多輸入多輸出技術已被廣泛應用於近期無線通訊系統以提高其傳輸率及改善訊號品質，為進一步確保傳輸的可靠性，糾錯能力接近薛農極限的渦輪碼亦是無線通訊系統的極佳選項。為了在接收端恢復多根傳送天線之訊號，目前已有眾多適用於多輸入多輸出之偵測器被提出，針對具有編碼之多輸入多輸出系統，軟性輸出之偵測器亦被提出以如供給渦輪解碼這類具有軟性輸入/輸出通道解碼器的事前資訊。但在瑞利衰弱通道下可能會因不可靠的軟性資訊而導致系統性能的下降，發展具高性能之編碼多輸入多輸出系統之接收器已是當前的一個重要研究課題。在本論文中，我們研製應用於編碼多輸入多輸出系統之高效能聯合遞迴式偵測器與解碼器。首先，研發具有低複雜度與高輸出率的複數型態QR分解器，並以管線式與摺疊式這兩種座標軸數位旋轉計算器模組為基礎來發展出大規模平行陣列架構以提升輸出率。針對44多輸入多輸出系統，其晶片實現結果顯示出此設計具有192.1K的等效邏輯閘個數，並可以運行在200M Hz的速度來達到最高3Gb/s的傳輸率；即使在以邏輯閘數與功耗對傳輸率進行正規化的前提下，相比於其他設計，所提出之架構設計也具有優勢。其次，基於無排序理念的多輸入多輸出偵測器，本論文發展以期望值為輔助之提前刪除技術，用以在維持位元錯誤率的條件下減少節點的計算量。在4×4天線陣列下之實驗結果顯示，相較於具相同系統配置的現存設計而言，所提出之重組式偵測器擁有較高的正規化輸出率。本論文亦探討高效率聯合遞迴式多輸入多輸出偵測器與渦輪解碼設計，於渦輪解碼器中，提出改良平行窗口式最大事後機率演算法來降低所需的事先計算量；在系統的初始迭代，透過所提出之樹狀擴展搜尋來改善偵測器的軟性資訊。在遞迴式系統中提出一種改良更新策略，可從偵測器獲得高可靠度的外部資訊，並且運用候選節點選擇策略來降低列表式球形偵測器用以計算對數相似比值的記憶體需求約94%。最後，依據不同迭代次數組合的分析結果顯示，所提出之聯合遞迴式系統可以用較少的整體節點搜尋數目來提升整體系統效能。

Multiple-input multiple-output (MIMO) techniques have been widely used to increase the transmission rate and improve the signal quality in modern wireless communication systems. To further ensure transmission reliability, error-correcting codes like turbo codes with performance close to the theoretical Shannon limit are adopted for wireless communication systems. Up to now, many MIMO detection algorithms have been proposed in the literature to recover the transmitted signals from the received noisy signals. In particular, soft-output MIMO detection algorithms can be used to provide a priori information of the codeword to the following soft-input soft-output (SISO) decoders, such as the turbo decoder in coded-MIMO systems. In some application scenarios with Rayleigh fading channels, the induced unreliable a priori information might result in system performance degradation. Exploring high-performance coded-MIMO systems thus becomes a challenging and crucial research area.
In this dissertation, we have developed a high-performance joint iterative detection and turbo decoding design in coded-MIMO systems. First, a low-complexity high-throughput complex-valued QR factorization (CQRF) design is presented. Based on coordinate rotation digital computer (CORDIC) arithmetic, a massively parallel array architecture consisting of pipelined and folded CORDIC modules was developed to enhance the throughput. The chip implementation result indicates the design, with an equivalent gate count of 192.1K, can operate at 200 MHz and accomplish the highest 3-Gb/s data rate in 4×4 MIMO systems. The proposed design also outperforms related designs in two compound performance indices: data rate normalized with respect to gate count and power consumption. Second, we developed a mean-aided early-pruned scheme in MIMO detector based on sort-free fixed-complexity sphere decoding algorithm. The modified MIMO detector can reduce the number of node computations while maintaining the BER performance of the original sort-free algorithm. Experimental results show that the proposed reconfigurable detector design with 4×4 antenna array has a higher normalized throughput than those of existing detectors using the same system configuration. Third, an efficient joint iterative MIMO detection and turbo decoding design was developed. For the turbo decoding, a modified parallel-window MAP algorithm was proposed to reduce the warm-up computation. In the initial iteration, the reliability of the soft information of a MIMO detector can be greatly improved by applying the proposed extended tree search scheme. A modified updating strategy is presented to acquire the highly reliable extrinsic information from the soft-output MIMO detector in iterative system development. Compared to the list sphere decoding (LSD) algorithm, about 94% reduction in the memory requirement of log-likelihood ratio (LLR) computation can be achieved by using the proposed candidate node selection strategy. Finally, based on the analysis of iteration profile, the overall system performance can be maintained with a fewer number of searched nodes than existing works.

