AWGN信道条件下基于Raptor Codes的传输与功率控制技术
|
摘要
随着认知无线电技术的飞速发展,可靠又高效的数据传输技术得到了越来越多的关注。由于很多时候通信环境相当复杂,难以准确地预知信道状态信息,无法自适应地选择合适的码率进行数据传输。无速率码(Rateless Codes)为我们提供了一种新的解决方法,它具有自适应链路适配特性,在发送端无须设置固定码率,只是以某种度分布源源不断地产生编码包并发送,且传输过程中发送端无须接收端的反馈,是一种高效、可靠的数据传输方式。本文针对适合于AWGN信道下的Rateless Codes——Raptor Codes展开研究,为AWGN信道下的Rateless Codes的研究作出了一定的贡献。
本文首先介绍了LDPC(Low Density Parity Check)码的一些基本概念,包括Tanner图、度分布、PEG(progressive edge growth)算法,这些对于Raptor Codes也是适用的。接着针对Raptor Codes现有度分布的不足,提出了更加适合于中短码长的Raptor Codes的度分布,通过仿真证明了新的度分布可以显著提高码的性能,并解决了原有度分布差错平台的问题。然后在改进的度分布的基础上,对Raptor Codes的内码LT Codes进行PEG构图,包括独立地进行PEG构图和结合外码LDPC码进行PEG构图两种方法,从而扩大了Tanner图中的环路,使得Raptor Codes的性能得到进一步提高。
本文接下去转入了在发送端对Raptor Codes进行功率控制的研究,通过仿真证明了发送端在总能量给定的前提下,通过减小发送功率、增长码长可以使性能得到显著提高,并给出了理论依据。然后将固定速率的LDPC码与Raptor Codes进行对比,发现由于LDPC码的度分布无法如Raptor Codes一样适用于任意码率,因此当码率随着码长的增长降低到一定程度后,性能即发生恶化。
本文最后给出了纠正Raptor Codes错误帧的几种方法。它们的基本思想都是根据某次迭代后的后验概率获得一小部分预编码包或是编码包,对它们进行初始后验概率的调整,然后开始新一轮再迭代译码。为了增大纠错成功的概率,需要通过多轮再迭代译码。对于仍然无法纠正的错误帧,本文提出了一种新的硬判决方法,可以在统计意义上减小错误概率
With the rapid development of cognitive technology, more and more attention has been paid to the reliable and efficient data transmission technology. As communication environment is complex in many cases, it is difficult to pre-know the exact channel state information. Rateless Codes provide us a new method to solve the problem, as a kind of efficient and reliable way for data transmission, they attribute the character of automatic rate adaption, and don't require feedback during the transmission,each symbol is generated independently from some distribution. This article is based on a kind of Rateless Codes over AWGN channel called Raptor Codes, and gives some contributions to Rateless Codes over AWGN channel.
Firstly, the basic concept of LDPC Codes is introduced, including Tanner graph,degree distribution,PEG alogrithm, which are also appropriate to Raptor Codes. Then considering the shortage of the existing degree distribution, we proposed a new distribution for moderate length Raptor Codes, our simulation showed that the new degree distribution could improve the performance apparently, also it could eliminate the error floor of Raptor Codes. At last,we use PEG algorithm to construct LT Tanner graph based on the new distribution, including PEG LT constructed independently and PEG LT constructed with LDPC Codes, these two methods could enlarge the cycles in Tanner graph, thereby the performance of Raptor Codes could be improved.
Thereafter, we investigated power control of Raptor Codes at the transmitter, our result showed that when the whole energy is equal at the transmitter,the performance of Raptor Codes could be improved clearly via reducing transmission power and increasing code length,also we gave theoretical basis.Then we compared the performance of fixed-rate LDPC Codes with Raptor Codes,we got as the distribution of LDPC Codes can't adapt to arbitrary rate, so when the rate decreased together with the code length increased, the performance of LDPC Codes went bad.
Finally.some methods of correcting error frame are investigated.The basic idea is to get posterior probability of a small part of information symbols after a certain iteration,then change the initial probability of those information symbols.and start a new round of BP decoding. In order to increase the probability of correcting the error frame,we should have many rounds of BP decoding. If the error frame still can't be corrected, we give a new hard decision method, and it can reduce the error probability statistically.
