基于LDPC码的MIMO系统关键技术研究
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摘要
近年来,无线个人通信有了长足的发展。然而,在有限的频谱资源上实现高速、可靠的无线信息传输仍然是一个巨大的挑战。本论文针对选择性衰落信道下的实时高速无线通信,提出了一种基于非规则重复累积(IRA)码的纹状分层空时频系统。该系统使用了多输入多输出(MIMO)、低密度奇偶校验(LDPC)码、正交频分复用(OFDM)、Turbo接收等技术。针对这些技术所存在的一些实际问题,本论文给出了相应的解决方案,重点放在相关信号处理算法的设计上。设计具体算法时,在保证性能的前提下,力求复杂度最低,而且对算法的稳健性做了充分考虑。
其一,在未编码MIMO系统方面,针对完美空时分组码(Perfect-STBC)提出了一种高效解码器。结合Perfect-STBC的结构特点,推导出一种等效的垂直贝尔实验室分层空时(V-BLAST)解码模型;在对该模型作最小均方误差-判决反馈均衡(MMSE-DFE)预处理之后,给出了一种具有边界约束的Fano树搜索解码算法。该解码器能以较低的复杂度逼近最大似然(ML)解码性能,而且对天线配置、调制星座均具有较好的适应性。
其二,针对空时比特交织编码调制(ST-BICM)系统,给出了外信息转移(EXIT)图的分析计算方法。对于实际应用中的有限长度系统,引入了EXIT带分析技术,并给出了具体分析算法。利用EXIT带分析工具,对几种典型的软输入软输出MIMO检测器做了对比分析。
其三,在软输入软输出MIMO检测器的设计方面,对List-TM算法做了改进,得到List-MTM检测器。首先对MIMO信道矩阵作无偏MMSE-DFE排序和滤波,得到一种树结构,使用TM树搜索算法构造出幸存路径集合;然后选择性地对部分长度路径进行扩展;最后联合使用幸存路径和扩展路径作软信息计算。List-MTM检测器具有灵活的性能-复杂度折中特性,而且为基于宽度优先的树搜索类MIMO检测器提供了一个统一框架。另外,通过添加一位互补矢量和设置特殊参数,由List-MTM检测器导出另一种高效检测器,称作U-MMSE-ITS检测器。该检测器不但能以相对较低的复杂度获得很好的检测性能,而且具有较强的稳健性;其处理复杂度几乎不随信道状况的变化而改变,有利于硬件实现。
其四,在LDPC码的编码和构造方面,首先针对一般LDPC码的编码问题,给出了将校验矩阵通过行列置换转化为近似下三角结构的一种实用算法,使用该方法完成在线编码只需准线性复杂度。其次,针对短长度IRA码的构造,结合IRA码的结构特点,对循序边增长(PEG)算法做了约束优化,并使用优化算法构造出了短长度好码。
其五,在LDPC码的解码器设计方面,结合LDPC编码MIMO系统的迭代接收机结构特点,对标准置信传播(BP)算法从校验节点信息保留、消息传递策略、校验节点信息更新计算方法等方面做了改进,得到一种高效率解码器。该解码器的收敛速率很快(只需大约5次迭代),而且节点的信息更新计算只需作少量加法和乘法操作;在解码性能方面,和标准BP算法相比,没有明显损失。
最后,结合以上研究结果,针对选择性信道下的低时延高速无线通信,本文提出了一种基于IRA码的纹状分层空时频系统。仿真结果表明,该系统能以较低的处理复杂度实现可靠的高速无线传输,而且系统对于天线配置和信道状况具有较好的鲁棒性。
The past decade has seen great improvements in wireless personal communication technologies. However, to provide new services over the wireless channel of strictly limited bandwidth is still very challenging for researchers and engineers. For high speed information transmition with low-delay and high reliability in selective-fading channels, an irregular repeat-accumulate (IRA) codes based, threaded layered space-time-frequency system is proposed. The proposed system employs several new techniques, such as multi-input multi-output (MIMO), low-density parity-check (LDPC) codes, orthogonal frequency division multiplexing (OFDM), and turbo iterative receiver. We give some solutions to solve the practical problems that arise in such technologies, with emphasis on the design of involved signal processing algorithms. In the design of these algorithms, we not only emphasize the tradeoff between performance and complexity but also give consideration to the robustness of them.
Firstly, an efficient decoder is proposed for the perfect space-time block (perfect-STBC) codes. Based on the special structure of perfect-STBC, an equivalent vertical Bell Labs layered space-time (V-BLAST) decoding model is derived. Minimum mean-square error decision feedback equalizer (MMSE-DFE) preprocessing is applied to this model and a decoder with boundary controlled Fano tree search algorithm is given. This decoder achieves almost maximum likelihood (ML) decoding performance at lower complexity than that of existed near-ML decoders. Furthermore, the decoder is robust to antenna configurations and to modulation constellations
Secondly, for space-time bit-interleaved coded modulation (ST-BICM) system, the analytical calculation of extrinsic information transfer (EXIT) chart is derived. In particular, the EXIT-band technique is introduced to the practical finite-length ST-BICM system and a detailed algorithm for the EXIT-band analysis and calculation is given. Using this algorithm, we give an analysis and comparison to several typical soft-input soft-output (SISO) MIMO detectors.
Thirdly, as to the SISO MIMO detector design, we improve the List-TM detector and obtain a robust detection algorithm named List-MTM. First, the unbiased MMSE-DFE filter is used to preprocess the MIMO channel and a tree-search structure is given. Second, the survived paths are constructed by the TM algorithm. Then, some partial-length paths are augmented selectively. Finally, the soft information of coded bits is calculated according to both the survived paths and the augmented paths. The proposed List-MTM detector behaves flexible in performance-complexity tradeoff and provides a unified framework for the breadth-first tree-search based MIMO detectors. In addition, by adding one-bit complement vectors and by setting particular parameters to the List-MTM algorithm, another efficient MIMO detector named U-MMSE-ITS is derived. This detector not only provides high detection performance at very low complexity but also is robust to antenna configurations and to MIMO channel conditions. The complexity of the U-MMSE-ITS detector is almost invariant for all channel conditions, which makes the hardware implementation conveniently.
Fourthly, for general LDPC codes encoding, we give a practical algorithm that transforms the parity check matrix into an approximate lower triangular form by performing row and column permutations only. Online encoding according to the check matrix of this approximate lower triangular form needs only linear time complexity. In addition, for the short-length IRA codes construction, we proposed a constraint optimization to the progressive edge growth (PEG) algorithm based on the special structure of IRA codes. Short-length IRA codes constructed by the optimized PEG algorithm exhibit very good performance.
Fifthly, based on the iterative receiver structure of the LDPC coded MIMO system, we improve the standard belief propagation (BP) decoding algorithm from the following three aspects: check-nodes information retain, message-passing schedule, and check-nodes information calculation method. The improved decoder not only converges very fast (5 iterations is sufficient) but also takes only a small amount of add operation and multiply operation to calculate the information updating. Compared to the standard BP decoder, it has almost no performance loss.
Finally, based on the above research, an IRA codes based threaded layered space-time-frequency system is proposed. The simulation results demonstrate that, with low processing complexity, the proposed system can provides high data rate with high reliability over selective-fading channels. Furthermore, this system is robust to arbitrary antenna configurations and to any MIMO channels.
其一,在未编码MIMO系统方面,针对完美空时分组码(Perfect-STBC)提出了一种高效解码器。结合Perfect-STBC的结构特点,推导出一种等效的垂直贝尔实验室分层空时(V-BLAST)解码模型;在对该模型作最小均方误差-判决反馈均衡(MMSE-DFE)预处理之后,给出了一种具有边界约束的Fano树搜索解码算法。该解码器能以较低的复杂度逼近最大似然(ML)解码性能,而且对天线配置、调制星座均具有较好的适应性。
其二,针对空时比特交织编码调制(ST-BICM)系统,给出了外信息转移(EXIT)图的分析计算方法。对于实际应用中的有限长度系统,引入了EXIT带分析技术,并给出了具体分析算法。利用EXIT带分析工具,对几种典型的软输入软输出MIMO检测器做了对比分析。
其三,在软输入软输出MIMO检测器的设计方面,对List-TM算法做了改进,得到List-MTM检测器。首先对MIMO信道矩阵作无偏MMSE-DFE排序和滤波,得到一种树结构,使用TM树搜索算法构造出幸存路径集合;然后选择性地对部分长度路径进行扩展;最后联合使用幸存路径和扩展路径作软信息计算。List-MTM检测器具有灵活的性能-复杂度折中特性,而且为基于宽度优先的树搜索类MIMO检测器提供了一个统一框架。另外,通过添加一位互补矢量和设置特殊参数,由List-MTM检测器导出另一种高效检测器,称作U-MMSE-ITS检测器。该检测器不但能以相对较低的复杂度获得很好的检测性能,而且具有较强的稳健性;其处理复杂度几乎不随信道状况的变化而改变,有利于硬件实现。
其四,在LDPC码的编码和构造方面,首先针对一般LDPC码的编码问题,给出了将校验矩阵通过行列置换转化为近似下三角结构的一种实用算法,使用该方法完成在线编码只需准线性复杂度。其次,针对短长度IRA码的构造,结合IRA码的结构特点,对循序边增长(PEG)算法做了约束优化,并使用优化算法构造出了短长度好码。
其五,在LDPC码的解码器设计方面,结合LDPC编码MIMO系统的迭代接收机结构特点,对标准置信传播(BP)算法从校验节点信息保留、消息传递策略、校验节点信息更新计算方法等方面做了改进,得到一种高效率解码器。该解码器的收敛速率很快(只需大约5次迭代),而且节点的信息更新计算只需作少量加法和乘法操作;在解码性能方面,和标准BP算法相比,没有明显损失。
最后,结合以上研究结果,针对选择性信道下的低时延高速无线通信,本文提出了一种基于IRA码的纹状分层空时频系统。仿真结果表明,该系统能以较低的处理复杂度实现可靠的高速无线传输,而且系统对于天线配置和信道状况具有较好的鲁棒性。
The past decade has seen great improvements in wireless personal communication technologies. However, to provide new services over the wireless channel of strictly limited bandwidth is still very challenging for researchers and engineers. For high speed information transmition with low-delay and high reliability in selective-fading channels, an irregular repeat-accumulate (IRA) codes based, threaded layered space-time-frequency system is proposed. The proposed system employs several new techniques, such as multi-input multi-output (MIMO), low-density parity-check (LDPC) codes, orthogonal frequency division multiplexing (OFDM), and turbo iterative receiver. We give some solutions to solve the practical problems that arise in such technologies, with emphasis on the design of involved signal processing algorithms. In the design of these algorithms, we not only emphasize the tradeoff between performance and complexity but also give consideration to the robustness of them.
