近年來以展頻(spread spectrum)技巧用於光通訊系統其相關設計、分析工作已廣受重視。我們所熟知質數碼(prime code)用於碼多工(code-division multiple-access,CDMA)光通訊系統的精確分析已被深入的探討。許多合適用於CDMA光通訊系統的光碼也陸續的被提出來，尤其最近有些研究結果顯示，經由合理的調整數碼的長度(length)及配重(weight)可以獲得更佳的系統性能。因而引起我們對此一課題的興趣並試圖尋找其他調整質數碼的法則來改善系統性能，使其在相對的系統容量、頻寬、複雜度之下可以得到較低的誤碼率(Bit Error Rate, BER)。
本論文基本上先建立較接近實際CDMA光通訊系統的數學模式，並用二種數學方法：高斯近似法(Gaussian approximation)及鞍點近似法(saddlepoint approximation)來進行相關性能計算、預估。我們將系統視為非同步多工狀態並將雪崩二極體(avalanche photodiode,APD)納入系統設計中以求儘量接近實際可能的光通訊系統。
本論文將參照質數碼彼此之間關連性(correlation)的特質，嘗試去調整減少碼的長度與配重，並發展出二種不同法則來產生二種修訂的質數碼：MP碼(Modified Prime, MP)及MFP碼(Modified Fibonacci Prime,MFP)，並設定篩選條件從碼群中選擇較恰當的碼型來供系統使用。同時，我們也針對在同步系統中常被提及的QC碼(Quadratic Congruence, QC)進行探討。因為此種光碼比質數碼具有極大量的不同碼型，若經由前述之篩選方式亦可以挑出較適合於非同步系統使用之碼型。本文中將以質數碼為參考基準來比較上述三種碼型在系統性能方面的表現。
經由有步驟的推導，我們除可以計算誤碼率之外也可預估系統設計上重要的參數，例如在特定誤碼率的需求下，我們可推算出信號強度、最佳APD增益、最佳臨界值等參數，同時經由這些性能的比較使我們瞭解所提出修改的質數碼型，將可以達到預期改善系統性能的目的，而QC碼也可經由篩選後用之於非同步光通訊系統。基於本文的探討我們提出了幾種合適的光碼供碼多工光通訊系統使用，而且描述建立了一個實體分析方法，可以做為光通訊系統有效的系統設計工具。

Optical multiple-access systems using code-division multiple-access technique is investigated. The overall system performance is calculated for prime codes, QC codes, modified prime codes and modified Fibonacci prime codes. Theoretical analysis of the output current distribution of optical receivers with avalanche photodiode (APD) is developed. The mean and variance of the output statistics are presented. The bit error rate (BER) can be estimated by using the Gaussian approximation and saddlepoint approximation. The effects of the multiple-user interference, shot noise, and receiver thermal noise are investigated. From the numerical results we find that when the multiple-user interference increases, the saddlepoint approximation yields satisfactory results, but the Gaussian approximation yields higher BER floors.
In this research we present two classes of modified prime codes with less weights and shorter lengths to improve the system performance. We also show the coding algorithm and the method for choosing the suitable optical codes for unsynchronous communication systems. We will show shown how to find the value of system parameters, such as the required signal strength, the APD gain and the decision level. Based on this research we present a realistically analytical method as an effective tool for the design of optical communication systems.

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