[1] V. Tarokh, N. Seshadri, and J. C. Belfiore, “On maximum likelihood detection and the search for the closet lattice point,” IEEE Trans. Inform. Theory, vol. 49, no. 10, pp. 2389-2402, Oct. 2003.
[2] U. Fincke and M. Pohst, “Improved methods for calculating vectors of short length in a lattice, including a complexity analysis,” Math. Comput., vol. 44, pp. 463-471, Apr. 1985.
[3] K. Wong, C. Tsui, R. Cheng, and W. Mow, “A VLSI architecture of a K-Best lattice decoding algorithm for MIMO channels,” in Proc. IEEE Int. Symp. Circuits and Syst., pp. 273-276, May 2002.
[4] Z. Guo and P. Nilsson, “Algorithm and implementation of the K-Best sphere decoding for MIMO detection,” IEEE J. Sel. Areas Commun., vol. 24, no. 3, pp. 491-503, Mar. 2006.
[5] L. G. Barbero and J. S. Thompson, “A fixed-complexity MIMO detector based on the complex sphere decoder,” in Proc. IEEE Workshop Signal Process. Advances in Wireless Commun., vol. 1, pp. 1-5, July 2006.
[6] B. Wu and G. Masera, “A novel VLSI architecture of fixed-complexity sphere decoder,” in Proc. Euromicro Conf. Digital Syst. Design: Architectures, Methods Tool, pp. 737-744, Sept. 2010.
[7] J. Jaldén, L. G. Barbero, B. Ottersten, and J. S. Thompson, “Full diversity detection in MIMO systems with a fixed-complexity sphere decoder,” in Proc. IEEE Int. Conf. Acoust., Speech and Signal Process., vol. 3, pp. 49-52, Apr. 2007.
[8] B. Hochwald and S. ten Brink, “Achieving near-capacity on a multiple-antenna channel,” IEEE Trans. Commun., vol. 51, no. 3, pp. 389-399, Mar. 2003.
[9] K. K. Y. Wong and P. J. McLane, “Bi-directional soft-output M-algorithm for iterative decoding,” in Proc. IEEE Int. Conf. Commun., vol. 2, pp. 792-797, June 2004.
[10] Y. L. C. de Jong and T. J. Wilink, “Iterative tree search detection for MIMO wireless systems,” IEEE Trans. Commun., vol. 53, no. 6, pp. 930-935, June 2005.
[11] J. W. Choi, B. Shim, and A. C. Singer, “Efficient soft-input soft-output tree detection via an improved path metric,” IEEE Trans. Inform. Theory, vol. 58, pp. 1518-1533, Mar. 2012.
[12] Yang Yu, S. Handa, F. Sasamori, and O. Takyu, “Improved soft-output M-algorithm for differential encoded LDPC coded systems with multiple-symbol differential detection,” IEEE Int. Symp. Personal Indoor and Mobile Radio Commun., pp. 1985-1991, Sept. 2012.
[13] L. G. Barbero and J. S. Thompson, “Extending a fixed-complexity sphere decoder to obtain likelihood information for turbo-MIMO systems,” IEEE Trans. Veh. Technol., vol. 57, no. 5, pp. 2804-2814, Sept. 2008.
[14] L. G. Barbero, T. Ratnarajah, and C. Cowan, “A low-complexity soft-MIMO detector based on the fixed-complexity sphere decoder,” in Proc. IEEE Inf. Conf. Acoust., Speech and Signal Process., pp. 2669-2672, Apr. 2008.
[15] A. J. Paulraj, D. A. Gore, R. U. Nabar, and H. Bölcskei, “An overview of MIMO communications—A key to gigabit wireless,” in Proc. IEEE, vol. 92, no. 2, pp. 198-218, Feb. 2004.