Firstly, an efficient decoder is proposed for the perfect space-time block (perfect-STBC) codes. Based on the special structure of perfect-STBC, an equivalent vertical Bell Labs layered space-time (V-BLAST) decoding model is derived. Minimum mean-square error decision feedback equalizer (MMSE-DFE) preprocessing is applied to this model and a decoder with boundary controlled Fano tree search algorithm is given. This decoder achieves almost maximum likelihood (ML) decoding performance at lower complexity than that of existed near-ML decoders. Furthermore, the decoder is robust to antenna configurations and to modulation constellations
Secondly, for space-time bit-interleaved coded modulation (ST-BICM) system, the analytical calculation of extrinsic information transfer (EXIT) chart is derived. In particular, the EXIT-band technique is introduced to the practical finite-length ST-BICM system and a detailed algorithm for the EXIT-band analysis and calculation is given. Using this algorithm, we give an analysis and comparison to several typical soft-input soft-output (SISO) MIMO detectors.
Thirdly, as to the SISO MIMO detector design, we improve the List-TM detector and obtain a robust detection algorithm named List-MTM. First, the unbiased MMSE-DFE filter is used to preprocess the MIMO channel and a tree-search structure is given. Second, the survived paths are constructed by the TM algorithm. Then, some partial-length paths are augmented selectively. Finally, the soft information of coded bits is calculated according to both the survived paths and the augmented paths. The proposed List-MTM detector behaves flexible in performance-complexity tradeoff and provides a unified framework for the breadth-first tree-search based MIMO detectors. In addition, by adding one-bit complement vectors and by setting particular parameters to the List-MTM algorithm, another efficient MIMO detector named U-MMSE-ITS is derived. This detector not only provides high detection performance at very low complexity but also is robust to antenna configurations and to MIMO channel conditions. The complexity of the U-MMSE-ITS detector is almost invariant for all channel conditions, which makes the hardware implementation conveniently.
Fourthly, for general LDPC codes encoding, we give a practical algorithm that transforms the parity check matrix into an approximate lower triangular form by performing row and column permutations only. Online encoding according to the check matrix of this approximate lower triangular form needs only linear time complexity. In addition, for the short-length IRA codes construction, we proposed a constraint optimization to the progressive edge growth (PEG) algorithm based on the special structure of IRA codes. Short-length IRA codes constructed by the optimized PEG algorithm exhibit very good performance.
Fifthly, based on the iterative receiver structure of the LDPC coded MIMO system, we improve the standard belief propagation (BP) decoding algorithm from the following three aspects: check-nodes information retain, message-passing schedule, and check-nodes information calculation method. The improved decoder not only converges very fast (5 iterations is sufficient) but also takes only a small amount of add operation and multiply operation to calculate the information updating. Compared to the standard BP decoder, it has almost no performance loss.
Finally, based on the above research, an IRA codes based threaded layered space-time-frequency system is proposed. The simulation results demonstrate that, with low processing complexity, the proposed system can provides high data rate with high reliability over selective-fading channels. Furthermore, this system is robust to arbitrary antenna configurations and to any MIMO channels.
引文
[1] Callendar M H. International mobile telecommunications-2000 standards efforts of the ITU. IEEE Personal Communications, 1997, 8, 4(4): 6-7.
[2] Kim Y, Jeong B J, Chung J. Beyond 3G: vision, requirements, and enabling technologies. IEEE Communications Magazine, 2003, 3, 41(3): 120-124.
[3] Hui S H, Yeung K H. Challenges in the migration to 4G mobile systems. IEEE Communications Magazine, 2003, 12, 41(12): 54-59.
[4] Bria A, Gessler F, Queseth O, et al. 4th-generation wireless infrastructures: scenarios and research challenges. IEEE Personal Communications, 2001, 12, 8(6): 25-31.
[5] Blostein S D, Leib H. Multiple antenna systems: their role and impact in future wireless access. IEEE Communications Magazine, 2003, 7, 41(7): 94-101.
[6]朱近康.未来移动通信的技术挑战和解决方案.电子学报, 2004, 12, 32(12A): 6-10.
[7]张磊,邱绍峰. 4G移动通信技术.通信技术, 2007, 11, 40(11): 193-195.
[8]徐丹,周峰,杨大成. 4G技术发展与挑战.移动通信. 2007, 12, 31(12): 39-42.
[9] Yang Hongwei. A road to future broadband wireless access: MIMO-OFDM-based air interface. IEEE Communications Magazine, 2005, 1, 43(1): 53-60.
[10] Hagenauer J. The turbo principle: tutorial introduction and state of the art. Proc International Symposium on Turbo Codes, Brest, France. 1997, 9: 1-11.
[11] Ten Brink S, Speidel J, Yan R. Iterative demapping and decoding for multilevel modulation. Proc IEEE GLOBECOM 1998, Sydney, Australia. 1998, 579-584.
[12] Caire G, Taricco G, Biglieri E. Bit-interleaved coded modulation. IEEE Trans Information Theory, 1998, 5, 44(3): 927-946.
[13] Sellathurai M, Haykin S. Turbo-BLAST for wireless communications: theory and experiments. IEEE Trans Signal Processing. 2002, 10, 50(10): 2538-2546.
[14] Hochwald B, Ten Brink S. Achieving near-capacity on a multiple-antenna channel. IEEE Trans Communications. 2003, 3, 51(3): 389-399.
[15] Haykin S, Sellathurai M, Jong Y, et al. Turbo-MIMO for wireless communications. IEEE Communications Magazine, 2004, 10, 42(10): 48-53.
[16]王新梅,肖国镇.纠错码-原理与方法(修订版).西安:西安电子科技大学出版社,2002.
[17] Lin S, Costello D J. Error Control Coding: Fundamentals and Applications (Second Edition). NJ: Prentice-Hall, 2004.
[18] Christian B S, Lance C P. Trellis and Turbo Coding. NJ: Wiley Press, 2004.
[19] Ten Brink S, Kramer G, Ashikhmin A. Design of low-density parity-check codes for modulation and detection. IEEE Trans Communications, 2004, 4, 52(4): 670-678.
[20] Hou J, Siegel P H, Milstein L B. Design of multi-input multi-output systems based on low-density parity-check codes. IEEE Trans Communications, 2005, 4, 53(4): 601-611.
[21] Suzuki H, Hedley M, Daniels G, et al. Performance of MIMO-OFDM-BICM on measured indoor channels. Proc IEEE VTC2006-Spring, Melbourne, Australia. 2006, 2073-2077.
[22] Chen J, Dholakia A, Eleftheriou E, et al. Reduced-complexity decoding of LDPC codes. IEEE Trans Communications, 2005, 8, 53(8): 1288-1299.
[23] Lu B, Wang X, Narayanan K R. LDPC-based space-time coded OFDM systems over correlated fading channels: performance analysis and receiver design. IEEE Trans Communications, 2002, 1, 50(1): 74-88.
[24] Lu B, Yue G, Wang X. Performance analysis and design optimization of LDPC-coded MIMO OFDM systems. IEEE Trans Signal Processing, 2004, 2, 52(2): 348-361.
[25] Gesbert D, Shafi M, Shan Shiu D, et al. From theory to practice: an overview of MIMO space-time coded wireless systems. IEEE J Selected Areas Communications, 2003, 4, 21(3): 281-302.
[26] Paulraj A, Nabar R, Gore D.空时无线通信导论(影印版).北京:清华大学出版社,2005.
[27] Telatar I E. Capacity of multi-antenna Gaussian channels. Bell Labs Tech Report, 1995.
[28] Foschini G J. Layered space-time architecture wireless Communication in a fading environment when using multi-element antenna. Bell Labs Tech Journal, 1996, 41-59.
[29] Foschini G J, Gans M J. On limits of wireless communications in a fading environment when using multiple antennas. Wireless Personal Communications, 1998, 6: 311-335.
[30] Jiang J, Ingram M A. Spherical wave model for short-range MIMO. IEEE Trans Communications, 2005, 5, 53(5): 905-905.
[31] Byers G J,Takawira F. Spatially and temporally corre1ated MIM0 channels: modeling and capacity analyis. IEEE Trans Vehicular Technology, 2004, 3, 3(3): 966-975.