本文首先介绍了LDPC(Low Density Parity Check)码的一些基本概念,包括Tanner图、度分布、PEG(progressive edge growth)算法,这些对于Raptor Codes也是适用的。接着针对Raptor Codes现有度分布的不足,提出了更加适合于中短码长的Raptor Codes的度分布,通过仿真证明了新的度分布可以显著提高码的性能,并解决了原有度分布差错平台的问题。然后在改进的度分布的基础上,对Raptor Codes的内码LT Codes进行PEG构图,包括独立地进行PEG构图和结合外码LDPC码进行PEG构图两种方法,从而扩大了Tanner图中的环路,使得Raptor Codes的性能得到进一步提高。
本文接下去转入了在发送端对Raptor Codes进行功率控制的研究,通过仿真证明了发送端在总能量给定的前提下,通过减小发送功率、增长码长可以使性能得到显著提高,并给出了理论依据。然后将固定速率的LDPC码与Raptor Codes进行对比,发现由于LDPC码的度分布无法如Raptor Codes一样适用于任意码率,因此当码率随着码长的增长降低到一定程度后,性能即发生恶化。
本文最后给出了纠正Raptor Codes错误帧的几种方法。它们的基本思想都是根据某次迭代后的后验概率获得一小部分预编码包或是编码包,对它们进行初始后验概率的调整,然后开始新一轮再迭代译码。为了增大纠错成功的概率,需要通过多轮再迭代译码。对于仍然无法纠正的错误帧,本文提出了一种新的硬判决方法,可以在统计意义上减小错误概率
With the rapid development of cognitive technology, more and more attention has been paid to the reliable and efficient data transmission technology. As communication environment is complex in many cases, it is difficult to pre-know the exact channel state information. Rateless Codes provide us a new method to solve the problem, as a kind of efficient and reliable way for data transmission, they attribute the character of automatic rate adaption, and don't require feedback during the transmission,each symbol is generated independently from some distribution. This article is based on a kind of Rateless Codes over AWGN channel called Raptor Codes, and gives some contributions to Rateless Codes over AWGN channel.
Firstly, the basic concept of LDPC Codes is introduced, including Tanner graph,degree distribution,PEG alogrithm, which are also appropriate to Raptor Codes. Then considering the shortage of the existing degree distribution, we proposed a new distribution for moderate length Raptor Codes, our simulation showed that the new degree distribution could improve the performance apparently, also it could eliminate the error floor of Raptor Codes. At last,we use PEG algorithm to construct LT Tanner graph based on the new distribution, including PEG LT constructed independently and PEG LT constructed with LDPC Codes, these two methods could enlarge the cycles in Tanner graph, thereby the performance of Raptor Codes could be improved.
Thereafter, we investigated power control of Raptor Codes at the transmitter, our result showed that when the whole energy is equal at the transmitter,the performance of Raptor Codes could be improved clearly via reducing transmission power and increasing code length,also we gave theoretical basis.Then we compared the performance of fixed-rate LDPC Codes with Raptor Codes,we got as the distribution of LDPC Codes can't adapt to arbitrary rate, so when the rate decreased together with the code length increased, the performance of LDPC Codes went bad.
Finally.some methods of correcting error frame are investigated.The basic idea is to get posterior probability of a small part of information symbols after a certain iteration,then change the initial probability of those information symbols.and start a new round of BP decoding. In order to increase the probability of correcting the error frame,we should have many rounds of BP decoding. If the error frame still can't be corrected, we give a new hard decision method, and it can reduce the error probability statistically.
引文
[1]S.Haykin."Congnitive Radio:Brain-Empowered Wireless Communication".IEEE JSAC,vol.23, no.2,February 2005.
[2]Caiying Guo, Tiankui Guo et al., "Investigation on Key Techniques and Applications of Cognitive Radio", http://www.paper.edu.cn.
[3]Ian F. Akyildiz et al., "Next generation/dynamic spectrum access/cognitive radio wireless networks:A survey"[J], in Computer Networks Journal (Elsevier), vol.50, pp.2127-2159, Sept.2006.
