On Bounded Weight Codes

The maximum size of a binary code is studied as a function of its length N, minimum distance D, and minimum codeword weight W. This function B(N,D,W) is first characterized in terms of its exponential growth rate in the limit as N tends to infinity for fixed d=D/N and w=W/N. The exponential growth rate of B(N,D,W) is shown to be equal to the exponential growth rate of A(N,D) for w <= 1/2, and equal to the exponential growth rate of A(N,D,W) for 1/2< w <= 1. Second, analytic and numerical upper bounds on B(N,D,W) are derived using the semidefinite programming (SDP) method. These bounds yield a non-asymptotic improvement of the second Johnson bound and are tight for certain values of the parameters

Skip-Sliding Window Codes

Constrained coding is used widely in digital communication and storage systems. In this paper, we study a generalized sliding window constraint called the skip-sliding window. A skip-sliding window (SSW) code is defined in terms of the length $L$ of a sliding window, skip length $J$, and cost constraint $E$ in each sliding window. Each valid codeword of length $L + kJ$ is determined by $k+1$ windows of length $L$ where window $i$ starts at $(iJ + 1)$th symbol for all non-negative integers $i$ such that $i \leq k$; and the cost constraint $E$ in each window must be satisfied. In this work, two methods are given to enumerate the size of SSW codes and further refinements are made to reduce the enumeration complexity. Using the proposed enumeration methods, the noiseless capacity of binary SSW codes is determined and observations such as greater capacity than other classes of codes are made. Moreover, some noisy capacity bounds are given. SSW coding constraints arise in various applications including simultaneous energy and information transfer.Comment: 28 pages, 11 figure

Performance Analysis of Double-Weight Optical CDMA Under the Same-Bit-Power Assumption

To provide differential quality-of-service in optical code-division multiple access, variable-weight codes were proposed and analyzed under a conventional assumption of identical power in every optical pulses (i.e., same chip power). To account for power limit of some laser sources, we assume the use of same optical power in each bit duration (i.e., same bit power) in this paper. For illustration, we focus our study on double-weight codes under both same-chip-power and same-bit-power assumptions. A new and better approximate performance-analytical model for double-weight codes is developed and validated with computer simulation. We show that heavy-weight codes do not always perform better than light-weight codes under the same-bit-power assumption, contrary to previous findings under the same-chip-power assumption

Double-Weight Optical CDMA Systems With The Same-Bit-Power Assumption

在這高速率傳輸且多樣化的時代，如何提供快速且高品質的多媒體通訊服務為重要的課題。在光纖分碼多工系統中，為了要滿足不同服務質量的品質需求，以往可變碼重光纖碼都是採用相同碼片功率之假設下進行討論跟分析。為了要考慮傳送光纖功率的限制，我們提出了光纖分碼多工系統採用傳送相同位元功率的課題下做討論。在本篇論文中，我們針對雙碼重光纖分碼多工系統採用傳送相同位元功率和採用相同碼片功率的系統表現作比較討論。我們設計了一種新的、較準確的分析模型來討論雙碼重光纖分碼多工系統的系統效能。最後，我們結果顯示出，較重碼重碼之系統效能表現不一定比較輕碼重之系統效能表現來的好。在相同位元功率的假設下，較輕碼重之系統效能將獲得改善，並且打破以往使用碼重越大系統效能越好的觀念。Communication technologies are expected to provide multiple-rate transmission and support the growing popularity of multimedia services flexibly and efficiently. To provide differential quality-of-service in optical code-division multiple access, variable-weight optical codes were designed and analyzed under a conventional assumption of identical power in every optical pulses (i.e., same chip power). To account for power limit of laser sources, we assume the use of same optical power in each bit duration (i.e., same bit power) in this thesis. For illustration, we focus our study on double-weight codes under both same-chip-power and same-bit-power assumptions. A new and accurate performance-analytical model for double-weight codes is developed and validated with computer simulation. We show that heavy-weight codes do not always perform better than light-weight codes under the same-bit-power assumption, contrary to previous findings under the same-chip-power assumption.Abstract iv Contents v List of Figures vi Chapter 1 Introduction 1 1.1 Background 1 1.2 Motivation and Outline of Thesis 1 Chapter 2 Variable-Weight O-CDMA With Same Bit Power 3 2.1 Double-Weight O-CDMA With Same Bit Power 3 2.2 Performance Analysis of Same-Bit-Power Double-Weight Codes 5 2.2.1 Analysis of Desired Heavy-Weight Code 5 2.2.2 Analysis of Desired Light-Weight Code 6 Chapter 3 Numerical Simulation and Comparison 9 3.1 Fixing Number of 2D Heavy-Weight Codes 9 3.2 Fixing Number of 2D Light-Weight Codes 11 3.3 Fixing Code Weight of 1D Heavy-Weight Code 12 3.4 Fixing Number of 1D Double-Weight Codes 14 Chapter 4 Conclusions 17 Appendix A Derivation of Error Probability of The Second Case 18 References 2