[32] Ertel R B, Cardieri P, Sowerby K W, et al. Overview of spatial channel models for antenna array communication systems. IEEE Personal Communications Magazine, 1998, 2, 5(1): 10-22.
[33] Weichselberger W, Herdin M, Ozcelik H, et al. A stochastic MIMO channel model with joint correlation of both link ends. IEEE Trans Wireless Communications, 2006, 1, 5(1): 90-100.
[34] Shafi M, Zhang M, Moustakas A L, et al. Polarized MIMO channels in 3-D: models, measurements and mutual information. IEEE J Selected Areas Communications, 2006, 3, 24(3): 514-527.
[35] Debbah M, Muller R R. MIMO channel modeling and the principle of maximum entropy. IEEE Trans Information Theory, 2005, 5, 51(5): 1667-1690.
[36] SADEK A K, SU W, LIU K. Diversity analysis for frequency-selective MIMO-OFDM systems with general spatial and temporal correlation model. IEEE Trans Communications, 2006, 5, 54(5): 878-888.
[37]高凯. MIMO信道的建模、仿真及无线衰落信道的Markov模型研究. [博士论文],长沙:国防科学技术大学, 2006.
[38] Chuah C, Tse D, Valensuela R. Capacity scaling in MIMO wireless systems under correlated fading. IEEE Trans Information Theory, 2002, 3, 48(3): 637-650.
[39] Lozano A, Tulino A M. Capacity of multiple-transmit multiple-receive antenna architectures. IEEE Trans Information Theory, 2002, 12, 48(12): 3117-3128.
[40] Kang M, Yang L, Alouini M S. Capacity of MIMO Rician channels with multiple correlated Rayleigh co-channel interferers. Proc IEEE GLOBECOM 2003, San Francisco, CA, 2003.
[41] Paulraj A J, Gore D A, Nabar R U, et al. An overview of MIMO communications - a key to gigabit wireless. Proceedings of the IEEE, 2004, 2, 92(2): 198-218.
[42] Wolniansky P, Foschini G, Golden G. V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel. Proc IEEE ISSSE 1998, Pisa, Italy. 1998, 295-300.
[43] Tarokh V, Seshadri N, Calderbank A R. Space–time codes for high data rate wireless communication: performance criterion and code construction. IEEE Trans Information Theory, 1998, 3, 44(3): 744-765.
[44] Alamouti S M. A simple transmit diversity technique for wireless communications. IEEE J Selected Areas Communications, 1998, 10, 16(10): 1451-1458.
[45] Tarokh V, Jafarkhani H, Calderbank A R. Space–time block coding for wireless communications: performance results. IEEE J Selected Areas Communications, 1999, 3, 17(3): 451-460.
[46] Tarokh V, Jafarkhani H, Calderbank A R. Space–time block codes from orthogonal designs. IEEE Trans Information Theory. 1999, 7, 45(7): 1456-1467.
[47] Hassibi B, Hochwald B M. High-rate codes that are linear in space and time. IEEE Trans Information Theory, 2002, 7, 48(7): 1804-1824.
[48] Gamal H E, Damen M O. Universal space–time coding. IEEE Trans Information Theory, 2003, 5, 49(5):1097-1119.
[49] Elia P, Kumar K R, Pawar S A, et al. Explicit space-time codes achieving the diversity-multiplexing gain tradeoff. IEEE Trans Information Theory, 2006, 9, 52(9): 3869-3884.
[50] Oggier F, Rekaya G, Belfiore JC, et al. Perfect space-time block codes. IEEE Trans Information Theory, 2006, 9, 52(9): 3885-3902.
[51] Elia P, Sethuraman B A, Vijay K P. Perfect space-time codes for any number of antennas. IEEE Trans Information Theory, 2007, 11, 53(11): 3853-3868.
[52] Tarokh V, Jafarkhani H, A differential detection scheme for transmit diversity. IEEE J Selected Areas Communications, 2000, 7, 18(7): 1169-1174.
[53] Hochwald B M, Marzetta T L. Unitary space-time modulation for multiple antenna communications in Rayleigh flat fading. IEEE Trans Information Theory, 2000, 3, 46(3): 543-564.
[54] Jafarkhani H, Tarokh V. Multiple transmit antenna differential detection from generalized orthogonal designs. IEEE Trans Information Theory, 2001, 9, 47(6): 2626-2631.
[55] Vucetic B, Yuan J. Space-Time Coding. England: Wiley Press, 2003.
[56] Damen M O, Gamal H E, Caire G. On maximum-likelihood detection and the search for the closest lattice point. IEEE Trans Information Theory, 2003, 10, 49(10): 2839-2401.
[57] Gamal H E, Caire G, Damen M O. Lattice coding and decoding achieve the optimal diversity–multiplexing tradeoff of MIMO channels. IEEE Trans Information Theory, 2004, 6, 50(6):968-985.
[58] Murugan A, Gamal H E, Damen M O, et al. A unified framework for tree search decoding: rediscovering the sequential decoder. IEEE Trans Information Theory, 2006, 3, 52(3): 933-953.
[59] Lu B, Wang X. Iterative receivers for multiuser space-time coding systems. EEE J Selected Areas Communications, 2000, 11, 18(11): 2322-2335.
[60] Jong Y, Willink T. Iterative tree search detection for MIMO wireless systems. IEEE Trans Communications, 2005, 6, 53(6):.930–935.
[61] B?ro S, Hagenauer J, Witzke M. Iterative detection of MIMO transmission using a list-sequential (LISS) detector. Proc IEEE ICC 2003, Anchorage, AK. 2003, 2653-2657.
[62] Vikalo H, Hassibi B, Kailath T. Iterative decoding for MIMO channels via modified sphere decoding. IEEE Trans Wireless Communications, 2004, 11, 3(6):2299-2311.
[63] Hagenauer J, Kuhn C. The list-sequential (LISS) algorithm and its application. IEEE Trans Communications. 2007, 5, 55(5): 918-928.
[64] Wolfgang A, Akhtman J, Chen S, et al. Iterative MIMO Detection for Rank-Deficient Systems. IEEE Signal Processing Letters. 2006, 11, 13(11): 699-702.
[65] Guo Z, Nilsson P. Algorithm and implementation of the K-best sphere decoding for MIMO detection. EEE J Selected Areas Communications, 2006, 3, 24(3): 491-503.
[66] Ruyet D L, Bertozzi T, ?zbek B. Breadth first algorithms for APP detectors over MIMO channels. Proc IEEE ICC 2004, Paris, France. 2004, 926-930.
[67] Zimmermann E, Fettweis G. Unbiased MMSE tree search detection for multiple antenna systems. Proc WPMC 2006, San Diego, USA. 2006, 17-20.
[68] Zimmermann E, Fettweis G. Generalized smart candidate adding for tree search based MIMO detection. Proc ITG/IEEE Workshop on Smart Antennas (WSA'07), Vienna. 2007.
[69] Aggarwal P, Prasad N, Wang X. An enhanced deterministic sequential Monte Carlo method for near-optimal MIMO demodulation with QAM constellations. IEEE Trans Signal Processing, 2007, 6, 55(6): 2395-2406.
[70] Steingrimsson B, Luo Z, Wong K. Soft quasi-maximum-likelihood detection for multiple-antenna wireless channels. IEEE Trans Signal Processing, 2003, 11, 51(11): 2710-2719.
[71]樊迅. MIMO无线通信系统中信号检测技术的研究. [博士论文],上海:上海交通大学, 2006.
[72] Tong L. Channel estimation for space-time orthogonal block codes. Proc ICC 2001, Helsinki, Finland. 2001, 1127-1131.
[73] Zeng Y, Ng T. A semi-blind channel estimation method for multi-user multi-antenna OFDM systems. IEEE Trans Signal Processing. 2004, 5, 52(5): 1419-1430.
[74] Bai W, He C, Jiang L, et al. Blind channel estimation in MIMO-OFDM systems. Proc IEEE GLOBECOM 2002, Taipei, Taiwan. 2002, 317-321.
[75]王兴林. MIMO-OFDM系统中接收机及信道估计技术研究. [博士论文],北京:北京邮电大学, 2006.
[76]魏旻. MIMO-OFDM系统实现方案及盲估计技术研究. [博士论文],成都:电子科技大学, 2007.
[77] Visotsky E, Madhow U. Space-time transmit precoding with imperfect feedback. IEEE Trans Information Theory, 2001, 9, 47(7): 2632-2639.
[78] Love D J, Heath R W. Limited feedback unitary precoding for spatial multiplexing systems. IEEE Trans Information Theory, 2005, 8, 51(8): 2967-2976.
[79]刘毅. MIMO信道预编码技术研究. [博士论文],西安:西安电子科技大学, 2007.
[80] Cimini L J, Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing. IEEE Trans Communications, 1985, 7, COM-33(7): 665-675.
[81] Sari H, Karam G, Jeanclaude I. Transmission techniques for digital terrestrial TV broadcasting. IEEE Communication Magazine, 1985, 2, 33(2): 100-109.
[82] Bolcskei H, Gesbert D, Paulraj A J. On the capacity of OFDM-based spatial multiplexing systems. IEEE Trans Communications, 2002, 2, 50(2): 225-234.
[83] Lee I, Chan A, Sundberg C. Space-time bit-interleaved coded modulation for OFDM systems. IEEE Trans Signal. Processing, 2004, 3, 52(3): 820-825.
