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研究生:吳柏均
研究生(外文):Po-Chun Wu
論文名稱:使用三維信號的柵狀編碼調變技術之效能分析
論文名稱(外文):Performance Analysis On Trellis-Coded Modulation Schemes Using Three-Dimensional Signal Sets
指導教授:李程輝
指導教授(外文):Tsern-Huei Lee
學位類別:碩士
校院名稱:國立交通大學
系所名稱:電信工程系所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:62
中文關鍵詞:柵狀編碼碼調變三維信號點
外文關鍵詞:TCMTrellis-Coded Modulationtrellis-coded modulationthree dimensional3 dimensional3 Dthree Dsignal setconstellation
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以傳統的柵狀編碼調變技術來說,二維的信號,比如說像是 -PSK或是 -QASK(其中 ),通常都會被用在許多傳輸系統當中。在這篇論文裡,我們將會介紹所謂「三維信號」的想法,以及「將三維信號視為二維信號的延伸」的概念。以傳統上使用二維信號的柵狀編碼調變技術為參考,我們會敘述建立三維信號的方式、將三維信號分解(partition)為小組(subset)的方式、以及將二進位的資料對應到這些信號的方式。相對於發送端的編碼,接收端使用了一種叫做「軟性決定維特比演算法」的方式來解碼。我們會舉出一些二維的以及三維的例子,並且將這些例子做分析比較。我們可以由結果來推斷,使用三維信號的柵狀編碼調變技術的錯誤品質會比使用二維信號的來得好。
In conventional trellis-coded modulation (TCM) schemes, two-dimensional constellations such as -PSK or -QASK, where , are generally used in many transmission systems. In this thesis, the idea of three-dimensional constellations is introduced and the concept of treating three-dimensional constellations as an expansion of two-dimensional constellations is presented. Conventional TCM schemes using two-dimensional constellations are taken as references. The method of constructing three-dimensional constellations and partitioning the signal points into subsets and mapping information bits into those signal points are described. Soft-decision Viterbi algorithm (SOVA) is applied for the decoding process of the presented TCM schemes. A number of examples are given and comparisons are made. We conclude that three-dimensional TCM schemes perform better than conventional two-dimensional TCM schemes.
Index

Chinese Abstract i

English Abstract ii

Acknowledgements iii

Index iv

List of Tables vii

List of Figures viii

Chapter 1 Introduction 1

1.1 Background 1

1.1.1 Channel Capacity and Channel Coding 1

1.1.2 Conventional Sense 1

1.1.3 Driving Force for New Code Design 2

1.1.4 Trellis-Coded Modulation 3

1.2 Channel Capacity of Multilevel/Phase Modulation Channels 4

1.2.1 In Terms of Channel Capacity 4

1.2.2 Interpretation of The Channel Capacity 8

1.3 Organization of the Thesis 9


Chapter 2 Ungerboeck’s TCM Scheme 11

2.1 Four-State Trellis Code for 8-PSK Modulation 12

2.1.1 Signal Sets And Trellis Diagrams 12

2.1.2 Rules for Assignment of The Signals 14

2.1.3 The Soft-Decision Decoding 15

2.1.4 The Free Distance And Error Events 17

2.2 Eight-State Trellis Code for Amplitude/Phase Modulation 19

2.2.1 The Effect of Set Partitioning 19

2.2.2 Examples of Error Bursts 22

2.3 Design of Trellis-Coded Modulation Schemes 24

2.3.1 General Structure of Encoder/Modulator for TCM 25

2.3.2 Mapping by Set Partitioning 26

2.3.3 Convolutional Codes for Trellis-Coded Modulation 29

Chapter 3 TCM Schemes Using 3-D Constellations 32

3.1 Four-State Trellis Code for 8-Point Cubic Modulation 32

3.1.1 Basic Structure of The Proposed Schemes 32

3.1.2 Rate-1/2 Convolutional Encodes 34

3.1.3 The Three-Dimensional Signal Set 35

3.1.4 The Modified Three-Dimensional Signal Set 37

3.1.5 Free Distances of Cubic and Cuboid Signal Sets 40

3.2 Eight-State Trellis Code for 16-Point Cubic Modulation 42

3.2.1 Two-Dimensional TCM Schemes 42

3.2.2 The Three-Dimensional Signal Set 43

3.2.3 The Modified Three-Dimensional Signal Set 45

3.2.4 Free Distances of Cubic and Cuboid Signal Sets 46

3.2.5 The Design Lemma of Three-Dimensional Signal Sets 48

Chapter 4 Computer-Aided Simulation Results 51

Chapter 5 Conclusions 59

Appendix:The Structure of Transmitter And Receiver 60

Bibliography 62








List of Tables

2-1 Comparison of uncoded 4-PSK to coded 8-PSK (at high SNR) 18

2-2 Four error paths at the free distance from 23

3-1 An error path at the free distance from 47







List of Figures

1-1 Channel signal sets of (a) one- (b) two-dimensional constellation 6

1-2 Channel capacity of band-limited AWGN channels with discrete-valued input and continuous-valued output. (a) One-dimensional modulation. (b) Two-dimensional modulation 8

