串聯碼(Concatenated Codes)是一個高效益的錯誤更正技術，且已廣泛的被用在各種通訊系統上，如: 行動通訊、廣播系統DVB-T2、太空通訊之CCSDS標準…等。串聯碼基本上是由一個具隨機錯誤更正能力的捲積碼與具突發錯誤更正能力的方塊碼串聯而成，並分別以Viterbi與代數解碼進行單次解碼。雖然這樣的解碼方式以可達成所需的設計目標，然而串聯碼所能提供的誤碼增益(Coding Gain)並未完全發揮出來。假使可以找出串聯碼的最大可能性(ML)解碼方法，提高串聯解碼性能，對提高既有通訊系統的使用效率將有莫大的助益。由於渦輪碼的發明，高性能遞迴解碼方法已逐漸的使用在新一代的通訊系統。如何以遞迴解碼的方法提高串聯解碼性能，是一個有趣的研究主題。
傳統的渦輪結構主要使用相同類型的元件碼(Component Code)串聯而成，如：Turbo Convolutional Codes、或Turbo Block Codes等，針對混合元件碼的渦輪碼研究較少，這也是前述串聯碼使用ML解碼尚未解決的議題。在本文中，將以混合渦輪碼(HTC, Hybrid Turbo Codes)為研究主題。探討Serial HTC (SHTC) 及Parallel HTC (PHTC)的編解碼架構、方法、性能與分析。在SHTC方面，我們提出兩種新的解碼方法並與傳統的渦輪解碼方法做一比較。我們發現所提的方法之一，得到優於傳統的渦輪解碼方法的性能表現。除此之外，我們也探討了BCJR及SOVA在HTC的效能差異，如預期一般BCJR仍然優於SOVA。在分析方面，我們將外部資訊轉換圖(EXIT Chart)分析技術延伸至混合渦輪解碼方法，其EXIT Chart均能準確預測所討論的方法。在白色高斯雜訊通道下，所提的PHTC與STHC在BER=10-5時分別能達到距離Shannon Limit 1.5dB與2dB的通道容量表現。

Concatenated codes are a class of powerful error-correction codes. It has been widely used in a variety of communication systems such as mobile communications, DVB-T2 broadcasting standard, and the CCSDS space communication standard. A typical concatenated code consists of a random-error correcting convolutional code and a burst-error correcting block code which are decoding with a Viterbi algorithm and an algebraic decoder, respectively. The error performance requirement is usually satisfied, however, the coding gain is still not fully exploited due to lack of maximum likelihood (ML) decoding. If ML decoding is possible, many existing communication systems can improve their performance further. Since the invention of turbo codes, high-performance turbo signal processing becomes a paradigm of new communication systems. How to improve the performance of concatenated codes via turbo decoding is an interesting research topic.
Traditional turbo codes consist of two identical component codes such as turbo convolutional codes and turbo block codes. The researches about hybrid-component turbo codes are rare, that is the open problem of ML decoding for concatenated codes. In this thesis, we will focus on the study of hybrid turbo codes (HTC). Many important issues of serial HTC (SHTC) and parallel HTC (PHTC) are studied in detail including the encoding/decoding architectures, decoding methods, performance and analysis. In SHTC, we propose two new decoding methods and one of the proposed methods outperforms the traditional decoding method. Both the BCJR and SOVA are employed. As expected, the BCJR is better than SOVA for all kind of decoding methods. We extend the extrinsic information transfer chart (EXIT Chart) to the analysis of HTCs and the performances prediction of EXIT chart is consistent with the simulation results. For AWGN channels and BER = 10-5, the capacity gap of the proposed PHTC and SHTC are 1.5dB and 2dB away from Shannon’s limits, respectively.