[84] Lee H, Lee I. New approach for error compensation in coded V-BLAST OFDM systems IEEE Trans Communications, 2007, 2, 55(2): 74-88.
[85] Huang Y, Wang J. A novel layered space-time-frequency architecture with convolutional coding. Proc IEEE VTC2007-Spring, Dublin, Ireland. 2007, 1816-1820.
[86] Huang Y, Wang J, Higuchi K, et al. Iterative signal processing for coded LSTF architectures. IEEE Trans Wireless Communications, 2007, 10, 6(10): 3712-3716.
[87] Andrews J G, Ghosh A, Muhamed R. Fundamentals of WiMAX—Understanding Broadband Wireless Networking. NJ: Prentice-Hall, 2007.
[88] IEEE P802.11n/D2.00 Draft IEEE Standard for Local and Metropolitan area Networks. Part 11: Wireless LAN medium access control (MAC) and physical Layer (PHY) specifications. NJ: IEEE Computer Society, 2007.
[89] Shannon C E, A mathematical theory of communication. Bell System Technical Journal, 1948, 7/10, 27, 379-423/623-656.
[90] Gallager R G. Low-density parity-check codes. IRE Trans Information Theory, 1962, 1, 8(1): 21-28.
[91] Gallager R G. Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963.
[92] Tanner R. M. A recursive approach to low complexity codes. IEEE Trans Information Theory, 1981, 9, 2(5): 533-547.
[93] Berrou C, Glavieux A,Thitimajshima P. Near Shannon limit error-correcting coding and decoding: turbo-codes. Proc ICC 1993, Geneva, Switzerland. 1993, 1064-1070.
[94] Sipser M, Spielman D A. Expander codes. IEEE Trans Information Theory, 1996, 11, 42(6): 1710-1722. See Also Proc. 35th Symp. Found. Comp. Sci., pp. 566-576, 1994.
[95] Spielman D A. Linear-time encodable and decodable error-correcting codes. IEEE Trans Information Theory, 1996, 11, 42(6): 1723-1731.
[96] Alon N, Luby M. A linear-time erasure-resilient code with nearly optimal recovery. IEEE Trans Information Theory, 1996, 11, 42(6): 1732-1736.
[97] MacKay D J C, Neal R M. Near Shannon limit performance of low density parity check codes. Electronics Letters, 1997, 3, 33(6): 457-458.
[98] MacKay D J C. Good error-correcting codes based on very sparse matrices. IEEE Trans Information Theory, 1999, 3, 45(2): 399-431.
[99] Wiberg N. Codes and Decoding on General Graphs. [博士论文], Sweden: Linkoping University, 1996.
[100] Special issue on Codes and Graphs and Iterative Algorithms. IEEE Trans Information Theory, 2001, 2, 47.
[101] Special issue on The Turbo Principle: From Theory to Practice, IEEE J Selected Areas Communications, 2001, 5, 19.
[102] Special issue on The Turbo Principle: From Theory to Practice II, IEEE J Selected Areas Communications, 2001, 9, 19.
[103] Kschischang F R, Frey B J, Loeliger H A. Factor graphs and the sum-product algorithm. IEEE Trans Information Theory, 2001, 2, 47(2): 498-519.
[104] Forney G D, Jr. Codes on graphs: normal realizations. IEEE Trans Information Theory, 2001, 2, 47(2): 520-548.
[105] Richardson T J, Urbanke R L. The capacity of low-density parity-check codes under message-passing decoding. IEEE Trans Information Theory, 2001, 2, 47(2): 599-618.
[106] Richardson T J, Shokrollahi A, Urbanke R L. Design of capacity-approaching low-density parity-check codes. IEEE Trans Information Theory, 2001, 2, 47(2): 619-637.
[107] Richardson T J, Urbanke R L. Efficient encoding of low-density parity-check codes. IEEE Trans Information Theory, 2001, 2, 47(2): 638-656.
[108] Kou Y, Lin S, Fossorier M P C. Low-density parity-check codes based on finite geometries: a rediscovery and new results. IEEE Trans Information Theory, 2001, 11, 47(11): 2711-2736.
[109] Xu J, Chen L, Lin S, et al. Construction of regular and irregular LDPC codes: geometry decomposition and masking. IEEE Trans Information Theory, 2007, 1, 53(1): 121-134.
[110] Djurdjevic I, Xu J, Lin S,et al. A class of low density parity check codes constructed based on Reed-Solomon codes with two information symbols. IEEE Communications Letters, 2003, 7, 7(7): 317-319.
[111] Fossorier M P C. Quasi-cyclic low-density parity-check codes from circulant permutation matrices. IEEE Trans Information Theory, 2004, 8, 50(8): 1788-1793.
[112] Tanner R M, Sridhara D, Sridharan A, et al. LDPC block and convolutional codes based on circulant matrices. IEEE Trans Information Theory, 2004, 12, 50(12): 2966-2984.
[113] Hu X Y, Eleftheriou E, Arnold D M. Regular and irregular progressive edge-growth Tanner graphs. IEEE Trans Information Theory, 2005, 1, 51(1): 386-398.
[114] Xiao H, Banihashemi A H. Improved progressive-edge-growth (PEG) construction of irregular LDPC codes. IEEE Communications Letters, 2004, 9, 8(9): 715-717.
[115] Vukobratovic D,Senk V. Generalized ACE constrained progressive edge-growth LDPC code design. IEEE Communications Letters, 2008, 1, 12(1): 32-34.
[116] Kim S H, Kim J S, Kim D S, et al. LDPC code construction with low error floor based on the IPEG algorithm. IEEE Communications Letters, 2007, 7, 11(7): 607-609.
[117] Tian T, Jones C, Villasenor J D, et al. Selective avoidance of cycles in irregular LDPC code construction. IEEE Trans Communications, 2004, 8, 52(8): 1242-1247.
[118] Jin H, Khandekar A, McEliece R. Irregular repeat-accumulate codes. Proc 2nd International Symposium on Turbo Codes, Brest, France. 2000, 1-8.
[119] Yang M, Ryan W E, Li Y. Design of efficiently encodable moderate-length high-rate irregular LDPC codes. IEEE Trans Communications, 2004, 4, 52 (4): 564-571.
[120] Dinoi L, Sottile F, Benedetto S. Design of variable-rate irregular LDPC codes with low error floor. Proc IEEE ICC2005, Seoul, Korea. 2005, 647-651.
[121] Zhang Y, Ryan W E. Structured IRA codes: performance analysis and construction. IEEE Trans Communications, 2007, 5, 55 (5): 837-844.
[122] Yue G, Lu B, Wang X. Analysis and design of finite-length LDPC codes. IEEE Trans Vehicular Technology, 2007, 56, (3): 1321-1332.
[123] McEliece R J, MacKay D J C, Cheng J-F. Turbo decoding as an instance of Pearl’s belief propagation algorithm. IEEE J Selected Areas Communications, 1998, 2, 16(2):140-152.
[124] Fossorier M P C, Mihaljevic M, Imai H. Reduced complexity iterative decoding of low density parity check codes. IEEE Trans Communications, 1999, 5, 47(5): 673-680.
[125] Chen J, Fossorier M P C. Near optimum universal belief propagation based decoding of low-density parity check codes. IEEE Trans Communications, 2002, 3, 50(3): 406-414.
[126] Chen J, Dholakla A, Eleftheriou E, et al. Reduced-complexity decoding of LDPC codes. IEEE Trans Communications, 2005, 8, 53(8):1288-1299.
[127] Pandya N, Honary B. Low-complexity decoding of LDPC codes. Electronics Letters, 2007, 8, 43 (18): 990-991.
[128] Papaharalabos S, Sweeney P, Evans B G, et al. Modified sum-product algorithms for decoding low-density parity-check codes. IET Communications, 2007, 3, 1(3): 294-300.
[129] He Z, Roy S, Fortier P. Lowering error floor of LDPC codes using a joint row-column decoding algorithm. Proc IEEE ICC 2007, Glasgow, Scotland. 2007, 920-925.
[130] Kschischang F R, Frey B J. Iterative decoding of compound codes by probability propagation in graphical models. IEEE J Selected Areas Communications, 1998, 2, 16(2): 219-230.
[131] Zhang J, Wang Y, Fossorier M P C, et al. Iterative decoding with replicas. IEEE Trans Information Theory, 2007, 5, 53(5): 1644-1663.
[132] Sharon E, Litsyn S, Goldberger J. Efficient serial message-passing schedules for LDPC decoding. IEEE Trans Information Theory, 2007, 11, 53(11): 4076-4091.
[133] Guilloud F, Boutillon E, Tousch J, et al. Generic description and synthesis of LDPC decoders. IEEE Trans Communications, 2007, 11, 55(11): 2084-2091.
[134]童胜.低密度奇偶校验码的收敛速率分析与设计. [博士论文],西安:西安电子科技大学, 2006.
[135] Feldman J. Decoding Error-Correcting Codes via Linear Programming. Cambridge, MA: Massachusetts Institute of Technology, 2003.
[136] Zhang J, Fossorier M P C. Mean field and mixed mean field iterative decoding of low-density parity-check codes. IEEE Trans Information Theory, 2006, 7, 52(7): 3168-3185.
[137] Davey M C, MacKay D J C. Low density parity check codes over GF(q). Proc Information Theory Workshop 1998, Killarney, Ireland. 1998, 6, 70-71.