[16] P. W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela, “V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel,” in Proc. URSI Int. Symp. Signals, Syst., and Electronics, pp.295-300, Oct. 1998.
[17] Z. Guo and P. Nilsson, “Algorithm and implementation of the K-best sphere decoding for MIMO detection,” IEEE J. Sel. Areas Commun., vol. 24, no. 3, pp. 491-503, Mar. 2006.
[18] A. Van Zelst, “Space division multiplexing algorithms,” in Proc. Elect. Conf., pp. 1218-1221, May 2000, vol. 3.
[19] X. Li and X. Cao, “Low complexity signal detection algorithm for MIMO-OFDM systems,” IEE Electronics Letters, vol. 41, no. 2, pp. 83-85, Jan. 2005.
[20] R. Bohnke, D. Wubben, V. Kuhn, and K. D. Kammeyer, “Reduced complexity MMSE detection for BLAST architectures,” in Proc. IEEE Global Telecommun. Conf., pp. 2258-2262, Dec. 2003.
[21] P. Luethi, A. Burg, S. Haene, D. Perels, N. Felber, and W. Fichtner, “VLSI Implementation of a High-Speed Iterative Sorted MMSE QR Decomposition,” in Proc. IEEE Int. Symp. Circuits Syst., pp. 1421-1424, May 2007.
[22] M. Wenk, M. Zellweger, A. Burg, N. Felber, and W. Fichtner, “K-best MIMO detection VLSI architecture achieving up to 424Mbps,” in Proc. IEEE Int. Symp. Circuits and Syst., pp. 1151-1154, May 2006.
[23] A. Maltsev, V. Pestretsov, R. Maslennikov, and A. Khoryaev, “Triangular systolic array with reduced latency for QR-decomposition of complex matrices,” in Proc. IEEE Int. Symp. Circuits and Syst., pp. 385-388, May 2006.
[24] Z. Y. Huang and P. Y. Tasi, “Efficient implementation of QR decomposition for gigabit MIMO-OFDM systems,” IEEE Trans. Circuit Syst. I, Reg. Papers, vol. 58, no. 10, pp. 2531-2542, Oct. 2011.
[25] Y. T. Hwang and W.D. Chen, “Design and implementation of a high-throughput fully parallel complex-valued QR factorization chips,” IET Circuits, Devices & Syst., vol. 5, no. 5, pp. 424-432, Sept. 2011.
[26] R. C. -H. Chang, C. H. Lin, K. H. Lin, C. L. Huang, and F. C. Chen, “Iterative QR decomposition architecture using the modified Gram-Schmidt algorithm for MIMO system, ” IEEE Trans. Circuits Syst. I. Reg. Paper, vol. 57, no. 5, pp. 1095-1102, May 2010.
[27] C. F. T. Tang, K. J. R. Liu, and S. A. Tretter, “On systolic arrays for recursive complex Householder transformations with applications to array processing,” in Proc. IEEE Acoustics, Speech, and Signal Process., pp. 1033-1036, Apr. 1991.
[28] S. F. Hsiao and J. M. Delsome, “Householder CORDIC algorithms,” IEEE Trans. Comput., vol. 44, no. 8, pp. 990-1001, Aug. 1995.
[29] K. H. Lin, R. C. Chang, C. L. Huang, F. C. Chen, and S. C. Lin, ”Implementation of QR decomposition for MIMO-OFDM detection systems,” in Proc. IEEE Int. Conf. Electronics, Circuits and Syst., pp.57-60, Sept. 2008.
[30] D. Patel, M. Shabany, and P. G. Gulak, “A Low-Complexity High-Speed QR Decomposition implementation for MIMO Receivers,” in Proc. IEEE Int. Symp. Circuits and Syst., pp. 33-36, May 2009.
[31] F. Sobhanmanesh and S. Nooshabadi, “Parametric minimum hardware QR-factoriser architecture for V-BLAST detection,” in IEE Proc. Circuits, Devices and Sys., vol. 153, no. 5, pp. 433-441, Oct. 2006.
[32] S. Y. Kung, “VLSI Array Processors”. Englewood Cliffs, NJ: Prentice-Hall, 1988.
