Deterministic Construction of Binary, Bipolar and Ternary Compressed Sensing Matrices

In this paper we establish the connection between the Orthogonal Optical Codes (OOC) and binary compressed sensing matrices. We also introduce deterministic bipolar $m\times n$ RIP fulfilling $\pm 1$ matrices of order $k$ such that $m\leq\mathcal{O}\big(k (\log_2 n)^{\frac{\log_2 k}{\ln \log_2 k}}\big)$. The columns of these matrices are binary BCH code vectors where the zeros are replaced by -1. Since the RIP is established by means of coherence, the simple greedy algorithms such as Matching Pursuit are able to recover the sparse solution from the noiseless samples. Due to the cyclic property of the BCH codes, we show that the FFT algorithm can be employed in the reconstruction methods to considerably reduce the computational complexity. In addition, we combine the binary and bipolar matrices to form ternary sensing matrices ($\{0,1,-1\}$ elements) that satisfy the RIP condition.Comment: The paper is accepted for publication in IEEE Transaction on Information Theor

Applications of perfect difference codes in fiber-optics and wireless optical code-division multiplexing/multiple-access systems

After establishing itself in the radio domain, Spread spectrum code-division multiplexing/multiple-access (CDMA) has seen a recent upsurge in optical domain as well. Due to its fairness, flexibility, service differentiation and increased inherent security, CDMA is proved to be more suitable for the bursty nature of local area networks than synchronous multiplexing techniques like Frequency/Wavelength Division Multiplexing (F/WDM) and Time Division Multiplexing (TDM). In optical domain, CDMA techniques are commonly known as Optical-CDMA (O-CDMA). All optical CDMA systems are plagued with the problem of multiple-access interference (MAI). Spectral amplitude coding (SAC) is one of the techniques used in the literature to deal with the problem of MAI. The choice of spreading code in any CDMA system is another way to ensure the successful recovery of data at the receiving end by minimizing the effect of MAI and it also dictates the hardware design of the encoder and decoder. This thesis focuses on the efficient design of encoding and decoding hardware. Perfect difference codes (PDC) are chosen as spreading sequences due to their good correlation properties. In most of the literature, evaluation of error probability is based on the assumptions of ideal conditions. Such assumptions ignore major physical impairments such as power splitting losses at the multiplexers of transmitters and receivers, and gain losses at the receivers, which may in practice be an overestimate or underestimate of the actual probability of error. This thesis aims to investigate thoroughly with the consideration of practical impairments the applications of PDCs and other spreading sequences in optical communications systems based on spectral-amplitude coding and utilizing codedivision as multiplexing/multiple-access technique. This work begins with a xix general review of optical CDMA systems. An open-ended practical approach has been used to evaluate the actual error probabilities of OCDM/A systems under study. It has been concluded from results that mismatches in the gains of photodetectors, namely avalanche photodiode (APDs), used at the receiver side and uniformity loss in the optical splitters results in the inaccurate calculation of threshold level used to detect the data and can seriously degrade the system bit error rate (BER) performance. This variation in the threshold level can be compensated by employing techniques which maintain a constant interference level so that the decoding architecture does not have to estimate MAI every time to make a data bit decision or by the use of balanced sequences. In this thesis, as a solution to the above problem, a novel encoding and decoding architecture is presented for perfect difference codes based on common zero code technique which maintains a constant interference level at all instants in CDM system and thus relieves the need of estimating interference. The proposed architecture only uses single multiplexer at the transmitters for all users in the system and a simple correlation based receiver for each user. The proposed configuration not only preserves the ability of MAI in Spectral-Amplitude Coding SAC-OCDM system, but also results in a low cost system with reduced complexity. The results show that by using PDCs in such system, the influence of MAI caused by other users can be reduced, and the number of active users can be increased significantly. Also a family of novel spreading sequences are constructed called Manchestercoded Modified Legendre codes (MCMLCs) suitable for SAC based OCDM systems. MCMLCs are designed to be used for both single-rate and Multirate systems. First the construction of MCMLCs is presented and then the bit error rate performance is analyzed. Finally the proposed encoding/decoding architecture utilizing perfect difference codes is applied in wireless infrared environment and the performance is found to be superior to other codes

Hybrid pulse interval modulation-code-division multiple-access for optical wireless communications.

