【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、譯碼復雜度低等優(yōu)點而成為一種重要的信道編碼方式,其構造方法是信道編碼領域的研究熱點之一。在LDPC碼的構造中,混合構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行擴展。其中,子碼對混合構造譯碼性能的影響至關重要,需要特別謹慎�？紤]到短碼具有較低的譯碼復雜度,在蕓蕓的分組碼中發(fā)現(xiàn)了兩種特殊的短碼,即(14,8)擴展?jié)h明碼(extended Hamming code,EHC)和(7,7,3,3,1)平衡不完全區(qū)組設計(balanced incomplete block designs,BIBD)碼。一方面,它們的結構中均無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。基于上述基矩陣與子碼,采用特定的映射規(guī)則,將EHC或BIBD碼和基矩陣進行組合即得到混合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。此外,以PEG算法構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碼為子碼構造了四種混合LDPC碼。AWGN信道中的仿真結果表明,基于PEG算法的基矩陣構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。最后,以EXIT圖為工具,分析了在二進制刪除信道(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.
【學位授予單位】：北京交通大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN911.22

【參考文獻】

相關期刊論文 前9條

1 李文雯;劉志偉;張炎林;劉麗麗;王齊;;基于環(huán)結構分析的準循環(huán)LDPC碼構造[J];電視技術;2016年11期

2 陳為剛;曹艷;夏曉曉;楊晉生;;面向衛(wèi)星導航系統(tǒng)的多進制LDPC碼的構造[J];計算機應用與軟件;2016年04期

3 李沖;韓益亮;;基于QC-LDPC碼的雙公鑰Niederreiter密碼方案[J];計算機應用研究;2016年11期

4 陳正康;張會生;李立欣;朱夢;;LDPC碼最小和譯碼算法的整數(shù)量化[J];系統(tǒng)工程與電子技術;2015年10期

5 ZHANG Lijun;LI Bing;CHENG Leelung;;Construction of Type-II QC LDPC Codes Based on Perfect Cyclic Difference Set[J];Chinese Journal of Electronics;2015年01期

6 吳軍;廖鑫;張小紅;;一種改進的LDPC碼低復雜度最小和算法[J];電視技術;2015年01期

7 ZHANG LiJun;LI Bing;CHENG LeeLung;;Constructions of QC LDPC codes based on integer sequences[J];Science China(Information Sciences);2014年06期

8 柳克會;李明杰;;LDPC碼在存儲及無線通信系統(tǒng)中的應用研究[J];電子技術與軟件工程;2014年04期

9 楊民;張文彥;鐘杰;吳杰;;準循環(huán)多進制LDPC碼構造[J];電子與信息學報;2013年02期

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