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工业互联网低功耗数据链算法设计综述——联合信源信道编码设计的必要性、现实与前景
王 琳① 刘三亚*① 陈 辰② 陈启望③
①(厦门大学信息学院 厦门 361005)
②(华侨大学信息科学与工程学院 厦门 361021)
③(宁波大学信息科学与工程学院 宁波 315000)
摘 要:原模图低密度奇偶校验(P-LDPC)码已经广泛应用于各种通信系统,为了使其能够满足不同应用场景下系统对纠错性能、硬件资源损耗以及功耗等方面的要求,需要对P-LDPC码进行进一步的设计优化。该文主要从标准信道环境下基于双P-LDPC(DP-LDPC)码的联合信源信道编码(JSCC)系统的属性研究、系统设计优化以及性能表现等角度入手,对近些年出现的针对该系统环境所做的优化分析工作进行了综述。表明进行的优化工作属实显著地改善了系统性能,为面向工业互联网(II)的LDPC码的研究工作提供些许思路。最后,该文对未来的研究工作进行了展望,为感兴趣的研究学者提供参考以继续推进。
关键词:工业互联网;低功耗;联合信源信道编码;原模图低密度奇偶校验码
1 引言
工业互联网(Industrial Internet, II)是各种工业设备终端的联网化,包含各种各样的应用场景,比如制造业、零售业、通用工业和运输业等领域。II应用需要考虑许多因素,例如节点成本、网络成本、电池寿命、数据传输速率(吞吐率)、延迟、移动性,网络覆盖范围以及部署类型等。无线通信技术是II传输的基础,不同的应用场景需要不同的无线通信模块,这些应用领域的增长引领了无线通信模块的主要增长。随着II应用的快速发展,无线通信网络需要支持数以亿计的无线设备[1],对无线通信技术提出了更高的要求,通信系统设计面临更加严峻的挑战。面临这个挑战性问题,联合信源信道编码(Joint Source-Channel Coding, JSCC)已经成为潜在的解决方案之一[2–8]。与传统的信源信道分离级联编译系统相比,JSCC可以更加有效地利用信源或者信道特征提高整体系统的性能,且需要的码长更短,因此更适合于资源有限、延迟敏感的物联网应用。
1963年,Gallager[9]提出一类新的线性分组纠错码,称为低密度校验(Low Density Parity Check, LDPC)码,它可以用其非常稀疏的校验矩阵来表示[2,3,6,8]。80年代初,研究学者提出了它的图形化的表示方法——Tanner图[10]。90年代,MacKay等人[11]采用迭代译码算法使得LDPC码具有逼近香农限的优异性能,从而引起了大量学者的广泛关注,掀起了信道编码理论界的研究热潮[12–22]。值得注意的还有Zyablov等[23]和Margulis[24]关于LDPC的研究工作,由于缺乏结构性,传统的L D P C码具有较高的编码和解码复杂度,在一定程度上限制了它们在通信系统中的应用。为了解决这个问题,学术界付出了巨大的努力寻找方法以设计出更高效的LDPC码[12,16,20,21,25–37]。文献[33,38–40]对LDPC码的迭代译码算法进行了改进,以获得更好的译码性能。近二十年,学者们研究了各种修正渐进分析工具,其中以高效、精确而突出的有密度进化(Density Evolution, DE)[5,31]、外部信息转移(EXtrinsic Information Transfer, EXIT)[26–28]和渐进重量分布(Asymptotic Weight Distribution,AWD)[41,42]。DE和EXIT作为两种最流行的优化LDPC码的辅助工具,在计算迭代译码阈值以及预测低信噪比区域的渐近误差性能尤为适用。AWD则适用于预测最小(汉明)距离以及高信噪比区域的渐近误差性能。另外,DE和EXIT与码型和信道类型均有关,而AWD只受码型影响。据之前的研究结果可知,LDPC码的要获得靠近容量限的译码阈值通常受到最小距离的影响,这就意味着,对于LDPC码来说,不管在低信噪比还是在高信噪比区,要获得出色的纠错性能还是非常困难的,这些理论的进步极大地推动了LDPC码的码型构造和译码设计。LDPC码在现代通信系统中发挥了重要作用,越来越受到学术界和工业界的关注[26–47]。如今,它已经广泛应用于各种通信和数据存储系统,例如深空通信系统[48,49]、无线通信系统[50]、光通信系统[51]、水声通信系统[52]和磁记录系统[53,54],成为信道编码领域的研究热点。LDPC码的综述类的文章可参考文献[22,35,55–58]。