[4]Joseph Mitola et al., "Cognitive radio:Making software radios more personal"[C], in IEEE Personal Communications, vol.6, no.4, pp.13-18, Aug.1999.
[5]Joseph Mitola, "Cognitive radio:An integrated agent architecture for software defined radio", Doctor of Technology, Royal Institute Technology (KTH), Stockholm, Sweden,2000.
[6]Simon Haykin, "Cognitive Radio:Brain-Empowered Wireless Communications"[J], in IEEE Journal on Selected Area Communications, vol.23, no.2, pp.201-220, Feb.2005.
[7]D.Cabric,S.M.Mishra,and R.W.Brodersen."lmplementation issuses in spectrum sensing for congnitive radios".Conference on Signals,Systems,and Computers,2004.
[8]A.Raghavan,E.Gebara,E.M.Tentzeris,and J.Laskar."Analysis and Design of an Interfenrence Canceller for Collocated Radios",IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,VOL53,NO.11,NOVEMBER 2005.
[9]Jae Yeon Won,Sung Bo Shim,Yun Hee Kim,Sung Hyun Hwang,Myung Sun Song,Chang Joo Kim."An Adaptive OFDMA Platform for IEEE 802.22 Based on Congnitive Radio".APCC'06,Page(s):1-5,Aug.2006.
[10]Hui-Ping Lien,Po-An Chen,Tzi-Dar Chiueh."Design of a MIMO OFDM baseband transceiver for cognitive radio system".ISCAS 2006,Page(s):4,21-24 May 2006.
[11]Batra,A.;Lingam,S.;Balakrishnan,J.;"Multi-band OFDM:a cognitive radio for UWB ",ISCAS 2006,Page(s):4,21-24 May 2006
[12]Tao Li,Wai Ho Mow,Vincent K.N. Lau."Robust joint interference detection and decoding for OFDM-based cognitive radio systems with unknown interference".IEEE Journal on Selected Areas in Communications,Volume 25,lssue 3,Page(s):566-575,April 2007.
[13]Yamaguchi,H.;" Active interference cancellation technique for MB-OFDM congnitive radio",34th European Microwave Conference,Volume 2,Page(s):1105-1108,2004.
[14]周向炜,张朝阳,程鹏.'An interference Avoidance Scheme for OFDM Cognitive Radio Systems",ICCT'06,Page(s):1-5,Nov.2006.
[15]Chakravarthy,V.;Nunez,A.S.;Stephens,J.P.;Shqw,A.K.;Temple,M.A.,"TDCS,OFDM,and MC-CDMA:a brief tutorial",IEEE Communications Magazine,Vol.43,Issue 9,Page(s):S11-S16, Sept.2005.
[16]Chuan Han;Jun Wang;Shaoqian Li;"A Spectrum Exchange Mechanism in Cognitive Radio Contexts",PIMRC'2006,pp 2413-2417,Seattle,USA,July 914,2006.
[17]D.J.C. MacKay,"Fountain Codes",IEE Proc.-Commun.,Vol.152,No.6,pp1062-1068,December 2005.
[18]Luby,M.,"LT Codes".Proc.43rd Ann.IEEE Symp.on Foundations of Computer Science,16-19 Nobmber 2002,pp.271-282
[19]Byers,J.,Luby,M.,Mitzenmacher,M.,and Rege,A.,"A digital fountain approach to reliable distribution of bulk data".Proc.ACM SIGCOMM'98,2-4 September 1998.
[20]Shokrollahi,A.,"Raptor Codes".Technical report,Laboratoired algorithmique,Ecole Polytechnique Federale de Lausanne,Lausanne,Switzerland,2003.Available from algo.epfl.ch.
[21]J.Ha,J.Kim,and S.W.McLaughlin,"Rate-compatible puncturing of low-density parity-check codes,"IEEE Trans.lnf.Theory,vol.50,no.11,pp.2824-2836,Nov.2004.
[22]Ravi Palanki,Jonathan S.Yedidia,"Rateless codes on noisy channels".
[23]霍媛圆,张朝阳,and吴可镝,适合于加性白高斯噪声信道的无速率码编译码方法.专利申请号：200710157177.2,2007.