[33] P. Salmela, A. Burian, H. Sorokin, and J. Takala, “Complex-valued QR decomposition implementation for MIMO receivers,” in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Process., pp.1433-1436, Apr. 2008.
[34] Z. Liu, K. Dickson, and J. V. McCanny, “Application-specific instruction set processor for SoC implementation of modern signal processing algorithms,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 4, pp. 755-765, Apr. 2005.
[35] A. Burg, M. Borgmann, M. Wenk, M. Zellweger, W. Fichtner, and H. Bölcskei, “VLSI implementation of MIMO detection using the sphere decoding algorithm,” IEEE J. Solid-State Circuits, vol. 40, no. 7, pp. 1566-1577, July 2005.
[36] M. Wenk, M. Zellweger, A. Burg, N. Felber, and W.Fichtner, “K-Best MIMO detection VLSI architecures achieving up to 424Mbps,”in Proc. IEEE Int. Symp. on Circuits and Syst., pp. 1151-1154, May 2006.
[37] Z. Guo and P. Nilsson, “A VLSI architecture for the Schnorr-Euchner decoder for MIMO system,” in Proc. IEEE 6th Circuits and Syst. Symp. Emerging Technol. Frontiers of Mobile and Wireless Commun., June 2004, pp. 65-68.
[38] K. Wong, C. Tsui, R. Cheng, and W. Mow, “A VLSI architecure of a K-best lattice decoding algorithm for MIMO channels,” in Proc. IEEE Int. Symp. Circuits and Syst., pp. 273-276, May 2002.
[39] T. H. Im, I. Park, J. Kim, J. Yi, J. Kim, S. Yu, and Y. S. Cho, “A new signal detection method for spatially multiplexed MIMO systems and its VLSI implementation,” IEEE Trans. Circuits Syst. II, Express Brief, vol. 56, no. 5, pp. 399-403, May. 2009.
[40] C. H. Liao, T. P. Wang, and T.-D. Chiueh, “A 74.8 mW soft-output detector IC for 8×8 spatial-multiplexing MIMO communications,” IEEE J. Solid-State Circuits, vol. 45, no. 2, pp. 411-421, Feb. 2010.
[41] K. Amiri, C. Dick, R. Rao, and J. Cavallaro, “Novel sort-free detector with modified real-valued decomposition (M-RVD) ordering in MIMO systems,” in Proc. IEEE Global Telecommun. Conf., pp. 1-5, Dec. 2008.
[42] C. P. Schnorr and M. Euchener, “Lattice basis reduction: Improved practical algorithms and solving subset sum problems,” Math Program., vol. 66, no. 2, pp. 181-191, Sept. 1994.
[43] H. Y. Hsu, A. Y. Wu, and J. C. Yeo, “Area-Efficient VLSI design of Reed-Solomon decoder for 10GBase-LX4 optical communication systems,” IEEE Trans. Circuits Syst. II, Express Brief, vol. 53, no. 11, pp. 1245-1249, Nov. 2006.
[44] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: Turbo codes,” in Proc. IEEE Int. Conf. Commun., pp. 1064-1070, May 1993.
[45] 3rd Generation partnership project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing and Channel Coding (Release 9), 3GPP Organizational Partners TS 36.212, Rev. 9.20, Jun. 2010.
[46] J. Hagenauer and L. Papke, “Decoding turbo codes with the soft output Viterbi algorithm (SOVA),” in Proc. IEEE Int. Symp. Inf. Theory, pp. 164, June 1994.
[47] L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inf. Theory, vol. IT-20, no. 2, pp. 284-287, Mar. 1974.
[48] Y. Tong, T. H. Yeap and J. Y. Chouinard “VHDL implementation of a turbo decoder with log-MAP-based iterative decoding,” IEEE Trans. Instrum. Meas., vol. 53, pp.1268-1278, Aug. 2004.
[49] C. M. Wu, M. D. Shieh, C. H. Wu, Y.-T. Hwang, and J.-H. Chen, “VLSI architectural design tradeoffs for sliding-window Log-MAP decoders,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 13, no.4, pp. 439-447, Apr. 2005.
[50] Y. Sun and J. R. Cavallaro, “Efficient hardware implement of a highly-parallel 3GPP LTE/LTE-advance turbo decoder,” Elsevier Science, no. 44, pp. 305-315, July 2010.
