近年來隨著光纖分碼多工技術的日益成熟，以及二維波長跳躍-時間展頻(或稱為波長-時間)編碼技術的蓬勃發展，帶動整個光纖通訊領域的研究風潮。相較於傳統僅使用一個維度的編碼技術，二維波長-時間編碼技術除了可以有效增加系統中可提供之同時使用者數目外，更具有改善系統效能與提供較彈性的設計等優點。因此，本論文將針對使用這種二維編碼技術的設計概念，提出數個應用於光纖分碼多工系統的二維波長-時間碼，並且提供其系統效能的理論分析與推導。
首先，在論文的第一部份提出一個具有較多碼數目與最大相關性函數值為2的新式二維波長-時間碼，稱之為二次同餘載波跳頻質數碼。並將其應用於多碼鍵移光纖分碼多工系統，藉由指定每個用戶多個碼字來進行資料傳輸，以取代傳統光纖分碼多工系統中僅分配每個用戶一個碼字來進行資料傳輸的開關鍵移系統。由於所傳送的每個碼字用來表示帶有數個位元資料的符元，因此不僅可以提高系統的資料傳輸速率，在碼字的保密方面也獲得改善。同時透過理論分析的結果可以發現，多碼鍵移光纖分碼多工系統在系統效能、資料傳輸速率、碼字的保密性與硬體複雜度上提供較佳的折衷解決辦法。
由於人們對於資料、語音及影像等多媒體通訊服務的高度需求，未來的通訊系統能夠同時支援不同的傳輸速度與服務品質的多媒體服務是必然的發展趨勢。因此將針對論文第一部份所提出的二次同餘載波跳頻質數碼，提出”多碼長”的編碼架構，利用指定每個用戶不同碼長的展頻碼來達到提供不同傳輸速率的通訊服務之目的。透過理論分析結果可知使用多碼長展頻碼之光纖分碼多工系統的效能表現，會隨著碼長的減少而獲得改善，相較於傳統使用單一碼長之展頻碼進行資料傳輸的光纖分碼多工系統，對於高傳輸品質需求的服務(如語音、影像等多媒體傳輸服務)具有較高優先權的傳輸特性，因此更適合應用於多媒體光纖分碼多工系統。此外，針對所提出多碼長二次同餘載波跳頻質數碼，探討正規化頻譜效益與碼長之間的關係。分析結果顯示正規化頻譜效益隨著使用短展頻碼的用戶數目的增加而獲得改善，但也同時減少系統中可支援之同時使用者數目。因此必須根據系統效益與可支援之同時使用者數目的重要性，有效率地分配系統中所採用展頻碼的碼長分佈。
除了傳輸速率外，在多媒體通訊服務中另一個必須考量的重要議題為系統的服務品質。在本論文提出數個多碼重多碼長展頻碼的編碼架構，透過使用不同碼重與碼長之展頻碼達到支援系統不同服務品質與多速率傳輸的多媒體應用服務之目的。同時由理論分析的結果可知，多速率傳輸的提供僅能利用調整展頻碼的碼長來達成，然而展頻碼的碼重相較於碼長為決定系統效能的主要因素。此外所設計的展頻碼由於具有多碼長編碼的特性，能夠優先提供高速率與高品質的多媒體傳輸，因此將更適合應用於多媒體光纖分碼多工系統。
最後，本論文提出一個新設計的二維波長-時間碼，稱之為雙極-雙極碼，主要是用來改善傳統使用一維展頻碼的光纖分碼多工系統中之可同時使用者數目與系統效能受限於展頻碼碼長的缺點。同時透過理論分析的結果可知，所提出的二維展頻碼在波長跳躍與時間展頻上均使用雙極碼，相較於僅在波長跳躍使用雙極碼，而在時間展頻上採用單極碼之雙極-單極碼而言，所提出的雙極-雙極碼在和雙極-單極碼有相同碼個數的條件下，具有較佳的系統效能表現。Two-dimensional (2-D) wavelength-hopping time-spreading (or so-called wavelength-time) coding schemes have been studied recently for supporting greater numbers of subscribers and simultaneous users than conventional one-dimensional approaches in optical code-division multiple-access (O-CDMA) systems. In this dissertation, several new families of wavelength-time codes are constructed and analyzed.
First, a new family of 2-D wavelength-time codes, so-called quadratic-congruence carrier-hopping prime codes (QC-CHPC) with expanded code cardinality and the maximum cross-correlation function of two (i.e., λc=2) is constructed and analyzed. One application of the large code cardinality of our λc=2 codes is multicode-keying wavelength-time O-CDMA, in which each user is allocated with multiple code matrices, instead of just one code matrix in the conventional on-off keying (OOK) O-CDMA. System throughput is increased because a lower baud rate O-CDMA system can be used to support higher bit-rate transmission since each code matrix is used to represent a "symbol" of several data bits. User code confidentiality is improved because of symbol transmission. The theoretical results show that there is a trade-off between the performance and the number of code matrices per user.
