低复杂度多进制LDPC码的设计

发布时间：2018-09-18 08:23

【摘要】：信道编码是保证数字通信系统中服务质量和可靠传输的一种有效方式。而LDPC(Low Density Parity Check,低密度校验)码则是近年来信道编码研究领域的一个研究热点。LDPC码具有优异的译码性能(可以逼近香农容量限),同时还具有可实现高速编译码的潜力。相对于二进制LDPC码,多进制LDPC码可以实现更加稀疏的表示和更优秀的译码表现(特别是当码长不是很长时),但其译码(计算)复杂度也高于二进制LDPC码。低复杂度多进制LDPC码的设计是LDPC码研究中的关键问题之一。本文从多进制LDPC码的度分布、二进制表示以及译码器的设计出发,提出了多种降低多进制LDPC码译码复杂度的方法,以实现不同的目的和适应不同的应用。本文的主要研究工作分为以下三个方面:1.EXIT(Extrinsic Information Transfer,外部信息转换)图是LDPC译码器迭代译码过程的模拟(可视化分析)工具。每一个LDPC码都有一组度分布和与之对应的EXIT图。针对EXIT图的不同定义方式,本文分别利用Gallager公式(基于消息错误概率的EXIT图)和外信息函数的级联(基于互信息的EXIT图)设计了两种多进制LDPC码的复杂度优化方法。两种方法均是通过优化多进制LDPC码的度分布,以达到降低译码器中迭代次数为目的,提高了译码器的译码收敛速度,降低了译码器的译码复杂度。实验仿真表明,通过优化多进制LDPC码的度分布,译码复杂度可以大幅度降低。2.本文利用有限域上元素的二进制向量和矩阵表示,引入了多进制LDPC码的二进制对等码,并利用二进制对等LDPC码设计了基于系数选择的低复杂度协作译码算法。这类算法将两个子译码过程结合起来,两者协作共同更新译码消息。如果协作译码器是由二进制子译码器和多进制子译码器构成,那么通过优化度分布和译码器参数,多进制LDPC码的译码复杂度可以得到进一步的降低。本文还通过引入矩阵求逆操作,设计了一种二进制合并译码器,这种译码器可以用于替代多进制子译码器,从而得到一种有效的辅助替代协作译码方法。另外,通过协作译码的方式,可以提高译码的自由度,这使得协作译码器不但可以应对随机错误还可以更好的应对连续错误(相对于二进制译码器)。而且,通过这种方式构造的协作译码器,相对于其子译码器,可以获得更低(针对非阈值优化的LDPC码,如某些规则码或某些结构化构造的LDPC码等)或者相近/相等的性能阈值(针对阈值优化的LDPC码)。3.针对多进制LDPC码,本文提出了一种广义的二进制表示,相对于二进制对等LDPC码,这种二进制表示可以更加自由的优化围长和度分布(因此,其适用范围也更广)。如果将广义二进制表示再加以推广,其还可以用来设计性能优化的二进制LDPC码。针对这种表示,本文设计了一种(二进制低复杂度的)混合并行译码器。通过这种译码方式,广义二进制表示的译码性能可以非常逼近其(性能优化的)多进制母码的译码性能。在二进制输入高斯信道上,混合并行译码器可以成为多进制LDPC码的一种有效辅助替代译码方案。
[Abstract]:Channel coding is an effective way to ensure the quality of service and reliable transmission in digital communication systems. LDPC (Low Density Parity Check) code is a research hotspot in the field of channel coding in recent years. Compared with binary LDPC codes, multiary LDPC codes can achieve more sparse representation and better decoding performance (especially when the code length is not very long), but their decoding complexity is also higher than binary LDPC codes. The design of low complexity multiary LDPC codes is one of the key issues in LDPC codes research. Starting from the design of degree distribution, binary representation and decoder of multiary LDPC codes, this paper proposes several methods to reduce the decoding complexity of multiary LDPC codes for different purposes and applications. Each LDPC code has a set of degree distributions and corresponding EXIT diagrams. According to different definitions of EXIT diagrams, Gallager formula (EXIT diagrams based on message error probability) and cascade of external information functions (EXIT diagrams based on mutual information) are used to design two kinds of LDPC codes. In order to reduce the number of iterations in the decoder, both methods improve the decoding convergence speed and reduce the decoding complexity of the decoder. The simulation results show that the decoding complexity is reduced by optimizing the degree distribution of the multiary LDPC code. In this paper, the binary vector and matrix representation of elements over a finite field are used to introduce binary LDPC codes, and a low complexity cooperative decoding algorithm based on coefficient selection is designed by using binary LDPC codes. If the cooperative decoder is composed of binary sub-decoder and multiary sub-decoder, the decoding complexity of multiary LDPC codes can be further reduced by optimizing degree distribution and decoder parameters. The decoder can be used to replace the multiary sub-decoder to obtain an effective auxiliary alternative cooperative decoding method. In addition, the degree of freedom of decoding can be improved by the cooperative decoding method, which makes the cooperative decoder not only cope with random errors but also cope with continuous errors better than the binary decoder. A cooperative decoder constructed in this way can obtain lower performance thresholds (for non-threshold-optimized LDPC codes, such as some regular codes or some structured LDPC codes) or similar/equal performance thresholds (for threshold-optimized LDPC codes) than its sub-decoders. 3. For multi-ary LDPC codes, a generalized binary is proposed. This binary representation can optimize the girth and degree distribution more freely than binary peer-to-peer LDPC codes (therefore, it has a wider range of applications). If generalized binary representation is extended, it can also be used to design binary LDPC codes for performance optimization. Hybrid parallel decoder with low complexity. By this decoding method, the decoding performance of generalized binary representation can be very close to that of its (performance-optimized) multiary master code. On binary input Gaussian channel, the hybrid parallel decoder can be an effective auxiliary alternative decoding scheme for multiary LDPC codes.
【学位授予单位】：上海交通大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.22

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