[51] C. Roth, S. Belfanti, C. Benkeser, and Q. Huang, “Efficient parallel turbo-decoding for high-throughput wireless systems,” IEEE Trans. Circuits Syst. I, vol. 61, no. 6, pp. 1824-1835, June 2014.
[52] Z. Wang, Z. Chi, and K. K. Parhi, “Area-efficient high-speed decoding schemes for turbo decoders,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 10, no. 6, pp. 902-912, Dec. 2002.
[53] M. M. Mansour and N. R. Shanbhag, “VLSI architectures for SISO-APP decoders,” IEEE Trans. Very Large Scale Integrat. (VLSI) Syst., vol. 11, no. 4, pp. 627-650, Aug. 2003.
[54] J. Vogt and A. Finger, “Improving the Max-Log-MAP turbo decoder,” Electronics Lett., vol. 36, no. 23, pp. 1937-1939, Nov. 2000.
[55] B. Hassibi and B. Hochwald, “High-rate codes that are linear in space and time,” IEEE Trans. Inform. Theory, vol. 48, pp. 1804-1824, July 2002.
[56] C. A. Shen, and A. M. Eltawil, “A radius adaptive K-Best decoder with early termination: algorithm and VLSI architecture,” IEEE Trans. Circuit Syst. I: Regular Papers, vol. 57, no. 9, pp. 2476-2486, Sept. 2010.
[57] C. Studer, A. Burg, and H. Bölcskei, “Soft-output sphere decoding: algorithms and VLSI implementation,” IEEE J. Sel. Areas Commun., vol. 26, no. 2, pp. 290-300, Feb. 2008.
[58] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error correction coding and decoding: Turbo-codes,” in Proc. IEEE Int. Conf. Commun., vol. 2, pp. 1064-1070, May 1993.
[59] P. Robertson, E. Villebrn, and P. Hoeher, “A comparison of optimal and sub-optimal MAP decoding algorithms operating in log domain,” in Proc. IEEE Int. Conf. Commun., pp. 1009-1013, June 1995.
[60] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, “Serial concatenation of interleaved codes: performance analysis, design and iterative decoding,” IEEE Trans. Inform. Theory, vol. 44, pp. 909-926, May 1998.
[61] S. Chen, T. Zhang, and Y. Xin, “Breadth-first tree search MIMO signal detector design and VLSI implementation,” in Proc. IEEE Military Commun. Conf., vol. 3, pp. 1470-1476, Oct. 2005.
[62] C. J. Huang, C. W. Yu, and H. P. Ma, "A power-efficient configurable low-complexity MIMO detector," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 56, no. 2, pp. 485-496, 2009.
[63] R. S. Yazdi and T. Kwasniewski, “Configurable K-best MIMO detector architecture,” in Proc. 3rd Inf. Symp. Commun. Control and Signal Process., pp. 1565-1569, Mar. 2008.
[64] H. L. Lin, R. C. Chang, and H. L. Chen, “A high-speed SDM-MIMO decoder using efficient candidate searching for wireless communication,” IEEE Trans. Circuits Syst. II, Express Brief, vol. 55, no. 3, pp. 289-293, Mar. 2008.
[65] S. Baero, J. Hagenauer, and M. Witzke, “Iterative detection of MIMO transmission using a list-sequential (LISS) detector,” in Proc. IEEE Int. Conf. Commun., vol. 4, pp. 2653-2657, May 2003.
[66] E. Zimmermann, S. Bittner, and G. Fettweis, “Complexity reduction in iterative MIMO receivers based on EXIT chart analysis,” 4th Int. Sym. Turbo Codes&Related Topics; 6th Int. ITG-Conf. Source and Channel Coding, pp. 1-6, Apr. 2006.
[67] J. S. Lin, S. H. Fang, M. D. Shieh, and Y. H. Jen, “Design of high-throughput MIMO detectors using sort-free and early-pruned techniques,” in Proc. IEEE Region 10 Conf., pp. 1513-1516, Nov. 2010.
[68] D. W. Waters and J. R. Barry, “The Chase family of detection algorithms for multiple-input multiple-output channels,” IEEE Trans. Signal Process., vol. 56, no. 2, pp. 739-747, Feb. 2008.
[69] R. Wang and G.B. Giannakis, “Approaching MIMO channel capacity with reduced-complexity soft sphere decoding,” in Proc. IEEE Wireless Commun. and Network Conf., vol.3, pp. 1620-1625, Mar. 2004.