[24]R.Gallage,Low Density Parity Check Codes,MIT Press,1963.
[25]C.Berrou,A.GIavieux.Near Optimum Error Correcting Coding and Decoding:Turbo-codes.lEEE Transaction on Communication.Vol.44,pp:1261-1271,October 1996.
[26]M.Luby,M.Mitzenmacher,M.A.Shokrollahi,D.A.Spielman.Improved low-density parity-check codes using irregular graphs.IEEE Transaction on Information Theory,vol.47,no.2;pp.585-598, Feb.2001.
[27]M.Luby,M.Mitzenmacher,M.A.Shokrollahi,D.A.Spielman. Efficient earsure-correcting codes.IEEE Transaction on Information Theory,vol.47,no.2,pp.569-584,Feb.2001.
[28]Thomas J.Richardson and Rudiger L.Urbanke."The Capacity of Low-Density Parity-Check Codes Under Message-Passing Decoding".IEEE Transaction on Information Theory,VOL.47,NO.2,FEBRUARY 2001.
[29]T.J,Richardson,R.Urbanke. "Design of Capacity-Approaching Irregular Low-Density Parity-Check Codes",IEEE Transaction on Information Theory,VOL.47,NO.2,FEBRUARY 2001.
[30]Sae-Young Chung."Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation".IEEE Transaction on Information Theory,VOL.47,N0.2,FEBRUARY 2001.
[31]Sae-Young Chung,G.David Forney,Jr.,Thomas J.Richardson and Rudiger L.Urbanke."On the Design of Low-Density Parity-Check Codes within 0.0045 dB of the Shannon Limit".IEEE Communications Letters,VOL.5.NO.2,FEBRUARY 2001.
[32]R.M.Tanner.A recursive approach to low complexity codes.IEEE Transaction on Information Theory,vol.IT-27,no.9,pp.533-547,Sep.1981.
[33]T.Richardson,R.Urbanke.Design of capacity-approaching irregular low-density parity-check codes.lEEE Transactions on Information Theory,vol.47,no.2,pp.619-637,2001.
[34]T.Richardson,R.Urbanke.The capacity of low-density parity-check codes under message-passing decoding.lEEE Transactions on Information Theory,vol.47,no.2,pp.599-618,2001.
[35]S.ten Brink.Convergence behavior of iteratively decoded parallel concatenated codes.IEEE Transaction on Communication,vol.49,no.10,pp.1727-1736,Oct.2001.
[36]A.Ashikhmin,G.Kramer,S.ten Brink.Extrinsic Information Transfer Function:model and erasure channel propertier.lEEE Transaction on Information Theory,vol.50,no.11,Nov.2004.
[37]S.ten Brink,G.Kramer,A.Ashikhmin.Design of low-density parity-check codes for modulation and detection.IEEE Transaction on Communication,vol.52,no.4,pp.670-678,April 2004.
[38]杨胜天.关于整数编码和Slepian-Wolf编码的研究.博士论文,浙江大学信电系,2005.
[39]X.-Y. Hu,E.Eieftheriou,and D.-M.Arnold,"Reguiar and irregular progressive edge-growth Tanner graphs,"IEEE Trans.Inform.Theory,vol.51,no.1,pp.386-398,2005.
[40]H.Lou and J.Garcia-Frias,"On the Application of Error-Correction Codes with Low-Density Generator Matrix over Different Quantum Channels,"Proc.International Symposium on turbo Codes,April 2006.
[41]H.Jin,A.Khandekar,R.McEliece,Irregular repeat-accumulate codes.Proceeding of 2nd Int.Symp.Turbo Codes and Related Topics,Brest,France,pp.1-8,Sep.2000.
[42]Lechner G.Convergence of sum-product algorithm for finite length low-density parity-check codes[R].Winter School on Coding and Information Theory,2003.
[43]Davey M C.Error-correction using low-density parity-check codes[D]:[Ph.D.dissertation].Cambridge:University of Cambridge.
[2]Caiying Guo, Tiankui Guo et al., "Investigation on Key Techniques and Applications of Cognitive Radio", http://www.paper.edu.cn.
