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BIBD循环置换矩阵的多进制LDPC码构造
刘冰,陶伟,窦高奇,高俊
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(解放军91469部队，北京 100841;海军工程大学电子工程学院，武汉 430033;海军装备研究院，北京 100161)

摘要:

提出了基于均衡不完全区组设计（Balanced Incomplete Block Design，BIBD）的多进制准循环LDPC（LowDensity ParityCheck）码代数构造方法。在该构造方法中提出了广义多进制位置向量的概念，并根据广义多进制位置向量和BIBD法对指数矩阵进行广义二维扩展，构造出具有循环置换子矩阵的多进制校验矩阵，由此得到girth不小于6的多进制LDPC码。仿真结果表明，采用FFT-QSPA（基于快速傅里叶变换的多进制和积算法）对构造出的LDPC码进行译码，在AWGN信道下相比于同参数的RS码来说可以取得明显的编码增益，并且优于多进制Mackay码。

关键词: 多进制低密度奇偶校验码准循环均衡不完全区组广义多进制位置向量二维扩展

DOI：

基金项目:国家自然科学基金资助项目(61004123)；广西自然科学基金资助

Construction of nonbinary LDPC codes based on BIBD circulant permutation matrices

LIU Bing,TAO Wei,DOU Gao-qi,GAO Jun

(Unit 91469 of PLA,Beijing 100841,China;College of Electronic Engineering, Naval University of Engineering,Wuhan 430 033,China;Naval Academy of Armament,Beijing 10 0161,China)

Abstract:

The algebraic method for constructing nonbinary quasicyclic(QC) lowdensity p aritycheck(LDPC) codes based on balanced incomplete block designs(BIBD) is presented. The generalized nonbinary location vector is proposed on construc tions. A nonbinary matrix, which consists of nonbinary circulant submatrices, is formed by generalized twodimensional matrix dispersion considering the genera l ized nonbinary location vector and BIBD method. The codes constructed by this me thod have girths at least 6. Experimental results show that signifi cant coding gains are achieved over ReedSolomon codes of the same parameters u nder the Additive White Gaussian Noise(AWGN) channel with iterative decoding Fas t Fourier Transform based q-ary Sum-Product Algorithm(FFTQSPA). And a good pe rformance is also achieved over nonbinary Mackay LDPC codes with almost the same conditions.

Key words: nonbinary low density parity check(LDPC) codes quasi cyclic balance d incomplete block design generalized nonbinary location vector two dimension al dispersion