[138] Song S, Zeng L, Lin S, et al. Algebraic constructions of nonbinary quasi-cyclic LDPC codes. Proc ISIT 2006, Seatle, USA. 2006, 83-87.
[139] Loeliger H A, Lustenberger F, Helfenstein M, et al. Probability propagation and decoding in analog VLSI. IEEE Trans Information Theory, 2001, 2, 47(2): 837-843.
[140] Darabiha A, Chan Carusone A, Kschischang F R. Power reduction techniques for LDPC decoders. IEEE J Solid-State Circuits, 2008, 8, 43(8): 1835-1845.
[141] Angelos D L, Xiong Z, Georghiades C N. Compression of binary sources with side information at the decoder using LDPC codes. IEEE Communications Letters, 2002, 10, 6(10): 440-442.
[142] Baldi M, Chiaraluce F, Garello R, et al. Quasi-cyclic low-density parity-check codes in the McEliece cryptosystem. Proc ICC 2007, Glasgow, Scotland. 2007, 951-956.
[143] Zheng L, Tse D. Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels. IEEE Trans Information Theory, 2003, 5, 49(5): 1073-1096.
[144] Elia P, Sethuraman B A, Kumar P V. Perfect space-time codes with minimum and non-minimum delay for any number of antennas. Proc International Conference on Wireless Networks, Communications and Mobile Computing. 2005, 722-727.
[145] Ten Brink S. Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Trans Communications, 2001, 10, 49(10): 1727-1737.
[146] Lee J W,Blahut R E. Generalized EXIT chart and BER analysis of finite-length turbo codes. Proc GLOBECOM 2003, San Francisco. 2003, 2067-2072.
[147]张贤达.矩阵分析与应用.北京:清华大学出版社, 2004.
[148] Golden G D, Foschini G J, Valenzuela R A, et al. Detection algorithm and initial laboratory results using V-BLAST space–time communication architecture. Electronics Letters, 1999, 1, 35(1): 14-16.
[149] Hassibi, B. An efficient square-root algorithm for BLAST. Proc IEEE ICASSP 2000, Istanbul, Turkey. 2000, 737-740.
[150] Benesty J, Huang Y, Chen J. A fast recursive algorithm for optimum sequential signal detection in a BLAST system. IEEE Trans Signal Processing, 2003, 7, 51(7): 1722-1730.
[151] Fano R M. A heuristic discussion of probabilistic decoding. IEEE Trans Information Theory, 1963, 4, 9(2): 64-74.
[152] Gresset N. New Space-Time Coding Techniques with Bit Interleaved Coded Modulations. [博士论文], Paris: ENST Paris, 2004.
[153] Gresset N, Brunel L, Boutros J. Space–time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels. IEEE Trans Information Theory, 2008, 5, 54(5): 2156-2178.
[154] Zhao L, Huber J, Gerstacker W. Design and analysis of bit interleaved coded space-time modulation. IEEE Trans Communications, 2008, 6, 56(6): 504-514.
[155] Zhang J, Lee H. Performance analysis of LDPC-coded space-time modulation over MIMO fading channels. IEEE Communications Letters, 2007, 3, 11(3): 234-236.
[156] Zehavi E. 8-PSK Trellis Codes for a Rayleigh channel. IEEE Trans Communications, 1992, 5, 40(5): 873-884.
[157] Li X, Ritcey J A. Bit-interleaved coded modulation with iterative decoding. IEEE Communications Letters, 1997, 11, 1(6): 169-171.
[158] Tonello A M. Space-time bit-interleaved coded modulation with an iterative decoding strategy. Proc VTC 2000-Fall, Boston. 2000, 24-28.
[159] Hagenauer J, Offer E, Papke L. Iterative decoding of binary and block convolutional codes. IEEE Trans Information Theory, 1996, 3, 42(2): 429-445.
[160] Belfiore J, Rekaya G, Viterbo E. The golden code: a 2×2 full-rate space-time code with nonvanishing determinants. IEEE Trans Information Theory, 2005, 4, 51(4): 1432-1436.
[161] Parker S, Sandell M, Yee M, et al. Space-time codes for future WLANs: principles, practice, and performance. IEEE Communications Magazine, 2004, 12, 42(12): 96-103.
[162] Richardson T. The geometry of turbo-decoding dynamics. IEEE Trans Information Theory, 2000, 1, 46 (1): 9-23.
[163] Chung S, Richardson T, Urbanke R. Analysis of sum-product decoding of low-density-parity-check codes using a Gaussian approximation. IEEE Trans Information Theory, 2001, 2, 47(2): 657-670.
[164] Tuchler M, Ten Brink S, Hagenauer J. Measures for tracing convergence of iterative decoding algorithms. Proc 4th IEEE/ITG Conference on Source and Channel Coding, Berlin, Germany. 2002, 53-60.
[165] Tuchler M. Design of serially concatenated systems depending on the block length. IEEE Trans Communications, 2004, 2, 52(2): 209-218.
[166] Ashikhmin A, Kramer G, Ten Brink S. Extrinsic information transfer functions: model and erasure channel properties. IEEE Trans Information Theory, 2004, 11, 50(11): 2657-2673.
[167] Li K, Wang X. EXIT chart analysis of turbo multiuser detection. IEEE Trans Wireless Communications, 2005, 1, 4(1): 300-311.
[168] Tan P, Li J. Finite-length extrinsic information transfer (EXIT) analysis for coded and precoded ISI channels. IEEE Trans Magnetics, 2008, 5, 44(5): 648-655.
[169] Anderson J, Mohan S. Sequential coding algorithms: a survey and cost analysis. IEEE Trans Communications, 1984, 2, 32(2): 169-176.
[170] Simmons S J. Breadth-first trellis decoding with adaptive effort. IEEE Trans Information Theory, 1990, 1, 38(1): 3-12.
[171] Foschini J, Golden G, Valenzuela R, et al. Simplified processing for high spectral efficiency wireless communication employing multi-element arrays. IEEE J Selected Areas Communications, 1999, 11, 17(11): 1841-1852.
[172] Mackay D J C, Hu X Y. Online database of low-density parity-check codes. 2005. http://www.inference.phy.cam.ac.uk/mackay/codes/data.html.
[173] Di C, Proietti D, Telatar I E, et al. Finite-length analysis of low-density parity-check codes on the binary erasure channel. IEEE Trans Information Theory, 2002, 6, 48(6): 1570-1579.
[174] Franceschini M, Ferrari G, Raheli R. Does the performance of LDPC codes depend on the channel. IEEE Trans Communications, 2006, 12, 54(12): 2129-2132.
[175] Chung S Y. On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit. IEEE Communications Letters, 2001, 2, 5(2): 58-60.
[176] Zhang J, Fossorier M P C. Shuffled iterative decoding. IEEE Trans Communications, 2005, 2, 53(2): 209-213.
[177] Zhang J, Fossorier M P C. Shuffled belief propagation decoding. Proc 36th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA. 2002, 8-15.
[178] Wang H S, Moayeri N. Finite-state Markov channel—a useful model for radio communication channels. IEEE Trans Vehicular Technology, 1996, 1, 44(1): 163-171
[2] Kim Y, Jeong B J, Chung J. Beyond 3G: vision, requirements, and enabling technologies. IEEE Communications Magazine, 2003, 3, 41(3): 120-124.
[3] Hui S H, Yeung K H. Challenges in the migration to 4G mobile systems. IEEE Communications Magazine, 2003, 12, 41(12): 54-59.
[4] Bria A, Gessler F, Queseth O, et al. 4th-generation wireless infrastructures: scenarios and research challenges. IEEE Personal Communications, 2001, 12, 8(6): 25-31.
[5] Blostein S D, Leib H. Multiple antenna systems: their role and impact in future wireless access. IEEE Communications Magazine, 2003, 7, 41(7): 94-101.
[6]朱近康.未来移动通信的技术挑战和解决方案.电子学报, 2004, 12, 32(12A): 6-10.
[7]张磊,邱绍峰. 4G移动通信技术.通信技术, 2007, 11, 40(11): 193-195.
[8]徐丹,周峰,杨大成. 4G技术发展与挑战.移动通信. 2007, 12, 31(12): 39-42.
[9] Yang Hongwei. A road to future broadband wireless access: MIMO-OFDM-based air interface. IEEE Communications Magazine, 2005, 1, 43(1): 53-60.
[10] Hagenauer J. The turbo principle: tutorial introduction and state of the art. Proc International Symposium on Turbo Codes, Brest, France. 1997, 9: 1-11.
[11] Ten Brink S, Speidel J, Yan R. Iterative demapping and decoding for multilevel modulation. Proc IEEE GLOBECOM 1998, Sydney, Australia. 1998, 579-584.
[12] Caire G, Taricco G, Biglieri E. Bit-interleaved coded modulation. IEEE Trans Information Theory, 1998, 5, 44(3): 927-946.
[13] Sellathurai M, Haykin S. Turbo-BLAST for wireless communications: theory and experiments. IEEE Trans Signal Processing. 2002, 10, 50(10): 2538-2546.
[14] Hochwald B, Ten Brink S. Achieving near-capacity on a multiple-antenna channel. IEEE Trans Communications. 2003, 3, 51(3): 389-399.
[15] Haykin S, Sellathurai M, Jong Y, et al. Turbo-MIMO for wireless communications. IEEE Communications Magazine, 2004, 10, 42(10): 48-53.
[16]王新梅,肖国镇.纠错码-原理与方法(修订版).西安:西安电子科技大学出版社,2002.