[70] P. Marsch, E. Zimmermann, and G. Fettweis, “Smart candidate adding: A new low-complexity approach towards near-capacity MIMO detection,” in Proc. 13th Eur. Signal Process. Conf., pp.1-4, Sept. 2005.
[71] C. Studer, A. Burg, and H. Bölcskei, “Soft-output sphere decoding: Algorithms and VLSI implementation,” IEEE J. Sel. Areas Commun., vol. 26, no. 2, pp. 290-300, Feb. 2008.
[72] C. Studer and H. Bölcskei, “Soft-input soft-output single tree-search sphere decoding,” IEEE Trans. Inform. Theory, vol. 56, no. 10, pp. 4827-4842, Oct. 2010.
[73] J. Jaldén and B. Ottersten, “Parallel implementation of a soft output sphere decoder,” in Proc. Asilomar Conf. Signals, Syst. and Computers, pp. 581-585, Nov. 2005.
[74] E. M. Witte, F. Borlenghi, G. Ascheid, R. Leupers, and H. Meyr, “A scalable VLSI architecture for soft-input soft-output single tree-search sphere decoding,” IEEE Trans. Circuits Syst. II, vol. 57, no. 9, pp. 706-710, Sept. 2010.
[75] J. Hagenauer and C. Kuhn, “The list-sequential (LISS) algorithm and its application,” IEEE Trans. Commun., vol. 55, no. 5, pp. 918-928, May 2007.
[76] K. Kilhwan, J. Yunho, L. Seongjoo, and K. Jaeseok, “Near-ML soft-MIMO detector with reduced complexity,” in Proc. IEEE Region 10 Conf., pp. 1-5, Nov. 2012.
[77] Y. Jianpeng, M. Jun, and M. Zhigang, “Parallel SFSD MIMO detection with SOFT-HARD combination enumeration,” IEEE Workshop on Signal Process. Syst., pp. 228-233, Oct. 2011.
[78] C. Xi, L. Jiangpeng, M. Jun, W. Junfeng, and H. Guanghui, “A low complexity soft-input soft-output fixed-complexity sphere decoding algorithm,” 8th Int. Conf. Wireless Commun., Networking and Mobile Computing, pp. 1-4, Sept. 2012.
[79] T. Tsubaki and H. Ochiai, “A new candidate adding algorithm for coded MIMO systems with fixed-complexity detection,” IEEE Int. Conf. Commun., pp. 4525-4529, June 2013.
[80] X. Wu and J. S. Thompson, “A fixed-complexity soft-MIMO detector via parallel candidate adding scheme and its FPGA implementation,” IEEE Commun. Letters, vol. 15, pp. 241-243, Feb. 2011.
[81] J. Hagenauer and P. Hoeher, “A Viterbi algorithm with soft-decision outputs and its applications,” in Proc. IEEE Global Telecom. Conf., vol. 3, pp. 1680-1686, Nov. 1989.
[82] P. Robertson, P. Hoeher, and E. Villebrun, “Optimal and sub-optimal maximum a posteriori algorithms suitable for turbo decoding,” European Trans. Telecommun., vol. 8, pp. 119-125, Mar./Apr. 1997.
[83] A. J. Viterbi, “An intuitive justification and simplified implementation of the MAP decoder for convolutional codes,” IEEE J. Sel. Areas Commun., vol. 16, no. 2, pp. 260-264, Feb. 1998.
[84] C. M. Wu, M. D. Shieh, and C. H. Wu, “Memory arrangements in turbo decoders using sliding-window BCJR algorithm,” in Proc. IEEE Int. Symp. Circuits Syst. (ISCAS’02), May 2002, pp. V-557-V-560.
[85] A. Worm, H. Lamm, and N. Wehn, “A high-speed MAP architectures with optimized memory and power consumption,” in Proc. IEEE Workshop Signal Process. Syst., pp. 265-274, Oct. 2000.
[86] E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, “Closest point search in lattices,” IEEE Trans. Inform. Theory, vol. 48, no. 8, pp. 2201-2214, Aug. 2002.
[87] C. Berrou, A. Glavieux and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: Turbo-codes,” in Proc. IEEE Inf. Conf. Commun., vol. 2, pp. 1064-1070, May 1993.