摘要
在這篇論文當中，我們主要考慮在多輸入多輸出區塊衰落通道 (Multi-Input Multi-Output Block Fading Channel) 下的通訊系統。我們嘗試去把在緩慢衰減通道 (Slow Fading Channel) 中表現良好的超正交籬柵時空碼 (Super- Orthogonal Space-Time Trellis Codes) 應用於此。一開始，我們先觀察簡單的阿拉蒙特時空碼 (Alamouti's Space-Time Code) 組態，找出了一些良好的特性並加以研究。其中，我們使用了星狀圖分割 (Constellation Partition) 的方法去劃分所使用的葛雷映射 (Gray Mapping) 星狀圖以獲得具有相同特性的訊號群。以此再配合上籬柵碼 (Trellis Code) 的基本特性，我們即可利用半規則性 (Quasi-Regularity) 的觀念去適當設計超正交籬柵時空碼的架構。在實際的運用上，我們選定了在網格編碼調變 (Trellis-Coded Modulation) 中所使用的線性系統回饋迴旋編碼器 (Linear Systematic Feedback Convolutional Encoder) 做為我們的基本編碼架構。並且，我們提供了一些在建造編碼器上一些簡單且可以拓展的方法與觀念。最後，在我們所考慮的通道上，我們就可以有系統的去建構應用於多輸入多輸出區塊衰落通道之全速率 (Full-Rate) 傳輸且帶有很大編碼增益 (Coding Gain) 和 分集增益 (Diversity Gain) 的超正交籬柵時空碼。將我們的結果與塊狀時空碼 (Space-Time Block Code) 作比較，可以看出在表現上會有很大的改善。進一步地，我們再去比較塊狀時空內碼與交錯位元編碼調變外碼 (Space-Time Block Code – Bit interleaved Coded Modulation) 之串接碼。此種系統架構可以提供較大的分集增益，但由於使用了較大的交錯器 (Interleaver)，會產生相當程度的時間延遲。可以看出在較少天線時，我們所提出的架構表現會比較差。但在天線數增加時，增強的編碼增益及分集增益則會在解碼複雜度 (Decoding Complexity) 差不多的情況之下，使兩者產生相近的結果。

In the thesis, we consider communication systems over the multi-input multi-output (MIMO)
block fading channels. We try to design super-orthogonal space-time trellis codes (SOSTTC),
which can provide great error performance in slow fading channels, for MIMO block fading
channels. The concept of constellation partition and (quasi-) regular property are used to
analyze the code construction. Then, the practical encoder construction and line connection
principle are proposed. We start from simple cases of 2-by-2 SOSTTC and then generalize
our design to di®erent constellations and antennas while full-rate transmission is still main-
tained. A systematic methodology to design powerful coding schemes for MIMO block fading
channels is thus introduced. Compared with the space-time block code (STBC) only system,
our codes can provide much better error performance because of large coding and diversity
gains. We also compare our codes with STBC-bit interleaved coded modulation (BICM)
schemes, which can provide extremely high diversity orders with large time delay. Although
our codes cannot achieve higher diversity orders, we find that the error performance will be
almost the same as those of STBC-BICM schemes at high signal-to-noise ratios and even
better at low signal-to-noise ratios when the numbers of antennas and states increase.

Bibliography
[1] G. J. Foschini and M. J. Gans, "On limits of wireless communications in fading environ-
ment when using multiple antennas," Wireless Personal Communications, vol. 6, pp.
311-335, 1998.
[2] E. Telatar, "Capacity of multi-antenna Gaussian channels," European Transactions on
Telecommunications, vol. 10, pp. 585-595, Nov./Dec. 1999.
[3] V. Tarokh, N. Seshadri, and A. R. Calderbank, "Space-time codes for high data rate
wireless communication: Performance criterion and code construction," IEEE Trans.
Inform. Theory, vol. 44, pp. 744-765, Mar. 1998.
[4] H. Jafarkhani and N. Seshadri, "Super-orthogonal space-time trellis codes," IEEE
Trans. Inform. Theory, vol. 49, pp. 937-950, April 2003.
[5] S. Siwamogsatham and M. P. Fitz, "Improved high rate space-time codes via orthogonal-
ity and set partitioning," in Proc. IEEE Int. Wireless Communications and Networking
Conf. (WCNC), Columbus, OH, Mar. 2002, pp. 264-270.
[6] S. Siwamogsatham and M. P. Fitz, "Improved high rate space-time codes via concate-
nation of expanded orthogonal block code and M-TCM," in IEEE Int. Conf. Commun.
(ICC), Columbus, OH, Apr. 2002, pp. 636-640.
[7] S. Siwamogsatham and M. P. Fitz, "Improved high-rate space-time codes via expanded
STBC-MTCM constructions," in Proc. IEEE Int. Symp. Information Theory (ISIT),
Lausanne, Switzerland, June/July 2002, p. 106.
[8] R. Vaze and B. S. Rajan, "High-rate STBC-MTCM schemes for quasi-static and block-
fading channels," in Proc. IEEE Global Telecommun. Conf., Dallas, Tx, Nov. 2004, pp.
535-539.
[9] S. M. Alamouti, "A simple transmitter diversity scheme for wireless communications,"
IEEE J. Select. Areas Commun., vol. 16, pp. 1451-1458, Oct. 1998.
[10] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, "Space-time block codes from orthog-
onal designs," IEEE Trans. Inform. Theory, vol. 45, pp. 1456-1467, July 1999.
[11] H. E. Gamal and A. R. Hammons, "On the design of algebraic space-time codes for
MIMO block fading channels," IEEE Trans. Inform. Theory, vol. 49, p. 314, Jan. 2003.
[12] E. Biglieri, D. Divsalar, P. J. McLane, and M. K. Simon, Introduction to Trellis-Coded
Modulation with Applications, New York: Maxwell Macmillan, 1991.
[13] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, "Space-time block coding for wireless
communications: Performance results," IEEE J. Select. Areas Commun., vol. 17, pp.
451-460, Mar. 1999.
[14] U. Wachsmann, R. F. H. Fischer, and J. B. Huber, "Multilevel codes: theoretical con-
cepts and practical design rules," IEEE Trans. Inform. Theory, vol. 45, pp. 1361-1391,
July 1999.
[15] L. H. J. Lampe, R. Schober, and R. F. H. Fischer, "Multielvel coding for multiple-
antenna transmission," IEEE Trans. Commun., vol. 3, pp. 203-208, Jan. 2004.
[16] H. Lee, M. Siti, W. Zhu, and M. P. Fitz, "Super-orthogonal space-time block code using
a unitary expansion," in Proc. IEEE Vehicular Tech. Conf., Milan, Italy, Sept. 2004,
pp. 2513-2517.