以线性分组码为子码的混合LDPC码构造

发布时间：2018-08-31 11:42

【摘要】：低密度奇偶校验(low density parity check,LDPC)码因其性能接近香农限、译码复杂度低等优点而成为一种重要的信道编码方式,其构造方法是信道编码领域的研究热点之一。在LDPC码的构造中,混合构造方法能有效生成长码,基矩阵和子码是该方法的两个重要因素。用通用的方法,如渐进边增长(progressive edge growth,PEG)算法,获得基矩阵之后,再由子码对基矩阵进行扩展。其中,子码对混合构造译码性能的影响至关重要,需要特别谨慎。考虑到短码具有较低的译码复杂度,在芸芸的分组码中发现了两种特殊的短码,即(14,8)扩展汉明码(extended Hamming code,EHC)和(7,7,3,3,1)平衡不完全区组设计(balanced incomplete block designs,BIBD)码。一方面,它们的结构中均无4环,另一方面,也是最为重要的,它们的和-积译码算法(sum-product algorithm,SPA)和最大似然译码(maximum likelihood decoding,MLD)算法具有几乎完全相同的性能,这对于译码大有裨益。基于上述基矩阵与子码,采用特定的映射规则,将EHC或BIBD码和基矩阵进行组合即得到混合LDPC码。首先,以EHC为子码得到两种码长的混合码。AWGN信道下的仿真结果表明,码长为3,920、列重为2的混合码距离香农限约2 dB,列重为3的混合码距离香农限约1.5 dB。列重为3的混合码译码性能优于列重为2的,即列重是影响译码性能的因素之一。在平坦Rayleigh衰落信道下的仿真结果表明,码长小于2,000的混合码与具有相近码参数的PEG码性能相当。此外,以PEG算法构造基矩阵的混合码平均迭代次数性能也优于Gallager算法的。然后,以BIBD码为子码构造了四种混合LDPC码。AWGN信道中的仿真结果表明,基于PEG算法的基矩阵构造的混合码距离香农限最近,约为1.3 dB。以PEG和DS为基矩阵的混合码在AWGN和平坦Rayleigh衰落信道下的仿真结果再次表明了基于PEG算法的混合码的性能优异性。此外,AWGN信道中,以EG算法构造基矩阵得到的混合码的性能则与相近参数的PEG码相当。最后,以EXIT图为工具,分析了在二进制删除信道(binary erasure channel,BEC)下,混合码的度分布对渐近性能的影响。选取了三种混合码的度分布,并观察度分布改变后渐近性能的变化,发现度分布改变后,信道容量额外损失了 0.0066、0.0043和0.0133。这表明,以EHC和BIBD码为子码的混合LDPC码,其度分布趋势是合理的。
[Abstract]:Low-density parity check (low density parity check,LDPC) codes have become an important channel coding method because of their performance close to Shannon limit and low decoding complexity. Its construction method is one of the research hotspots in the field of channel coding. In the construction of LDPC codes, the hybrid construction method can effectively generate growth codes, and the base matrix and subcode are two important factors of the method. The basis matrix is obtained by using a general method, such as the asymptotic edge-growing (progressive edge growth,PEG algorithm, and then the base matrix is extended by subcodes. Among them, the influence of subcode on the performance of hybrid construction decoding is very important, so we need to be very careful. Considering the low decoding complexity of short codes, two special short codes are found in the block codes, namely (14 / 8) extended hamming code (extended Hamming code,EHC) and (7 / 7 / 3 / 3 / 3 / 1) balanced incomplete block design (balanced incomplete block designs,BIBD) code. On the one hand, there are no four rings in their structures, on the other hand, they are the most important. Their sum-product decoding algorithm (sum-product algorithm,SPA) and maximum likelihood decoding (maximum likelihood decoding,MLD) algorithm have almost the same performance, which is beneficial for decoding. Based on the base matrix and subcode, the hybrid LDPC code is obtained by combining the EHC or BIBD code with the base matrix using specific mapping rules. First of all, the simulation results of two hybrid codes with different code lengths. AWGN channel using EHC as subcodes show that the range of mixed codes with code length of 3n920 and column weight of 2 is about 2 dB, and the range of mixed code is about 1.5 dB. with Shannon limit of about 2 dB, and column weight of 3. The decoding performance of mixed code with column weight 3 is better than that of column weight 2, that is, column weight is one of the factors affecting decoding performance. The simulation results in flat Rayleigh fading channel show that the performance of hybrid codes with code length less than 2000 is comparable to that of PEG codes with similar code parameters. In addition, the average number of iterations of hybrid codes constructed by PEG algorithm is better than that of Gallager algorithm. Then, four kinds of hybrid LDPC codes. AWGN channel are constructed using BIBD codes as subcodes. The simulation results show that the base matrix based on PEG algorithm has the nearest Shannon limit, which is about 1.3 dB.. The simulation results of hybrid codes based on PEG and DS in AWGN and flat Rayleigh fading channels show that the hybrid codes based on PEG algorithm have excellent performance. In addition, in the AWGN channel, the performance of the hybrid codes constructed by the EG algorithm is comparable to that of the PEG codes with similar parameters. Finally, the influence of the degree distribution of the mixed codes on the asymptotic performance under the binary delete channel (binary erasure channel,BEC is analyzed by using the EXIT diagram. The degree distributions of three kinds of hybrid codes are selected, and the asymptotic performance changes after the change of degree distribution are observed. It is found that after the change of degree distribution, the additional loss of channel capacity is 0.0066, 0. 0043 and 0. 0133. This shows that the degree distribution trend of hybrid LDPC codes with EHC and BIBD codes as subcodes is reasonable.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.22

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