中文摘要................................................................................................. I
英文摘要................................................................................................ II
誌謝.......................................................................................................IV
圖目錄................................................................................................. VII
第1 章 、緒論.......................................................................................1
1.1 簡介...........................................................................................1
1.2 研究動機....................................................................................2
1.3 本文架構....................................................................................4
第2 章 、相關原理介紹........................................................................5
2.1 基本通道編碼............................................................................5
2.1.1 Convolutional Code編碼.................................................5
2.1.2 BCH code 編碼...............................................................7
2.2 渦輪碼分類..............................................................................11
2.2.1 傳統渦輪編碼................................................................11
2.2.2 混合渦輪編碼................................................................13
2.2.3 並聯混合渦輪編碼(PHTC)............................................14
2.2.4 串聯混合渦輪編碼(SHTC)............................................15
2.3 SISO 解碼演算法.....................................................................17
2.3.1 最大事後機率演算法....................................................17
2.3.2 軟式輸出Viterbi演算法...............................................24
2.4 外部資訊轉換圖分析..............................................................28
第3 章 、混合渦輪碼解碼演算法......................................................32
3.1 並聯混合渦輪解碼..................................................................32
3.2 串聯混合渦輪解碼：Z0法......................................................37
3.3 串聯混合渦輪解碼：Zp法......................................................40
3.4 串聯混合渦輪解碼：Z1法......................................................44
第4 章 、混合渦輪碼解碼分析..........................................................48
4.1 各解碼器之外部資訊轉換圖分析...........................................48
4.2 並聯混合渦輪解碼之系統架構分析.......................................54
4.3 串聯混合渦輪解碼之系統架構分析.......................................57
4.3.1 串聯混合渦輪解碼Z0法之系統架構分析....................57
4.3.2 串聯混合渦輪解碼Z1法之系統架構分析....................62
第5 章 、結論與未來展望..................................................................67
參考文獻...............................................................................................68

[1] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit
error-correcting coding and decoding: Turbo-codes,” in Proc. IEEE
International Communications Conference (ICC’93), Geneva,
Switzerland, May. 1993, pp. 1064–1070.
[2] C. Xu, “Soft decoding algorithm for RS-CC concatenated codes in
WiMAX system,” in Proceedings of the 65th IEEE International
Conference on Vehicular Technology Conference, pp. 740–742. 2007.
[3] S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara, “Soft-output
decoding algorithms in iterative decoding of turbo codes,” in TDA
Progress Report 42–124, Jet Propulsion Lab, NASA, Feb. 15, 1996.
[4] S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara, “A soft-input
soft-output maximum a posteriori (MAP) module to decode parallel and
serial concatenated codes," in TDA Progress Report 42–127, Jet
Propulsion Lab, NASA, Nov. 15, 1996.
[5] J. Hagenauer, E. Offer and L. Papke, “Iterative decoding of binary block
and convolutional codes,” IEEE Trans. Inform. Theory, vol. 42, no. 2,
pp. 429–445, Mar. 1996.
[6] J. K. Wolf, “Efficient maximum likelihood decoding of linear Block
codes using a trellis,” IEEE Trans. Inform. Theory, vol. IT-24, no. 1, pp.
76–80. Sept. 1978.
[7] L. R. Bahl, J. Cocke, F. Jeinek and J. Raviv, “Optimal decoding of
linear codes for minimizing symbol error rate,” IEEE Trans. Inform.
Theory, vol. IT-20, no. 2, pp. 248–287, Mar. 1974.
[8] J. Hagenauer, and P. Hoeher, “A Viterbi algorithm with soft-decision
outputs and its application,” in Proc. IEEE Global Communications
Conf. (GLOBECOM’89), vol. 3, Nov. 1989, pp.1680–1686.
[9] R. M. Pydiah, “Near-optimum decoding of product codes: block turbo
codes,” IEEE Trans Commun., vol. 46, no. 8, pp.1003–1010, Aug.
1998.
[10] M. P. C. Fossorier and S. Lin, “Soft-input soft-output decoding of linear
block codes based on ordered statistics,” in Proc. IEEE Global
Communications Conf. (GLOBECOM’98), Sydney, Australia, Nov.