早期多数靠近容量限的LDPC码是非规则的,非规则结构导致它们2次编码的复杂。为了克服这个缺点,Richardson等人[22,59]提出了一类新的LDPC码,即多边类型(Multi-Edge-Type, MET)LDPC码。2003年,Thorpe[60]提出了一种基于模板的新型结构的LDPC码,称为原模图LDPC(Protograph LDPC, P-LDPC)码,属于MET-LDPC码的子类。原模图是具有相对较少节点的Tanner图,可用于构造任意大小的LDPC码,并且可以用于预测该LDPC码的性能。与传统的LDPC码相比,P-LDPC码具有更好的纠错性能和较低的复杂性[61–63],可实现线性编码以及快速译码[46,64–68],并且易于硬件实现[62,63]。文献[37,69]与文献[56–58]分别提出了原模图EXIT(Protograph EXIT, PEXIT)算法和渐进重量计数器以便于P-LDPC的分析与设计,构造出具有接近容量限和最小线性距离属性的P-LDPC码。喷气推进实验室(Jet Propulsion Laboratory,JPL)提出的累加-重复-3-累加(Accumulate-Repeat-3-Accumulate, AR3A)码和累加-重复-4-判决-累加(Accumulate-Repeat-by-4-Jagged-Accumulate,AR4JA)码即为两种经典的P-LPCD码[61–63]。
与分离级联的信源信道编码系统相比,通过利用信源压缩后的冗余信息在译码端进行联合译码的JSCC系统可以获得显著的编码增益。2010年,普林斯顿大学的Vincent Poor团队提出在编码端使用两个LDPC码(非结构化的规则LDPC码和非规则LDPC码)分别用做信源压缩和信道纠错,在译码端采用联合信源信道(Joint Source-Channel,JSC)译码器,该系统被称为双LDPC(Double LDPC,D-LDPC)码的JSCC系统[70]。双P-LDPC (Double P-LDPC, DP-LDPC)码的JSCC系统使用结构简单、码率扩展性好的P-LDPC码代替传统的LDPC码,它是基于D-LDPC码JSCC系统的改进。研究表明,基于DP-LDPC码的JSCC系统相比基于D-LDPC码的JSCC系统可以获得更好的性能[71]。的仿真结果发现,满足无失真信源编码条件的前提下,基于DP-LDPC码的JSCC系统处理低熵值的信源性能更好,且信源熵值是影响系统性能的主导性因素,而且,传输较低熵值的信源时,能够极大地降低译码所需要的迭代次数以及时延。此外,对于熵值大于信源编码码率的信源,在译码端引入适当的边信息,依然可以实现该信源在系统中的可靠传输,而且在高信噪比区,边信息的引入可以显著降低传输较低熵值信源时译码的错误地板。
图 3 不同熵值、不同传输码率时基于DP-LDPC码的
JSCC系统BER性能
3.2 基于DP-LDPC码的JSCC系统可行性研究
图像的低频分量熵值较高,即信息量大,不适合进行数据压缩,也不适合用DP-LDPC码进行编码。因为只有熵足够低才能用DP-LDPC码进行编码,而且熵值越低,系统BER性能越好。而图像的高频分量熵值很低,几乎为0,即它们信息量低,冗余较多,因此,应该对其进行适当压缩以提高系统的效率。文献[82]采用基于DP-LDPC码的JSCC系统的编码方式对高频部分进行编码,不仅能够对高频的数据进行适当地压缩,而且能够取得很好的效果。图像高频部分使用基于DP-LDPC的JSCC系统进行处理的不等保护传输系统框图如图4所示。
文献[82]提出两种不同的方案:第1种方案将采用不同的码率来构造UEP策略,记为UEP-2;第2种方案,将通过构造DP-LDPC码,使其具有UEP性能,然后应用于图像传输,记为UEP-3。为了更清楚直观地比较不同的UEP方案的优劣,文献[82]还跟文献[85]中的UEP方案(记为UEP-1)进行了对比。文献[82]采用的图像为JPEG格式的医学X射线图像,先对其进行8×8分块离散余弦变换(DCT),之后再进行量化,把量化后的系数转换为二进制流,并在系统中进行分帧传输。图像进行DCT变换之后,可分为低频分量(含直流分量)和高频分量。低频分量表示图像中最重要的信息,对噪声最敏感,而高频分量描述的是图像的细节信息,属于图像的次要信息,对噪声较不敏感。因此,如前所述,用LDPC码对低频分量进行信道编码,用 JSCC 编码方式对高频部分进行编码。
图5中所示为SNR=0 dB时的恢复图像。可以直观地看到SNR=0 dB时,由UEP-3保护恢复出的3张图像基本得到完全恢复,没有任何噪点的存在,而由UEP-1和UEP-2方案保护恢复出来的3张图像显然仍然存在噪点。