Bounds on the size and asymptotic rate of subblock-constrained codes

The study of subblock-constrained codes has recently gained attention due to their application in diverse fields. We present bounds on the size and asymptotic rate for two classes of subblock-constrained codes. The first class is binary constant subblock-composition codes (CSCCs), where each codeword is partitioned into equal sized subblocks, and every subblock has the same fixed weight. The second class is binary subblock energy-constrained codes (SECCs), where the weight of every subblock exceeds a given threshold. We present novel upper and lower bounds on the code sizes and asymptotic rates for the binary CSCCs and SECCs. For a fixed subblock length and small relative distance, we show that the asymptotic rate for CSCCs (respectively SECCs) is strictly lower than the corresponding rate for constant weight codes (CWCs) [respectively heavy weight codes (HWCs)]. Furthermore, for codes with high weight and low relative distance, we show that the asymptotic rate for CSCCs is strictly lower than that of SECCs, which contrasts with the fact that the asymptotic rate for the CWCs is equal to that of the HWCs. We also provide a correction to an earlier result by Chee et al. (2014) on the asymptotic CSCC rate. In addition, we present several numerical examples comparing the rates for the CSCCs and SECCs with those for the CWCs and HWCs.Ministry of Education (MOE)Accepted versionH. M. Kiah was supported by the SingaporeMinistry of Education under Research Grants MOE2016-T1-001-156 andMOE2015- T2-2-086. This paper was presented in part at the 2017 IEEEInternational Symposium on Information Theor

Study of Variable-Weight Codes for Wavlength-Time Optical CDMA Systems with Different QoS Requirements