1998, pp. 2828–2833.
[11] S. ten Brink, “Convergence behavior of iteratively decoded parallel
concatenated codes,” IEEE Trans. Commun., vol. 49, no. 10, pp.
1727–1737, 2001.
[12] F. Brannstrom, “Convergence analysis and design of multiple
concatenated codes,” Ph.D. dissertation, Chalmers Univ. Technol.,
Goteborg, Sweden, Mar. 2004.
[13] S. ten Brink, “Iterative Decoding Trajectories of Parallel Concatenated
Codes”, Proc. 3rd IEEE/ITG Conference on Source and Channel
Coding, pp. 75–80, Munich, Jan. 2000.
[14] M. Tuchler, S. ten Brink and J. Hagenauer, “Measures for tracing
convergence of iterative decoding algorithms,” in Proc. 4th Int. ITG
Conf. Source and Channel Coding, Berlin, Germany, Jan. 2002, pp.
53–60.
[15] M. Isaka, P. A. Martin and P. C. Fossorier, “Design of high-rate serially
concatenated codes with low error floor,” IEICE Trans. on
Fundamentals of Electronics, Communications and Computer Sciences,
vol. E90-A, no. 9, Sept. 2007.
[16] A. Ashikhmin, G. Kramer, and S. ten Brink, “Extrinsic information
transfer functions: Model and erasure channel properties,” IEEE Trans.
Inf. Theory, vol. 50, no. 11, pp. 2657–2673, Nov. 2004.
[17] P. Adde, R. Pyndiah and C. Berrou, “Performance of hybrid turbo
codes,” IEEE Electron Lett., vol. 32, no. 24, pp. 2209–2210, Nov. 1996.
[18] E. Berlekamp, “On decoding binary Bose-Chaudhuri-Hocquenghem
codes,” IEEE Trans. Inform. Theory, vol. 11, no. 4, pp. 577–579, 1965.
[19] J. Massey, “Step-by-step decoding of the
Bose-Chaudhuri-Hocquenghem codes,” IEEE Trans. Inform. Theory,
vol. 11, no. 4, pp. 580–585, Oct. 1965.
[20] J. Massey, “Shift-register synthesis and BCH decoding,” IEEE
Transactions on Information Theory, vol. IT-15, no. 1, pp. 122–127, Jan.
1969.
[21] J. Viterbi, “Error bounds for convolutional codes and an asymptotically
optimum decoding algorithm,” IEEE Trans. Inform. Thoery, vol. IT-13,
no. 2, pp. 260–269, Apr. 1967.
[22] Berrou and A. Glavieux, “Near optimum error correcting coding and
decoding: Turbo-codes,” IEEE Trans. Commun., vol. 44, no. 10, pp.
1261–1271, Oct. 1996
[23] T. H. Liew, B. L. Yeap, J. P. Woodard and L. Hanzo, “Modified MAP
algorithm for extended turbo BCH codes and turbo equalisers,” in Proc.
The First International Conference on 3G Mobile Communication
Technologies, London, United Kingdom, Mar. 2000, pp. 185–189.
[24] 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, no. 3, pp.
909–926, May 1998.
[25] L. Hanzo, T. H. Liew and B. L. Yeap, Turbo coding, Turbo equalization
and Space-time Coding for Transmission over fading channel. John
Wiley & Sons, 2002.
[26] R. H. Morelos-Zaragoza, The Art of Error Correcting Coding. 2nd ed.
John Wiley & Sons, 2006.
[27] T. K. Moon, Error Correction Coding Mathematical Methods and
Algorithms. John Wiley & Sons, 2005.
[28] J. C. Moreira and P. G. Farrell, Essentials of Error-Control Coding.
John Wiley & Sons, 2006.
[29] 楊哲雄, “RS 編碼和迴旋碼：串接碼的軟式決定解碼法,” 交通大學
碩士論文, Aug. 2006.