proposed according to the linear constraint relation between symbols of recursive systematic convolutional codes. The parameter estimation of convolutional codes is transformed into the minimal value of the cost function. And the optimization is accomplished via a simple iterative process by conjugate gradient. Simulation results show that, compared with the existing algorithms, the new algorithm significantly improves the performance while it is also applicable to the estimation of general convolutional codes and has a fast convergence speed.

Key words: parameter estimation of convolutional codes, recursive systematic convolutional codes, soft-decision demodulation, optimization method, conjugate gradient method

中图分类号:

TN911.7

陈增茂, 陆丽, 孙志国, 孙溶辰. 基于共轭梯度求解代价函数的卷积码参数识别算法[J]. 系统工程与电子技术, 2022, 44(10): 3235-3242.

Zengmao CHEN, Li LU, Zhiguo SUN, Rongchen SUN. Parameter estimation algorithm of convolutional codes with solving cost function based on conjugate gradient[J]. Systems Engineering and Electronics, 2022, 44(10): 3235-3242.

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m	生成多项式	d
2	g₀(D)=1+D+D², g₁(D)=1+D²	5
4	g₀(D)=1+D³+D⁴, g₁(D)=1+D+D²+D⁴	7
6	g₀(D)=1+D²+D³+D⁵+D⁶, g₁(D)=1+D+D²+D³+D⁴+D⁶	11

m	生成多项式
2	g₀(D)=1+D+D², g₁(D)=1+D²
3	g₀(D)=1+D+D³, g₁(D)=1+D+D²+D³
4	g₀(D)=1+D³+D⁴, g₁(D)=1+D+D²+D⁴
5	g₀(D)=1+D²+D⁴+D⁵, g₁(D)=1+D+D²+D³+D⁵
6	g₀(D)=1+D²+D³+D⁵+D⁶, g₁(D)=1+D+D²+D³+D⁴+D⁶

码率	生成多项式
1/2	g₀(D)=1+D+D²+D³+D⁴+D⁶, g₁(D)=1+D²+D³+D⁵+D⁶
1/3	g₀(D)=1+D+D²+D³+D⁵+D⁶, g₁(D)=1+D+D³+D⁴+D⁶, g₂(D)=1+D²+D³+D⁴+D⁵
1/4	g₀(D)=1+D+D³+D⁴+D⁵+D⁶, g₁(D)=1+D²+D³+D⁴+D⁶, g₂(D)=1+D+D³+D⁴+D⁵, g₃(D)=1+D³+D⁵+D⁶

算法	加法复杂度	乘法复杂度
本文算法	O(nmτμ)	O(nm²τμ)
LS算法^[22]	O(n²m²τμ)	O(n²m²τμ)
MC算法^[23]	O(nmτμ)	O(nm²τμ)
WHT算法^[9]	O(N²)=O(2^2l)	－

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基于共轭梯度求解代价函数的卷积码参数识别算法

Parameter estimation algorithm of convolutional codes with solving cost function based on conjugate gradient

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