It is expected that future communication systems support a variety of services (e.g., data, voice, and video). Users with different bit-rate and quality-of service (QoS) requirements will be accommodated simultaneously. To support multimedia services with different discrete bit-rate requirements, "multiple-length" QC-CHPCs are constructed algebraically in the dissertation. In contrary to conventional single-length codes, our analysis shows that the performance of these multiple-length codes improves as the code length decreases, thus supporting services prioritization in O-CDMA. Moreover, the relationship of the normalized spectral efficiency (NSE) and code lengths of the multiple-length QC-CHPCs is studied. Our results show that the NSE improves as the number of simultaneous users with short code matrices increases, which, however, decreases the total number of simultaneous users in the systems. Thus, the choice of which code-length distribution to use depends on whether system efficiency or total number of the simultaneous users is important.
Furthermore, QoS is another important issue to be considered in multimedia applications. One way to adjust QoS in O-CDMA is through weight variations in code matrices, besides changing length. In the dissertation, the constructions of the variable-weight, multiple-length CHPC, Extended CHPC (ECHPC), and mutli-wavelength optical orthogonal code (MWOOC) are proposed and analyzed. Our results show that the performance of these variable- weight, multilength codes could be controlled by matrix length, weight, but bit rate is only controlled by matrix length. Our study also shows that short-length codes generate stronger interference than long-length codes. This supports services prioritization in O-CDMA. Moreover, we also show that code weight is the dominating factor in controlling code performance and, thus, is important in guaranteeing the QoS of those media (e.g., video) that require high bit-rate and real support.
Finally, a new family of 2-D wavelength-time codes, so-called bipolar-bipolar codes, is proposed for supporting substantially more subscribers and simultaneous users than conventional 1-D O-CDMA codes in the dissertation. The new codes use bipolar codes for both wavelength hopping and time spreading. As a result, the performance of the bipolar-bipolar coding scheme is better than the bipolar-unipolar coding scheme which uses bipolar codes for wavelength hopping, but unipolar codes for time spreading, while the code cardinality is as good as the latter.1 Introduction 1
2 Wavelength-Time Codes with Maximum Cross-Correlation
Function of Two for Multicode-Keying Optical CDMA 4
2.1 Introduction ........................................4
2.2 Quadratic-Congruence Carrier-Hopping Prime Codes ....6
2.3 Analysis of OOK O-CDMA with QC-CHPCs ...............10
2.4 Analysis of Multicode-Keying O-CDMA with QC-CHPCs ..11
2.5 Analysis of Multicode-Keying O-CDMA with
Time-Shifted QC-CHPCs ..............................17
2.6 Summary ............................................20
3 Spectral Efficiency Study of QC-CHPCs in Multirate
Optical CDMA System 21
3.1 Introduction .......................................21
3.2 Multiple-Length QC-CHPCs ...........................22
3.2.1 Construction Algorithm .......................23
3.2.2 Correlation Properties .......................25
3.3 Performance Analyses ...............................27
3.3.1 Multiple-Length QC-CHPCs in OOK O-CDMA .......28
3.3.2 Multiple-Length QC-CHPCs in Multicode-Keying
O-CDMA .......................................31
3.4 Normalized Spectral Efficiency .....................35
3.4.1 Single-Length CHPCs and QC-CHPCs .............37
3.4.2 Multiple-Length QC-CHPCs .....................38
3.5 Summary ............................................41
4 Variable-Weight, Multiplength Optical Codes for
Wavelength-Time O-CDMA Multimedia Systems 43
4.1 Introduction .......................................43
4.2 Variable-Weight, Multilength Wavelength-Time Codes..44
4.3 Performance Analysis ...............................47
4.4 Numerical Examples .................................53
4.5 Summary ..............................................55
5 Wavelength-Hopping Time-Spreading O-CDMA with
Bipolar Codes 60
5.1 Introduction .......................................60
5.2 Construction of Bipolar-Bipolar Codes ..............61
5.2.1 Cardinality ..................................65
5.3 Performance Analysis ...............................65
5.3.1 Spectral Efficiency ..........................69
5.4 Hardware Implementation ............................71
5.5 Summary ............................................75
6 Conclusions 77
A Proof of Theorem 2.1 79
B Proof of Lemma 3.1 80
C Derivation of Fj'' of the MWOOC 81
D Analysis of Double-Weight, Triple-Length ECHPC 84
E Analysis of Triple-Weight, Triple-Length CHPC 86
F Proof of Lemma 5.1 89
Bibliography 9
