【摘要】：低密度奇偶校驗(low density parity check,LDPC)碼因其性能接近香農(nóng)限、譯碼復(fù)雜度低等優(yōu)點而成為一種重要的信道編碼方式,其構(gòu)造方法是信道編碼領(lǐng)域的研究熱點之一。在LDPC碼的構(gòu)造中,混合構(gòu)造方法能有效生成長碼,基矩陣和子碼是該方法的兩個重要因素。用通用的方法,如漸進(jìn)邊增長(progressive edge growth,PEG)算法,獲得基矩陣之后,再由子碼對基矩陣進(jìn)行擴(kuò)展。其中,子碼對混合構(gòu)造譯碼性能的影響至關(guān)重要,需要特別謹(jǐn)慎�？紤]到短碼具有較低的譯碼復(fù)雜度,在蕓蕓的分組碼中發(fā)現(xiàn)了兩種特殊的短碼,即(14,8)擴(kuò)展?jié)h明碼(extended Hamming code,EHC)和(7,7,3,3,1)平衡不完全區(qū)組設(shè)計(balanced incomplete block designs,BIBD)碼。一方面,它們的結(jié)構(gòu)中均無4環(huán),另一方面,也是最為重要的,它們的和-積譯碼算法(sum-product algorithm,SPA)和最大似然譯碼(maximum likelihood decoding,MLD)算法具有幾乎完全相同的性能,這對于譯碼大有裨益�；谏鲜龌仃嚺c子碼,采用特定的映射規(guī)則,將EHC或BIBD碼和基矩陣進(jìn)行組合即得到混合LDPC碼。首先,以EHC為子碼得到兩種碼長的混合碼。AWGN信道下的仿真結(jié)果表明,碼長為3,920、列重為2的混合碼距離香農(nóng)限約2 dB,列重為3的混合碼距離香農(nóng)限約1.5 dB。列重為3的混合碼譯碼性能優(yōu)于列重為2的,即列重是影響譯碼性能的因素之一。在平坦Rayleigh衰落信道下的仿真結(jié)果表明,碼長小于2,000的混合碼與具有相近碼參數(shù)的PEG碼性能相當(dāng)。此外,以PEG算法構(gòu)造基矩陣的混合碼平均迭代次數(shù)性能也優(yōu)于Gallager算法的。然后,以BIBD碼為子碼構(gòu)造了四種混合LDPC碼。AWGN信道中的仿真結(jié)果表明,基于PEG算法的基矩陣構(gòu)造的混合碼距離香農(nóng)限最近,約為1.3 dB。以PEG和DS為基矩陣的混合碼在AWGN和平坦Rayleigh衰落信道下的仿真結(jié)果再次表明了基于PEG算法的混合碼的性能優(yōu)異性。此外,AWGN信道中,以EG算法構(gòu)造基矩陣得到的混合碼的性能則與相近參數(shù)的PEG碼相當(dāng)。最后,以EXIT圖為工具,分析了在二進(jìn)制刪除信道(binary erasure channel,BEC)下,混合碼的度分布對漸近性能的影響。選取了三種混合碼的度分布,并觀察度分布改變后漸近性能的變化,發(fā)現(xiàn)度分布改變后,信道容量額外損失了 0.0066、0.0043和0.0133。這表明,以EHC和BIBD碼為子碼的混合LDPC碼,其度分布趨勢是合理的。
[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.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN911.22

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