[3]Ian F. Akyildiz et al., "Next generation/dynamic spectrum access/cognitive radio wireless networks:A survey"[J], in Computer Networks Journal (Elsevier), vol.50, pp.2127-2159, Sept.2006.
[4]Joseph Mitola et al., "Cognitive radio:Making software radios more personal"[C], in IEEE Personal Communications, vol.6, no.4, pp.13-18, Aug.1999.
[5]Joseph Mitola, "Cognitive radio:An integrated agent architecture for software defined radio", Doctor of Technology, Royal Institute Technology (KTH), Stockholm, Sweden,2000.
[6]Simon Haykin, "Cognitive Radio:Brain-Empowered Wireless Communications"[J], in IEEE Journal on Selected Area Communications, vol.23, no.2, pp.201-220, Feb.2005.
[7]D.Cabric,S.M.Mishra,and R.W.Brodersen."lmplementation issuses in spectrum sensing for congnitive radios".Conference on Signals,Systems,and Computers,2004.
[8]A.Raghavan,E.Gebara,E.M.Tentzeris,and J.Laskar."Analysis and Design of an Interfenrence Canceller for Collocated Radios",IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,VOL53,NO.11,NOVEMBER 2005.
[9]Jae Yeon Won,Sung Bo Shim,Yun Hee Kim,Sung Hyun Hwang,Myung Sun Song,Chang Joo Kim."An Adaptive OFDMA Platform for IEEE 802.22 Based on Congnitive Radio".APCC'06,Page(s):1-5,Aug.2006.
[10]Hui-Ping Lien,Po-An Chen,Tzi-Dar Chiueh."Design of a MIMO OFDM baseband transceiver for cognitive radio system".ISCAS 2006,Page(s):4,21-24 May 2006.
[11]Batra,A.;Lingam,S.;Balakrishnan,J.;"Multi-band OFDM:a cognitive radio for UWB ",ISCAS 2006,Page(s):4,21-24 May 2006
[12]Tao Li,Wai Ho Mow,Vincent K.N. Lau."Robust joint interference detection and decoding for OFDM-based cognitive radio systems with unknown interference".IEEE Journal on Selected Areas in Communications,Volume 25,lssue 3,Page(s):566-575,April 2007.
[13]Yamaguchi,H.;" Active interference cancellation technique for MB-OFDM congnitive radio",34th European Microwave Conference,Volume 2,Page(s):1105-1108,2004.
[14]周向炜,张朝阳,程鹏.'An interference Avoidance Scheme for OFDM Cognitive Radio Systems",ICCT'06,Page(s):1-5,Nov.2006.
[15]Chakravarthy,V.;Nunez,A.S.;Stephens,J.P.;Shqw,A.K.;Temple,M.A.,"TDCS,OFDM,and MC-CDMA:a brief tutorial",IEEE Communications Magazine,Vol.43,Issue 9,Page(s):S11-S16, Sept.2005.
[16]Chuan Han;Jun Wang;Shaoqian Li;"A Spectrum Exchange Mechanism in Cognitive Radio Contexts",PIMRC'2006,pp 2413-2417,Seattle,USA,July 914,2006.
[17]D.J.C. MacKay,"Fountain Codes",IEE Proc.-Commun.,Vol.152,No.6,pp1062-1068,December 2005.
[18]Luby,M.,"LT Codes".Proc.43rd Ann.IEEE Symp.on Foundations of Computer Science,16-19 Nobmber 2002,pp.271-282
[19]Byers,J.,Luby,M.,Mitzenmacher,M.,and Rege,A.,"A digital fountain approach to reliable distribution of bulk data".Proc.ACM SIGCOMM'98,2-4 September 1998.
[20]Shokrollahi,A.,"Raptor Codes".Technical report,Laboratoired algorithmique,Ecole Polytechnique Federale de Lausanne,Lausanne,Switzerland,2003.Available from algo.epfl.ch.
[21]J.Ha,J.Kim,and S.W.McLaughlin,"Rate-compatible puncturing of low-density parity-check codes,"IEEE Trans.lnf.Theory,vol.50,no.11,pp.2824-2836,Nov.2004.
