在這篇論文中,我們將介紹兩個整合等化(Equalization)與通道編碼(Channel coding)的系統.
第一個系統使用了Tomlinson-Harashima 預編碼的技術.推廣性低密度查核碼(Generalized Low Density Codes)以及渦輪碼(Turbo Codes)將在此系統中被使用到. 推廣性低密度查核碼可看作是低密度查核碼的一種推廣型式.在性能表現上, 推廣性低密度查核碼也能與渦輪碼相提並論.與渦輪碼相似地,重複性的演算法(BCJR, SOVA)將被使用在推廣性低密度查核碼的解碼上.在預編碼系統中,我們知道,接收到的資訊是傳輸信號的一個週期性延伸,再加上白色高斯雜訊.因此在白色高斯雜訊通道上所使用的解碼方式,不能直接地在此預編碼系統上使用.為了補償此一闕漏,我們在BCJR演算法上做了一些修正.除此之外,我們亦提出了一個方式,可以降低Tomlinson-Harashima 預編碼系統的平均傳送功率.經由模擬的驗證,我們發覺降低傳送功率後的系統,其位元錯誤率可以有大約0.2~0.5dB的增益.針對此降低傳功率的方法,我們也考慮如何將低其複雜度.我們發覺複雜度可以被將低很多,而性能的損失卻不多.
第二個系統是渦輪等化系統.此系統中使用了推廣性低密度查核碼來作為它的架購.在此系統中,一般的方式與低複雜度的方式將被列入考慮.

Abstract
In this thesis, two systems which integrate the design of equali- zation and channel coding are investigated.
The first system employs Tomlinson-Harashima precoding. Generalized Low Density (GLD) codes and Turbo codes are used in this system. GLD codes can be considered as the generalization of Low Density Parity Check (LDPC) codes. The performance of GLD codes is comparable to that of Turbo codes. Similar to Turbo codes, iterative algorithms (BCJR, SOVA) are used in the decoding of GLD codes. In the precoding system, the received data is a periodic extension of the transmitted data constellation, plus the white noise. Thus the decoding algorithms used in the AWGN channel can not be directly applied to this system. To compensate for this problem, we make a little modification on the original BCJR algorithm. In addition, an approach for reducing the average transmitted power in Tomlinson -Harashima precoding is proposed. Through simulation, we find that the bit error rate (BER) of the power-reduced system can achieve a gain about 0.2~0.5dB. A complexity-reduced approach for power reduction is also considered. The complexity can be greatly reduced with little loss in performance.
The second system is Turbo Equalization that uses GLD codes as its coding scheme. Both conventional and low-complexity approaches for joint Turbo Equalization and GLD codes are considered.

Contents
1 Introduction 1
2 Preliminaries
3
A. Equivalent discrete-time white noise filter model and
Equalization…………………..………………………………..3
B. Iterative Decoding and Equalization─Turbo Equalization….7
C. Equalization at the Transmitter─Tomlinson-Harashima
Precoding………………………………………………………10
D. Generalized Low Density Codes……………………………..16
3 A Study On Combined Turbo Equalization and
GLD decoding 23
3.1 Introduction…………………………………………………23
3.2 Conventional Schemes……………………………………..23
3.2-1 System structures …………………………………23
3.2-2 Simulation Results...……………………………..24
3.3 Low Encoding Complexity Schemes… ..…………………27
3.3-1 System structures …………………………………27
3.3-2 Simulation Results.. .……………………………..31
4 Coded Tomlinson-Harashima Precoding Systems 36
4.1 Introduction…………………………………………………36
4.2 Transmitter…..….……………………………………….….37
4.3 Receiver and Decoder ( Binary Case)…………………….41
4.3-1 Receiver…………...………………………………41
4.3-2 Decoding─the Extended Constellation and modified MAP algorithms…………………………42
4.3-3 Simulation results ..………… ……………………51
4.4 Receiver and Decoder (Nonbinary Case)………………….53
4.4-1 Receiver…………………………………………..53
4.4-2 Demapper. …………………………………………54
4.4-3 Decoding Schemes. .………………………………58
4.4-4 Simulation Results. ……………………………….63
5 Transmitted Power Reduction In TH Precoding
Systems 67
5.1 Introduction………………………………………………. 67
5.2 Reducing the Average Transmitted Power by Using M
Sequence… ……………………………………….……….. 67
5.3 Simulation Results. ..………….…………………………..74
5.4 Complexity-Reduced Approach……………………………79
5.5 Power Reduction for Different Channels………………….82
6 Conclusions and Future Works 83

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