The communication technologies have made great progress in the past decade. It isexpected to provide multiple-rate transmission and support the growing popularity ofmultimedia services with more flexible support efficiently. Therefore, how to design aflexible communication system with variety of data rates and quality-of-services (QoS)requirements for these multimedia services become an important topic. Since optical fibercan offer the vast bandwidth to satisfy the need of multimedia applications, opticalcommunications have been widely applied in multimedia communication systems.Optical code-division multiple-access (O-CDMA) is one of the most popular systemsbecause of the rapid growth of the wavelength-hopping time-spreading (or so-calledwavelength-time) coding technology. In this proposal, we are focusing on how toeffectively provide the number of simultaneous users and required QoS in O-CDMAsystems. Moreover, we will provide the new O-CDMA systems to support multimediaservices with different QoS requirements.In the first year, we shall present the new double-weight O-CDMA system toprovide differential QoS. It is because code weight plays a dominant role in determiningthe performance of an O-CDMA system as heavy-weight codes always outperformlight-weight codes under the assumption of identical power in every optical pulses (i.e.,same chip power). We assume the use of optical codes with the same power in bitduration. In other words, heavy-weight codes do not always perform better thanlight-weight codes since heavy-weight have less power per chip than light-weight codes.We develop a new and more accurate analytical method to evaluate the performance ofthese double-weight codes. The proposed system will be implemented by using Matlab.We shall compare the performance of the new scheme with other approaches and identifythe design issues.In the second year, we shall present the other double-weight O-CDMA system byrelaxing the maximum cross-correlation value in order to improve both the total numbers of subscribers and simultaneous users. The proposed scheme can provide more codecardinality than the original double-weight O-CDMA system with the maximum cross -correlation value of at most one. We shall propose the new double-weight codes witharbitrary cross-correlation values and their system performance analysis. Moreover, weshall analyze the system performance with previous proposed techniques and provide thestrategies on selecting these techniques and identify the design issues.In the third year, we shall present the multiple-weight O-CDMA system to supportmultimedia service with different QoS requirements. The new multiple-weight codeshave three or more kinds of code weights. We shall propose the new wavelength-timecoding design and its system performance analysis. Finally, we shall also compare theperformance of the new scheme with other approaches and identity the design issues.The work from this proposal, as we expect, should prove useful in the success of thedesign and deployment of O-CDMA communication systems with multimedia services.由於人們對於多媒體資訊傳輸的品質要求與日俱增，因此在這高速率傳輸且多樣化的時代，如何提供快速且高品質的多媒體通訊服務為重要的課題。而具有高頻寬、可同時提供大通訊量、傳輸時不易受電磁波干擾與支援遠距離傳輸等優點的光纖通訊就成為提供整合數據、語音與影像等多媒體應用服務中熱門的通訊方式。同時波長跳躍-時間展頻(或稱為波長-時間)編碼技術的快速進步，也帶動了光纖通訊相關領域之產學業界的研究風潮。在本計劃中，申請者將研究如何在光纖分碼多工系統中，有效率的提供可同時使用之用戶數目及所需之傳輸品質。此外我們也將提出一個新的光纖分碼多工系統，以達到在多媒體服務中支援不同服務品質的需求。在本計劃第一年，申請者將提出一個新設計的雙碼重光纖分碼多工系統，針對兩種不同碼重的系統，運用在相同位元能量的假設之下，以改善較輕碼重之系統效能，並且打破以往使用碼重越大系統效能越好的觀念。但此假設造成不同碼重之片能量不同，解調端的門檻會隨片能量而變動，使得不同碼重使用者間所構成的干擾程度會有差異性。另外在展頻碼之最大互相關函數值方面，使用最大互相關函數值為一的二維展頻碼，其目的是為了有效降低用戶之間互相干擾的影響。再藉由透過適當的選取碼的重量、波長及長度等系統參數，可以使所設計的新系統能夠有效率的提供系統之同時使用之用戶數及所需之傳送品質。本計畫提供一套完整的系統效能之理論分析與推導。同時也將使用Matlab 製作模擬系統，藉以評估各種影響系統效能的因素，發展出適合的系統架構。在本計劃第二年，申請者將提出廣義雙碼重光纖分碼多工系統，用以改善第一年所提出之雙碼重光纖分碼多工系統的同時使用之用戶數目及系統效能。此系統設計之參數將因此增加一項碼之互相關值，因為碼之互相關值與其重量相關，所以設計出一有效的方式來改變展頻碼之重量，使系統效能的選擇有更多之彈性將是本年度計畫的重點。我們將提出一具任意相關值之雙碼重碼之設計，選擇適當之碼重與系統參數以達到系統的同時使用者之數目增加並且效能提高之目的。同時將提出系統效能的理論分析推導，並且與前一年度之雙碼重光纖分碼多工系統作比較，以提供計畫之第三年設計新的二維光纖分碼多工系統時的參考。在本計劃的第三年，為了能因應具有不同服務品質之多媒體服務，申請者將提出多碼重光纖分碼多工系統來提供這項問題之解決方法。此設計的主要概念是放寬第一年只有兩種碼重之系統假設，並提出可具三種或更多種碼重的系統架構，在維持傳輸相同位元能量的假設下，達到支援不同服務品質的目的。為了提出更多展頻碼之重量選擇系統，我們將設計更精確的方法來達到這些目標。同時我們也將提供一套完整的系統效能之理論分析與推導，透過軟體程式的模擬對系統架構作先前的評估與輔助理論之研究，以驗證系統運作的可行性。預期本計劃之完成，將對未來之多媒體光纖通訊系統的建立扮演重要的角色