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

Abstract

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

CLC Number:

TN911.7

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.

Figures/Tables 11

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References 30

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

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