2-1 (a) Uncoded four-phase modulation (4-PSK). (b) Four-state trellis-coded eight-phase modulation (8-PSK) 13

2-2 A realization of an encoder-modulator for four-state coded 8-PSK 5

2-3 Shortest path diagram 16

2-4 Error-event probability versus signal-to-noise ratio for uncoded 4-PSK and four-state 8-PSK 18

2-5 Set partitioning of 16-QASK and 32-CROSS signal sets 20

2-6 The trellis diagram of eight-state amplitude/phase modulation 21

2-7 General structure of encoder/modulator for TCM 25

2-8 Set partitioning of 8-PSK signals with increasing 27

2-9 A four-state trellis diagram 28

2-10 Two realizations of rate- , convolutional encoders. (a) Systematic encoder with feedback (b) Feedback-free encoder 31

3-1 Simplified System Diagram (For Computer Simulation) 32

3-2 Basic structure of four state trellis code for 8-Point Cubic Modulation 33

3-3 Three realizations of rate- convolutional encoders.(a) Feedback-free encoder with . (b) Systematic encoder with feedback and . (c) Feedback-free encoder with 34

3-4 8-point cubic signal set 35

3-5 Set partitioning diagram of 8-point cubic signal set 36

3-6 Subset for (a) 8-PSK (b) 8-point cubic, signal sets 38

3-7 Subset for modified 8-point cubic signal set 38

3-8 Modified 8-point cubic signal set 39

3-9 Set partitioning diagram of modified 8-point cuboid signal set 40

3-10 Set partitioning diagram of a redundant 16-QASK signal set 42

3-11 16-point cubic signal set 43

3-12 Set partitioning diagram of the 16-point cubic signal set 44

3-13 Modified 16-point cubic signal set 45

3-14 Set partitioning diagram of the 16-point cuboid signal set 46

3-15 The trellis diagram of 8-state 16-point cubic TCM 47

3-16 The design lemma of the 16-point cuboid signal set 49

3-17 A 3-D signal set and its corresponding 2-D reference 50

4-1 Uncoded 4-PSK and uncoded 8-PSK 51

4-2 Uncoded 8-point cubic and cuboid signal sets 52

4-3 Uncoded 4-PSK, 4-state 8-PSK TCM 53

4-4 4-state 8-PSK TCM, 4-state 8-point cubic and cuboid TCM 54

4-5 Uncoded 8-PSK, 8-state 16-QASK TCM 55

4-6 A rate- convolutional encoder and a trellis diagram 55

4-7 8-state 16-QASK, 16-point cubic and 16-point cuboid TCM 56

4-8 4-state 8-PSK TCM and 64-state 8-PSK TCM 57

4-9 4-state 8-point cubic, cuboid TCM schemes and 64-state 8-point cubic, cuboid TCM schemes 58

A-1 The structure of the three-dimensional signal transmitter. 60

A-2 The structure of the three-dimensional signal receiver. 61
[1] Ungerboeck, G., “Channel coding with multilevel/phase signals,” Information Theory, IEEE Transactions on , Volume: 28 , Issue: 1 , Jan 1982 Pages:55 - 67.
[2] Ungerboeck, G., “Trellis-coded modulation with redundant signal sets Part I: Introduction,” Communications Magazine, IEEE , Volume: 25 , Issue: 2 , Feb 1987 Pages:5 – 11
[3] Ungerboeck, G., “Trellis-coded modulation with redundant signal sets Part II: State of the art,” Communications Magazine, IEEE , Volume: 25 , Issue: 2 , Feb 1987 Pages:12 – 21
[4] R. G. Gallager, Information Theory and Reliable Communication. New York, Wiley, 1968, p. 74.
[5] Ungerboeck, G. and Csajka I., “On improving data-link performance by increasing the channel alphabet and introducing sequence coding,” Int. Symp. Inform. Theory, Ronneby, Sweden, June 1976.
[6] Bossert, M. “Channel Coding for Telecommunications,” John Wiley & Sons, October 1999.
[7] G. D. Forney, Jr., “Convolutional codes I:Algebraic structure,” Information Theory, IEEE Transactions on , Volume: IT-16 , Nov. 1970. Pages:720 - 738.
[8] G. D. Forney, Jr., R. G. Gallager. G. R. Lang, F. M. Longstaff, and S. U. Qureshi, “Efficient modulation for band-limited channels,” IEEE Trans. Selected Area in Comm. , Vol. SAC-2, pp.632-647, Sep. 1984.
[9] Rodger, E. Ziemer. and Roger, L. Peterson., “Introduction to digital communication 2nd edition.” Prentice-Hall, Inc. 2001.
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