[22]Ravi Palanki,Jonathan S.Yedidia,"Rateless codes on noisy channels".
[23]霍媛圆,张朝阳,and吴可镝,适合于加性白高斯噪声信道的无速率码编译码方法.专利申请号：200710157177.2,2007.
[24]R.Gallage,Low Density Parity Check Codes,MIT Press,1963.
[25]C.Berrou,A.GIavieux.Near Optimum Error Correcting Coding and Decoding:Turbo-codes.lEEE Transaction on Communication.Vol.44,pp:1261-1271,October 1996.
[26]M.Luby,M.Mitzenmacher,M.A.Shokrollahi,D.A.Spielman.Improved low-density parity-check codes using irregular graphs.IEEE Transaction on Information Theory,vol.47,no.2;pp.585-598, Feb.2001.
[27]M.Luby,M.Mitzenmacher,M.A.Shokrollahi,D.A.Spielman. Efficient earsure-correcting codes.IEEE Transaction on Information Theory,vol.47,no.2,pp.569-584,Feb.2001.
[28]Thomas J.Richardson and Rudiger L.Urbanke."The Capacity of Low-Density Parity-Check Codes Under Message-Passing Decoding".IEEE Transaction on Information Theory,VOL.47,NO.2,FEBRUARY 2001.
[29]T.J,Richardson,R.Urbanke. "Design of Capacity-Approaching Irregular Low-Density Parity-Check Codes",IEEE Transaction on Information Theory,VOL.47,NO.2,FEBRUARY 2001.
[30]Sae-Young Chung."Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation".IEEE Transaction on Information Theory,VOL.47,N0.2,FEBRUARY 2001.
[31]Sae-Young Chung,G.David Forney,Jr.,Thomas J.Richardson and Rudiger L.Urbanke."On the Design of Low-Density Parity-Check Codes within 0.0045 dB of the Shannon Limit".IEEE Communications Letters,VOL.5.NO.2,FEBRUARY 2001.
[32]R.M.Tanner.A recursive approach to low complexity codes.IEEE Transaction on Information Theory,vol.IT-27,no.9,pp.533-547,Sep.1981.
[33]T.Richardson,R.Urbanke.Design of capacity-approaching irregular low-density parity-check codes.lEEE Transactions on Information Theory,vol.47,no.2,pp.619-637,2001.
[34]T.Richardson,R.Urbanke.The capacity of low-density parity-check codes under message-passing decoding.lEEE Transactions on Information Theory,vol.47,no.2,pp.599-618,2001.
[35]S.ten Brink.Convergence behavior of iteratively decoded parallel concatenated codes.IEEE Transaction on Communication,vol.49,no.10,pp.1727-1736,Oct.2001.
[36]A.Ashikhmin,G.Kramer,S.ten Brink.Extrinsic Information Transfer Function:model and erasure channel propertier.lEEE Transaction on Information Theory,vol.50,no.11,Nov.2004.
[37]S.ten Brink,G.Kramer,A.Ashikhmin.Design of low-density parity-check codes for modulation and detection.IEEE Transaction on Communication,vol.52,no.4,pp.670-678,April 2004.
[38]杨胜天.关于整数编码和Slepian-Wolf编码的研究.博士论文,浙江大学信电系,2005.
[39]X.-Y. Hu,E.Eieftheriou,and D.-M.Arnold,"Reguiar and irregular progressive edge-growth Tanner graphs,"IEEE Trans.Inform.Theory,vol.51,no.1,pp.386-398,2005.
[40]H.Lou and J.Garcia-Frias,"On the Application of Error-Correction Codes with Low-Density Generator Matrix over Different Quantum Channels,"Proc.International Symposium on turbo Codes,April 2006.
[41]H.Jin,A.Khandekar,R.McEliece,Irregular repeat-accumulate codes.Proceeding of 2nd Int.Symp.Turbo Codes and Related Topics,Brest,France,pp.1-8,Sep.2000.
[42]Lechner G.Convergence of sum-product algorithm for finite length low-density parity-check codes[R].Winter School on Coding and Information Theory,2003.
[43]Davey M C.Error-correction using low-density parity-check codes[D]:[Ph.D.dissertation].Cambridge:University of Cambridge.