基于BIBD的多进制准循环LDPC码构造

Construction of nonbinary quasi-cyclic LDPC codes based on balanced incomplete block designs

随机多进制低密度奇偶校验码(low-density parity-check,LDPC)的编码相当复杂,而具有特定结构的准循环LDPC码具有线性复杂度编码的特点。提出基于均衡不完全区组设计(balanced incomplete block design,BIBD)的具有高性能且能有效编码的多进制准循环LDPC码代数构造方法,构造出的多进制校验矩阵非零值的位置和数值分别建立于2个不同的域。结合BIBD和新定义的多进制位置向量进行广义二维扩展生成素数大小的多进制准循环矩阵,由此构造出的3类多进制LDPC码girth均不小于6。仿真结果表明,采用FFTQSPA对构造的LDPC码进行译码,在AWGN信道下相比于同等比特长度同等码率的RS码来说可以取得明显的编码增益。

The encoding complexity of quasi-cyclic （QC） low-density parity-check （LDPC） codes with special structure is linear while that of computer-generated random nonbinary LDPC codes is rather high. The algebraic method for constructing high performance and efficiently encodable nonbinary QC LDPC codes based on balanced incomplete block designs （BIBD） is presented. The position and the value of non -zeros are selected from two various Galois fields. A prime-size nonbinary circulant matrix is formed using generalized two dimensional dispersions considering BIBD and defined nonbinary location vector. The codes constructed by this method have girths at least 6. Experimental results show that with iterative decoding using a fast Fourier transform based sum-product algorithm, they achieve significant coding gains over reed- solomon codes of the same bit lengths and rates over the AWGN channel.