综上所述,文献[82]提出的两种UEP方案中,都对图像进行了DCT变换,并且把系数分为两个等级:重要信息和次要信息。不同的是,两个码率的UEP方案UEP-2中,将两个不同等级的系数分离,分别进行编码,而在同一码率的UEP方案UEP-3中,并没有将不同等级的系数分离,它们将进行统一的编码。这也表明,基于同一码率的UEP方案比基于不同码率的UEP方案更加简洁,硬件复杂度更低。图13所示,在仿真码长L=3200的情况下,与(R4JA, AR4JA) 进行对比,提出的码型在p(1)=0.04与p (1)=0.06下分别有1 dB与0.7 dB的性能增益。
图 4 图像高频部分使用基于DP-LDPC的JSCC系统进行处理的不等保护传输系统框图
图 12 (R4JA, AR4JA)与针对渐近无限长码设计的码型BER性能对比
4.2.2 以度为2的变量节点为导向的联合优化
通过研究已知度为2的变量节点对系统的影响较大,在基于DP-LDPC码的JSCC系统中含有更多的度为2的变量节点时,在瀑布区和地板区的性能可能会有明显的改善。将DP-LDPC码作为一个整体,可以从整体的角度去设计,特别是度为2的变量节点的分配问题。
文献[81]采用差分进化算法搜索最优的 BJ, 其中,消耗函数为JPEXIT算法计算的联合译码阈值(Eb/N0)th 。通过对优化的B J观察,针对基于DPLDPC码的JSCC系统中整合角度设计 BJ的步骤可以归纳为:
(1) 根据p (1), m s,ns, m c,nc确定度为2的变量节点的数量,然后确定预编码结构和度较高的变量节点数量;
(2) 确定度为2变量节点的分配方案( os,oc),如有需要,对这些度为2的变量节点,搜索最优的排列方式;
图 13 (R4JA, AR4JA) 与针对中短长码设计的码型BER性能对比 (L=3200)
(3) 为了减少搜索空间和复杂度,初始化预编码结构和度为3的结构;
(4) 给出其余元素的约束条件,然后利用差分算法以译码阈值为消耗函数搜索最优的B J。
如图14所示,与, B和对比,分别在 1×10−5 , 1 ×10−6 和1 ×10−7的BER水平处有0.8 dB, 0.4 dB以及0.1 dB的编码增益。如图15所示,随着度为2变量节点的数量增加,,和的BER水平逐渐下降,它们相对于在1 ×10−7的BER水平处分别有0.30 dB, 0.40 dB和0.45 dB的编码增益。从编码复杂度的角度来讲,尽管信道P-LDPC码随着度为2的变量节点的增加,其边链接在减少,但是信源P-LDPC码的边链接是在增加,因此,整体的边链接数量基本保持不变,即整体的算法复杂度保持不变。在p(1)=0.04的情况下,整体的复杂度略有降低。
图 14 不同B J 在统计概率为p (1)=0.01时的BER性能对比
图 15 不同B J 在统计概率为p (1)=0.04时的BER性能对比
总之,文献[81]针对尺寸匹配的 BJ提出了一种整体的分配设计方案。从整体的角度出发,考虑到度为2的变量节点在编码设计中的重要性,确定了BJ满 足线性最小距离前提下度为2变量节点的最大数量。并且通过分析得出了度为2变量节点在信道P-LDPC码和信源P-LDPC码的分配方案:即尽可能多地分配度为2变量节点给信道P-LDPC码,可以获得更好的瀑布区性能。最后,给出了一般化的整体角度设计的步骤。仿真结果表明改进的 BJ具有更好的性能,即分配度为2变量节点的最优方案能够使得系统性能得到改善,并且含有最大数量的度为2变量节点的B J的性能最优。
5 结束语
随着信息时代的爆炸式发展,面对II中巨大的通信传输能耗,P-LDPC码在各种通信系统中已经显示出它们的优势,成为低功耗、低成本JSCC系统候选者。如何在JSCC方案中找到最佳码型仍然是一个值得继续探究的问题。本文针对P-LDPC码及其在各种改进系统中进行的相关研究分析以及部分设计优化工作做了总结归纳,这些设计理念也将启发其他类型码(例如猛禽代码[86]和极性代码[87])的分析与设计优化,以更加适用于各种各样的现代通信系统。
该研究领域已经引起较多学者的关注,未来尚有许多问题需要解决:
(1) 基于全部要素的联合基础矩阵优化,以同时提高瀑布区和地板区的性能;
(2) 从全局的角度出发,应用环境(包括信源统计和信道状态)与系统设计参数(包括信源码率和信道码率)之间的匹配标准有待进一步研究;
(3) 整体联合基础矩阵设计或者系统译码算法[88–90]结构优化有待研究,以降低系统复杂性更加易于硬件实现;
(4) 针对不同信源类型、不同信道环境以及有损信源编码系统等等的探究工作也尚待展开。