[17] Lin S, Costello D J. Error Control Coding: Fundamentals and Applications (Second Edition). NJ: Prentice-Hall, 2004.
[18] Christian B S, Lance C P. Trellis and Turbo Coding. NJ: Wiley Press, 2004.
[19] Ten Brink S, Kramer G, Ashikhmin A. Design of low-density parity-check codes for modulation and detection. IEEE Trans Communications, 2004, 4, 52(4): 670-678.
[20] Hou J, Siegel P H, Milstein L B. Design of multi-input multi-output systems based on low-density parity-check codes. IEEE Trans Communications, 2005, 4, 53(4): 601-611.
[21] Suzuki H, Hedley M, Daniels G, et al. Performance of MIMO-OFDM-BICM on measured indoor channels. Proc IEEE VTC2006-Spring, Melbourne, Australia. 2006, 2073-2077.
[22] Chen J, Dholakia A, Eleftheriou E, et al. Reduced-complexity decoding of LDPC codes. IEEE Trans Communications, 2005, 8, 53(8): 1288-1299.
[23] Lu B, Wang X, Narayanan K R. LDPC-based space-time coded OFDM systems over correlated fading channels: performance analysis and receiver design. IEEE Trans Communications, 2002, 1, 50(1): 74-88.
[24] Lu B, Yue G, Wang X. Performance analysis and design optimization of LDPC-coded MIMO OFDM systems. IEEE Trans Signal Processing, 2004, 2, 52(2): 348-361.
[25] Gesbert D, Shafi M, Shan Shiu D, et al. From theory to practice: an overview of MIMO space-time coded wireless systems. IEEE J Selected Areas Communications, 2003, 4, 21(3): 281-302.
[26] Paulraj A, Nabar R, Gore D.空时无线通信导论(影印版).北京:清华大学出版社,2005.
[27] Telatar I E. Capacity of multi-antenna Gaussian channels. Bell Labs Tech Report, 1995.
[28] Foschini G J. Layered space-time architecture wireless Communication in a fading environment when using multi-element antenna. Bell Labs Tech Journal, 1996, 41-59.
[29] Foschini G J, Gans M J. On limits of wireless communications in a fading environment when using multiple antennas. Wireless Personal Communications, 1998, 6: 311-335.
[30] Jiang J, Ingram M A. Spherical wave model for short-range MIMO. IEEE Trans Communications, 2005, 5, 53(5): 905-905.
[31] Byers G J,Takawira F. Spatially and temporally corre1ated MIM0 channels: modeling and capacity analyis. IEEE Trans Vehicular Technology, 2004, 3, 3(3): 966-975.
[32] Ertel R B, Cardieri P, Sowerby K W, et al. Overview of spatial channel models for antenna array communication systems. IEEE Personal Communications Magazine, 1998, 2, 5(1): 10-22.
[33] Weichselberger W, Herdin M, Ozcelik H, et al. A stochastic MIMO channel model with joint correlation of both link ends. IEEE Trans Wireless Communications, 2006, 1, 5(1): 90-100.
[34] Shafi M, Zhang M, Moustakas A L, et al. Polarized MIMO channels in 3-D: models, measurements and mutual information. IEEE J Selected Areas Communications, 2006, 3, 24(3): 514-527.
[35] Debbah M, Muller R R. MIMO channel modeling and the principle of maximum entropy. IEEE Trans Information Theory, 2005, 5, 51(5): 1667-1690.
[36] SADEK A K, SU W, LIU K. Diversity analysis for frequency-selective MIMO-OFDM systems with general spatial and temporal correlation model. IEEE Trans Communications, 2006, 5, 54(5): 878-888.
[37]高凯. MIMO信道的建模、仿真及无线衰落信道的Markov模型研究. [博士论文],长沙:国防科学技术大学, 2006.
[38] Chuah C, Tse D, Valensuela R. Capacity scaling in MIMO wireless systems under correlated fading. IEEE Trans Information Theory, 2002, 3, 48(3): 637-650.
[39] Lozano A, Tulino A M. Capacity of multiple-transmit multiple-receive antenna architectures. IEEE Trans Information Theory, 2002, 12, 48(12): 3117-3128.
[40] Kang M, Yang L, Alouini M S. Capacity of MIMO Rician channels with multiple correlated Rayleigh co-channel interferers. Proc IEEE GLOBECOM 2003, San Francisco, CA, 2003.
[41] Paulraj A J, Gore D A, Nabar R U, et al. An overview of MIMO communications - a key to gigabit wireless. Proceedings of the IEEE, 2004, 2, 92(2): 198-218.
[42] Wolniansky P, Foschini G, Golden G. V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel. Proc IEEE ISSSE 1998, Pisa, Italy. 1998, 295-300.
[43] Tarokh V, Seshadri N, Calderbank A R. Space–time codes for high data rate wireless communication: performance criterion and code construction. IEEE Trans Information Theory, 1998, 3, 44(3): 744-765.
[44] Alamouti S M. A simple transmit diversity technique for wireless communications. IEEE J Selected Areas Communications, 1998, 10, 16(10): 1451-1458.
[45] Tarokh V, Jafarkhani H, Calderbank A R. Space–time block coding for wireless communications: performance results. IEEE J Selected Areas Communications, 1999, 3, 17(3): 451-460.
[46] Tarokh V, Jafarkhani H, Calderbank A R. Space–time block codes from orthogonal designs. IEEE Trans Information Theory. 1999, 7, 45(7): 1456-1467.
[47] Hassibi B, Hochwald B M. High-rate codes that are linear in space and time. IEEE Trans Information Theory, 2002, 7, 48(7): 1804-1824.
[48] Gamal H E, Damen M O. Universal space–time coding. IEEE Trans Information Theory, 2003, 5, 49(5):1097-1119.
[49] Elia P, Kumar K R, Pawar S A, et al. Explicit space-time codes achieving the diversity-multiplexing gain tradeoff. IEEE Trans Information Theory, 2006, 9, 52(9): 3869-3884.
[50] Oggier F, Rekaya G, Belfiore JC, et al. Perfect space-time block codes. IEEE Trans Information Theory, 2006, 9, 52(9): 3885-3902.
[51] Elia P, Sethuraman B A, Vijay K P. Perfect space-time codes for any number of antennas. IEEE Trans Information Theory, 2007, 11, 53(11): 3853-3868.
[52] Tarokh V, Jafarkhani H, A differential detection scheme for transmit diversity. IEEE J Selected Areas Communications, 2000, 7, 18(7): 1169-1174.
[53] Hochwald B M, Marzetta T L. Unitary space-time modulation for multiple antenna communications in Rayleigh flat fading. IEEE Trans Information Theory, 2000, 3, 46(3): 543-564.
[54] Jafarkhani H, Tarokh V. Multiple transmit antenna differential detection from generalized orthogonal designs. IEEE Trans Information Theory, 2001, 9, 47(6): 2626-2631.
[55] Vucetic B, Yuan J. Space-Time Coding. England: Wiley Press, 2003.
[56] Damen M O, Gamal H E, Caire G. On maximum-likelihood detection and the search for the closest lattice point. IEEE Trans Information Theory, 2003, 10, 49(10): 2839-2401.
[57] Gamal H E, Caire G, Damen M O. Lattice coding and decoding achieve the optimal diversity–multiplexing tradeoff of MIMO channels. IEEE Trans Information Theory, 2004, 6, 50(6):968-985.
[58] Murugan A, Gamal H E, Damen M O, et al. A unified framework for tree search decoding: rediscovering the sequential decoder. IEEE Trans Information Theory, 2006, 3, 52(3): 933-953.
[59] Lu B, Wang X. Iterative receivers for multiuser space-time coding systems. EEE J Selected Areas Communications, 2000, 11, 18(11): 2322-2335.
[60] Jong Y, Willink T. Iterative tree search detection for MIMO wireless systems. IEEE Trans Communications, 2005, 6, 53(6):.930–935.
[61] B?ro S, Hagenauer J, Witzke M. Iterative detection of MIMO transmission using a list-sequential (LISS) detector. Proc IEEE ICC 2003, Anchorage, AK. 2003, 2653-2657.
[62] Vikalo H, Hassibi B, Kailath T. Iterative decoding for MIMO channels via modified sphere decoding. IEEE Trans Wireless Communications, 2004, 11, 3(6):2299-2311.
[63] Hagenauer J, Kuhn C. The list-sequential (LISS) algorithm and its application. IEEE Trans Communications. 2007, 5, 55(5): 918-928.
[64] Wolfgang A, Akhtman J, Chen S, et al. Iterative MIMO Detection for Rank-Deficient Systems. IEEE Signal Processing Letters. 2006, 11, 13(11): 699-702.
[65] Guo Z, Nilsson P. Algorithm and implementation of the K-best sphere decoding for MIMO detection. EEE J Selected Areas Communications, 2006, 3, 24(3): 491-503.
[66] Ruyet D L, Bertozzi T, ?zbek B. Breadth first algorithms for APP detectors over MIMO channels. Proc IEEE ICC 2004, Paris, France. 2004, 926-930.
[67] Zimmermann E, Fettweis G. Unbiased MMSE tree search detection for multiple antenna systems. Proc WPMC 2006, San Diego, USA. 2006, 17-20.
[68] Zimmermann E, Fettweis G. Generalized smart candidate adding for tree search based MIMO detection. Proc ITG/IEEE Workshop on Smart Antennas (WSA'07), Vienna. 2007.