因此,未来需要付出更多的努力致力于该低功耗、低成本系统的进一步研究。
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Overview of Low Power Data Link Algorithms Design for Industrial Internet——Necessity, Reality and Prospect of JSCC Design
WANG Lin① LIU Sanya① CHEN Chen② CHEN Qiwang③
①(College of Information, Xiamen University, Xiamen 361005, China)
②(College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China)
③(College of Information Science and Engineering, Ningbo University, Ningbo 315000, China)
Abstract: Protograph Low Density Parity Check (P-LDPC) code is widely used in various communication systems. In order to meet the requirements of error correction performance, hardware resource loss and power consumption in different application scenarios, further design optimization of P-LDPC codes is needed. This paper focuses on the properties of Joint Source-Channel Coding (JSCC) system based on Double P-LDPC (DPLDPC) codes in standard channel environment, the optimization of code design and performance behavior, etc.The design and optimization for the system environment in recent years is summarized. It shows that the design optimization work has significantly improved the system performance, which provides some ideas for the research of Industrial Internet (II)-oriented LDPC code. Finally, the future research work is discussed for the reference and promotion of interested scholars.
Key words: Industrial Internet (II); Low power consumption; Joint Source-Channel Coding (JSCC); Protograph Low Density Parity Check (P-LDPC) code
中图分类号:TN911.22
文献标识码:A
文章编号:1009-5896(2020)01-0249-14
DOI: 10.11999/JEIT190762
收稿日期:2019-10-08;改回日期:2019-11-16;网络出版:2019-11-25
*通信作者: 刘三亚 sanyaliu1106@gmail.com
基金项目:国家自然科学基金(61671395)
Foundation Item: The National Natural Science Foundation of China (61671395)
王 琳:男,1963年生,教授,研究方向为信息论与宽带无线通信理论.
刘三亚:女,1988年生,博士生,研究方向为联合信源信道编码.
陈 辰:女,1990年生,讲师,研究方向为联合信源信道编码.
陈启望:男,1990年生,讲师,研究方向为联合信源信道编码.
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