[69] Aggarwal P, Prasad N, Wang X. An enhanced deterministic sequential Monte Carlo method for near-optimal MIMO demodulation with QAM constellations. IEEE Trans Signal Processing, 2007, 6, 55(6): 2395-2406.
[70] Steingrimsson B, Luo Z, Wong K. Soft quasi-maximum-likelihood detection for multiple-antenna wireless channels. IEEE Trans Signal Processing, 2003, 11, 51(11): 2710-2719.
[71]樊迅. MIMO无线通信系统中信号检测技术的研究. [博士论文],上海:上海交通大学, 2006.
[72] Tong L. Channel estimation for space-time orthogonal block codes. Proc ICC 2001, Helsinki, Finland. 2001, 1127-1131.
[73] Zeng Y, Ng T. A semi-blind channel estimation method for multi-user multi-antenna OFDM systems. IEEE Trans Signal Processing. 2004, 5, 52(5): 1419-1430.
[74] Bai W, He C, Jiang L, et al. Blind channel estimation in MIMO-OFDM systems. Proc IEEE GLOBECOM 2002, Taipei, Taiwan. 2002, 317-321.
[75]王兴林. MIMO-OFDM系统中接收机及信道估计技术研究. [博士论文],北京:北京邮电大学, 2006.
[76]魏旻. MIMO-OFDM系统实现方案及盲估计技术研究. [博士论文],成都:电子科技大学, 2007.
[77] Visotsky E, Madhow U. Space-time transmit precoding with imperfect feedback. IEEE Trans Information Theory, 2001, 9, 47(7): 2632-2639.
[78] Love D J, Heath R W. Limited feedback unitary precoding for spatial multiplexing systems. IEEE Trans Information Theory, 2005, 8, 51(8): 2967-2976.
[79]刘毅. MIMO信道预编码技术研究. [博士论文],西安:西安电子科技大学, 2007.
[80] Cimini L J, Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing. IEEE Trans Communications, 1985, 7, COM-33(7): 665-675.
[81] Sari H, Karam G, Jeanclaude I. Transmission techniques for digital terrestrial TV broadcasting. IEEE Communication Magazine, 1985, 2, 33(2): 100-109.
[82] Bolcskei H, Gesbert D, Paulraj A J. On the capacity of OFDM-based spatial multiplexing systems. IEEE Trans Communications, 2002, 2, 50(2): 225-234.
[83] Lee I, Chan A, Sundberg C. Space-time bit-interleaved coded modulation for OFDM systems. IEEE Trans Signal. Processing, 2004, 3, 52(3): 820-825.
[84] Lee H, Lee I. New approach for error compensation in coded V-BLAST OFDM systems IEEE Trans Communications, 2007, 2, 55(2): 74-88.
[85] Huang Y, Wang J. A novel layered space-time-frequency architecture with convolutional coding. Proc IEEE VTC2007-Spring, Dublin, Ireland. 2007, 1816-1820.
[86] Huang Y, Wang J, Higuchi K, et al. Iterative signal processing for coded LSTF architectures. IEEE Trans Wireless Communications, 2007, 10, 6(10): 3712-3716.
[87] Andrews J G, Ghosh A, Muhamed R. Fundamentals of WiMAX—Understanding Broadband Wireless Networking. NJ: Prentice-Hall, 2007.
[88] IEEE P802.11n/D2.00 Draft IEEE Standard for Local and Metropolitan area Networks. Part 11: Wireless LAN medium access control (MAC) and physical Layer (PHY) specifications. NJ: IEEE Computer Society, 2007.
[89] Shannon C E, A mathematical theory of communication. Bell System Technical Journal, 1948, 7/10, 27, 379-423/623-656.
[90] Gallager R G. Low-density parity-check codes. IRE Trans Information Theory, 1962, 1, 8(1): 21-28.
[91] Gallager R G. Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963.
[92] Tanner R. M. A recursive approach to low complexity codes. IEEE Trans Information Theory, 1981, 9, 2(5): 533-547.
[93] Berrou C, Glavieux A,Thitimajshima P. Near Shannon limit error-correcting coding and decoding: turbo-codes. Proc ICC 1993, Geneva, Switzerland. 1993, 1064-1070.
[94] Sipser M, Spielman D A. Expander codes. IEEE Trans Information Theory, 1996, 11, 42(6): 1710-1722. See Also Proc. 35th Symp. Found. Comp. Sci., pp. 566-576, 1994.
[95] Spielman D A. Linear-time encodable and decodable error-correcting codes. IEEE Trans Information Theory, 1996, 11, 42(6): 1723-1731.
[96] Alon N, Luby M. A linear-time erasure-resilient code with nearly optimal recovery. IEEE Trans Information Theory, 1996, 11, 42(6): 1732-1736.
[97] MacKay D J C, Neal R M. Near Shannon limit performance of low density parity check codes. Electronics Letters, 1997, 3, 33(6): 457-458.
[98] MacKay D J C. Good error-correcting codes based on very sparse matrices. IEEE Trans Information Theory, 1999, 3, 45(2): 399-431.
[99] Wiberg N. Codes and Decoding on General Graphs. [博士论文], Sweden: Linkoping University, 1996.
[100] Special issue on Codes and Graphs and Iterative Algorithms. IEEE Trans Information Theory, 2001, 2, 47.
[101] Special issue on The Turbo Principle: From Theory to Practice, IEEE J Selected Areas Communications, 2001, 5, 19.
[102] Special issue on The Turbo Principle: From Theory to Practice II, IEEE J Selected Areas Communications, 2001, 9, 19.
[103] Kschischang F R, Frey B J, Loeliger H A. Factor graphs and the sum-product algorithm. IEEE Trans Information Theory, 2001, 2, 47(2): 498-519.
[104] Forney G D, Jr. Codes on graphs: normal realizations. IEEE Trans Information Theory, 2001, 2, 47(2): 520-548.
[105] Richardson T J, Urbanke R L. The capacity of low-density parity-check codes under message-passing decoding. IEEE Trans Information Theory, 2001, 2, 47(2): 599-618.
[106] Richardson T J, Shokrollahi A, Urbanke R L. Design of capacity-approaching low-density parity-check codes. IEEE Trans Information Theory, 2001, 2, 47(2): 619-637.
[107] Richardson T J, Urbanke R L. Efficient encoding of low-density parity-check codes. IEEE Trans Information Theory, 2001, 2, 47(2): 638-656.
[108] Kou Y, Lin S, Fossorier M P C. Low-density parity-check codes based on finite geometries: a rediscovery and new results. IEEE Trans Information Theory, 2001, 11, 47(11): 2711-2736.
[109] Xu J, Chen L, Lin S, et al. Construction of regular and irregular LDPC codes: geometry decomposition and masking. IEEE Trans Information Theory, 2007, 1, 53(1): 121-134.
[110] Djurdjevic I, Xu J, Lin S,et al. A class of low density parity check codes constructed based on Reed-Solomon codes with two information symbols. IEEE Communications Letters, 2003, 7, 7(7): 317-319.
[111] Fossorier M P C. Quasi-cyclic low-density parity-check codes from circulant permutation matrices. IEEE Trans Information Theory, 2004, 8, 50(8): 1788-1793.
[112] Tanner R M, Sridhara D, Sridharan A, et al. LDPC block and convolutional codes based on circulant matrices. IEEE Trans Information Theory, 2004, 12, 50(12): 2966-2984.
[113] Hu X Y, Eleftheriou E, Arnold D M. Regular and irregular progressive edge-growth Tanner graphs. IEEE Trans Information Theory, 2005, 1, 51(1): 386-398.
[114] Xiao H, Banihashemi A H. Improved progressive-edge-growth (PEG) construction of irregular LDPC codes. IEEE Communications Letters, 2004, 9, 8(9): 715-717.
[115] Vukobratovic D,Senk V. Generalized ACE constrained progressive edge-growth LDPC code design. IEEE Communications Letters, 2008, 1, 12(1): 32-34.
[116] Kim S H, Kim J S, Kim D S, et al. LDPC code construction with low error floor based on the IPEG algorithm. IEEE Communications Letters, 2007, 7, 11(7): 607-609.
[117] Tian T, Jones C, Villasenor J D, et al. Selective avoidance of cycles in irregular LDPC code construction. IEEE Trans Communications, 2004, 8, 52(8): 1242-1247.
[118] Jin H, Khandekar A, McEliece R. Irregular repeat-accumulate codes. Proc 2nd International Symposium on Turbo Codes, Brest, France. 2000, 1-8.
[119] Yang M, Ryan W E, Li Y. Design of efficiently encodable moderate-length high-rate irregular LDPC codes. IEEE Trans Communications, 2004, 4, 52 (4): 564-571.
[120] Dinoi L, Sottile F, Benedetto S. Design of variable-rate irregular LDPC codes with low error floor. Proc IEEE ICC2005, Seoul, Korea. 2005, 647-651.
[121] Zhang Y, Ryan W E. Structured IRA codes: performance analysis and construction. IEEE Trans Communications, 2007, 5, 55 (5): 837-844.
[122] Yue G, Lu B, Wang X. Analysis and design of finite-length LDPC codes. IEEE Trans Vehicular Technology, 2007, 56, (3): 1321-1332.
[123] McEliece R J, MacKay D J C, Cheng J-F. Turbo decoding as an instance of Pearl’s belief propagation algorithm. IEEE J Selected Areas Communications, 1998, 2, 16(2):140-152.
[124] Fossorier M P C, Mihaljevic M, Imai H. Reduced complexity iterative decoding of low density parity check codes. IEEE Trans Communications, 1999, 5, 47(5): 673-680.
[125] Chen J, Fossorier M P C. Near optimum universal belief propagation based decoding of low-density parity check codes. IEEE Trans Communications, 2002, 3, 50(3): 406-414.
[126] Chen J, Dholakla A, Eleftheriou E, et al. Reduced-complexity decoding of LDPC codes. IEEE Trans Communications, 2005, 8, 53(8):1288-1299.
[127] Pandya N, Honary B. Low-complexity decoding of LDPC codes. Electronics Letters, 2007, 8, 43 (18): 990-991.
[128] Papaharalabos S, Sweeney P, Evans B G, et al. Modified sum-product algorithms for decoding low-density parity-check codes. IET Communications, 2007, 3, 1(3): 294-300.
[129] He Z, Roy S, Fortier P. Lowering error floor of LDPC codes using a joint row-column decoding algorithm. Proc IEEE ICC 2007, Glasgow, Scotland. 2007, 920-925.
[130] Kschischang F R, Frey B J. Iterative decoding of compound codes by probability propagation in graphical models. IEEE J Selected Areas Communications, 1998, 2, 16(2): 219-230.
[131] Zhang J, Wang Y, Fossorier M P C, et al. Iterative decoding with replicas. IEEE Trans Information Theory, 2007, 5, 53(5): 1644-1663.
[132] Sharon E, Litsyn S, Goldberger J. Efficient serial message-passing schedules for LDPC decoding. IEEE Trans Information Theory, 2007, 11, 53(11): 4076-4091.
[133] Guilloud F, Boutillon E, Tousch J, et al. Generic description and synthesis of LDPC decoders. IEEE Trans Communications, 2007, 11, 55(11): 2084-2091.
[134]童胜.低密度奇偶校验码的收敛速率分析与设计. [博士论文],西安:西安电子科技大学, 2006.
[135] Feldman J. Decoding Error-Correcting Codes via Linear Programming. Cambridge, MA: Massachusetts Institute of Technology, 2003.
[136] Zhang J, Fossorier M P C. Mean field and mixed mean field iterative decoding of low-density parity-check codes. IEEE Trans Information Theory, 2006, 7, 52(7): 3168-3185.
[137] Davey M C, MacKay D J C. Low density parity check codes over GF(q). Proc Information Theory Workshop 1998, Killarney, Ireland. 1998, 6, 70-71.
[138] Song S, Zeng L, Lin S, et al. Algebraic constructions of nonbinary quasi-cyclic LDPC codes. Proc ISIT 2006, Seatle, USA. 2006, 83-87.
[139] Loeliger H A, Lustenberger F, Helfenstein M, et al. Probability propagation and decoding in analog VLSI. IEEE Trans Information Theory, 2001, 2, 47(2): 837-843.
[140] Darabiha A, Chan Carusone A, Kschischang F R. Power reduction techniques for LDPC decoders. IEEE J Solid-State Circuits, 2008, 8, 43(8): 1835-1845.
[141] Angelos D L, Xiong Z, Georghiades C N. Compression of binary sources with side information at the decoder using LDPC codes. IEEE Communications Letters, 2002, 10, 6(10): 440-442.
[142] Baldi M, Chiaraluce F, Garello R, et al. Quasi-cyclic low-density parity-check codes in the McEliece cryptosystem. Proc ICC 2007, Glasgow, Scotland. 2007, 951-956.
[143] Zheng L, Tse D. Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels. IEEE Trans Information Theory, 2003, 5, 49(5): 1073-1096.
[144] Elia P, Sethuraman B A, Kumar P V. Perfect space-time codes with minimum and non-minimum delay for any number of antennas. Proc International Conference on Wireless Networks, Communications and Mobile Computing. 2005, 722-727.
[145] Ten Brink S. Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Trans Communications, 2001, 10, 49(10): 1727-1737.
[146] Lee J W,Blahut R E. Generalized EXIT chart and BER analysis of finite-length turbo codes. Proc GLOBECOM 2003, San Francisco. 2003, 2067-2072.
[147]张贤达.矩阵分析与应用.北京:清华大学出版社, 2004.
[148] Golden G D, Foschini G J, Valenzuela R A, et al. Detection algorithm and initial laboratory results using V-BLAST space–time communication architecture. Electronics Letters, 1999, 1, 35(1): 14-16.
[149] Hassibi, B. An efficient square-root algorithm for BLAST. Proc IEEE ICASSP 2000, Istanbul, Turkey. 2000, 737-740.
[150] Benesty J, Huang Y, Chen J. A fast recursive algorithm for optimum sequential signal detection in a BLAST system. IEEE Trans Signal Processing, 2003, 7, 51(7): 1722-1730.
[151] Fano R M. A heuristic discussion of probabilistic decoding. IEEE Trans Information Theory, 1963, 4, 9(2): 64-74.
[152] Gresset N. New Space-Time Coding Techniques with Bit Interleaved Coded Modulations. [博士论文], Paris: ENST Paris, 2004.
[153] Gresset N, Brunel L, Boutros J. Space–time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels. IEEE Trans Information Theory, 2008, 5, 54(5): 2156-2178.
[154] Zhao L, Huber J, Gerstacker W. Design and analysis of bit interleaved coded space-time modulation. IEEE Trans Communications, 2008, 6, 56(6): 504-514.
[155] Zhang J, Lee H. Performance analysis of LDPC-coded space-time modulation over MIMO fading channels. IEEE Communications Letters, 2007, 3, 11(3): 234-236.
[156] Zehavi E. 8-PSK Trellis Codes for a Rayleigh channel. IEEE Trans Communications, 1992, 5, 40(5): 873-884.
[157] Li X, Ritcey J A. Bit-interleaved coded modulation with iterative decoding. IEEE Communications Letters, 1997, 11, 1(6): 169-171.
[158] Tonello A M. Space-time bit-interleaved coded modulation with an iterative decoding strategy. Proc VTC 2000-Fall, Boston. 2000, 24-28.
[159] Hagenauer J, Offer E, Papke L. Iterative decoding of binary and block convolutional codes. IEEE Trans Information Theory, 1996, 3, 42(2): 429-445.
[160] Belfiore J, Rekaya G, Viterbo E. The golden code: a 2×2 full-rate space-time code with nonvanishing determinants. IEEE Trans Information Theory, 2005, 4, 51(4): 1432-1436.
[161] Parker S, Sandell M, Yee M, et al. Space-time codes for future WLANs: principles, practice, and performance. IEEE Communications Magazine, 2004, 12, 42(12): 96-103.
[162] Richardson T. The geometry of turbo-decoding dynamics. IEEE Trans Information Theory, 2000, 1, 46 (1): 9-23.
[163] Chung S, Richardson T, Urbanke R. Analysis of sum-product decoding of low-density-parity-check codes using a Gaussian approximation. IEEE Trans Information Theory, 2001, 2, 47(2): 657-670.
[164] Tuchler M, Ten Brink S, Hagenauer J. Measures for tracing convergence of iterative decoding algorithms. Proc 4th IEEE/ITG Conference on Source and Channel Coding, Berlin, Germany. 2002, 53-60.
[165] Tuchler M. Design of serially concatenated systems depending on the block length. IEEE Trans Communications, 2004, 2, 52(2): 209-218.
[166] Ashikhmin A, Kramer G, Ten Brink S. Extrinsic information transfer functions: model and erasure channel properties. IEEE Trans Information Theory, 2004, 11, 50(11): 2657-2673.
[167] Li K, Wang X. EXIT chart analysis of turbo multiuser detection. IEEE Trans Wireless Communications, 2005, 1, 4(1): 300-311.
[168] Tan P, Li J. Finite-length extrinsic information transfer (EXIT) analysis for coded and precoded ISI channels. IEEE Trans Magnetics, 2008, 5, 44(5): 648-655.
[169] Anderson J, Mohan S. Sequential coding algorithms: a survey and cost analysis. IEEE Trans Communications, 1984, 2, 32(2): 169-176.
[170] Simmons S J. Breadth-first trellis decoding with adaptive effort. IEEE Trans Information Theory, 1990, 1, 38(1): 3-12.
[171] Foschini J, Golden G, Valenzuela R, et al. Simplified processing for high spectral efficiency wireless communication employing multi-element arrays. IEEE J Selected Areas Communications, 1999, 11, 17(11): 1841-1852.
[172] Mackay D J C, Hu X Y. Online database of low-density parity-check codes. 2005. http://www.inference.phy.cam.ac.uk/mackay/codes/data.html.
[173] Di C, Proietti D, Telatar I E, et al. Finite-length analysis of low-density parity-check codes on the binary erasure channel. IEEE Trans Information Theory, 2002, 6, 48(6): 1570-1579.
[174] Franceschini M, Ferrari G, Raheli R. Does the performance of LDPC codes depend on the channel. IEEE Trans Communications, 2006, 12, 54(12): 2129-2132.
[175] Chung S Y. On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit. IEEE Communications Letters, 2001, 2, 5(2): 58-60.
[176] Zhang J, Fossorier M P C. Shuffled iterative decoding. IEEE Trans Communications, 2005, 2, 53(2): 209-213.
[177] Zhang J, Fossorier M P C. Shuffled belief propagation decoding. Proc 36th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA. 2002, 8-15.
[178] Wang H S, Moayeri N. Finite-state Markov channel—a useful model for radio communication channels. IEEE Trans Vehicular Technology, 1996, 1, 44(1): 163-171