The work in this thesis investigates the properties of the IR diffuse wireless link with regard to: the use of sets of signature sequences with good message separation properties (hence providing low BER), the suitability of a hPIM-CDMA scheme for the IR diffuse wireless systems under the constraint of eye safety regulations (i.e. when all users are transmitting simultaneously), the quality of message separation due to multipath propagation. The suitability of current DS-CDMA systems using other modulation techniques are also investigated and compared with hPIM-CDMA for the performances in power efficiency, data throughput enhancement and error rate.A new algorithm has also been proposed for generating large sets of (n,3,1,1)OOC practically with reduced computation time. The algorithm introduces five conditions that are well refined and help in speeding up the code construction process. Results for elapsed computation times for constructing the codes using the proposed algorithm are compared with theory and show a significant achievement. The models for hPIM-CDMA and hPPM-CDMA systems, which were based on passive devices only, were also studied. The technique used in hPIM-CDMA, which uses a variable and shorter symbol duration, to achieve higher data throughput is presented in detail. An in-depth analysis of the BER performance was presented and results obtained show that a lower BER and higher data throughput can be achieved. A corrected BER expression for the hPPM-CDMA was presented and the justification for this detailed. The analyses also show that for DS-CDMA systems using certain sets of signature sequences, the BER performance cannot be approximated by a Gaussian function

Fiber-optic code division multiple access : multi-class optical orthogonal codes, optical power control, and polarization encoding

Ever since the mid- 1980s when the single-mode fiber-optic media were believed to become the main highways of future telecommunications networks for transporting high-volume high-quality multipurpose information, the need for all-optical multi-access networking became important. An all-optical multi-access network is a collection of multiple nodes where the interconnection among various nodes is via single- or multi-mode fiber optics and for which they perform all their essential signal processing requirements such as switching, add-drop, multiplexing/demultiplexing and amplification in the optical domain. Optical CDMA networking is one possible technique that allows multiple users in local area networks to access the same fiber channel asynchronously with no delay or scheduling. Optical CDMA networks are not without their own problems. Search for codes suitable to the optical domain is one of the important topics addressed in the literature on optical CDMA. Existing codes developed in the late 80's are limited to single class traffic or can support multiclass traffic but with restrictions on code lengths and weights. Also the number of generated codes is severely limited due to orthogonality issues. In this thesis, we pay particular attention to propose new codes that can support multiclass traffic with arbitrary code weights and lengths. Therefore, data sources with varying traffic demands can be accommodated by optical CDMA networks using the proposed codes. We also present a simple generation technique for the proposed multiclass codes and analyze their performance. The number of users supported by the proposed multiclass codes will be limited since it is an extension of existing code designs with such limitation. We then propose the use of polarization dimension in order to double the number of supported users. On the other hand, incoherent optical CDMA systems are considered as positive systems meaning that only unipolar codes can be considered for such systems. Therefore, multiple access interference will be quite high in optical CDMA due to the nature of incoherent power detection. Reducing the effect of the interference on the performance of optical CDMA is an important topic. We propose the use of power control to decrease the effects of interference in optical star networks in which users' fiber lengths and data rates are not equal. We consider the case of optically amplified network with amplifier noise as the main source. We then elaborate by considering the nonlinearity in the photodetection process and propose the use of an iterative algorithm to find the solution of the non-linear optical power control problem. Finally, we propose an optical CDMA system based on polarization encoding. Since the encoding is performed in the spatial domain, therefore, positive and negative levels can be realized. This approach leads to increasing the number of supported users of optical CDMA by the use of known codes, such as Gold and Hadamard codes, with enhanced performance.reviewe

Dark signalling and code division multiple access in an optical fibre LAN with a bus topology

This thesis describes an optical fibre network that uses a bus topology and Code Division Multiple Access (CDMA). Various potential configurations are analysed and compared and it is shown that a serious limitation of optical CDMA schemes using incoherent correlators is the effect of optical beating due to the presence of multiple incoherent optical signals at the receiver photodiode. The network proposed and analysed in this thesis avoids beating between multiple optical fields because it only uses a single, shared, optical source. It does this through the SLIM (Single Light-source with In-line Modulation) configuration in which there is a continuously-operating light source at the head-end of a folded bus, and modulators at the nodes to impose signals on the optical field in the form of pulses of darkness which propagate along the otherwise continuously bright bus. Optical CDMA can use optical-fibre delay-line correlators as matched filters, and these may be operated either coherently or incoherently.Coherent operation is significantly more complex than incoherent operation, but incoherent correlators introduce further beating even in a SLIM network. A new design of optical delay-line correlator, the hybrid correlator, is therefore proposed, analysed and demonstrated. It is shown to eliminate beating. A model of a complete network predicts that a SLIMbus using optical CDMA with hybrid correlators can be operated at TeraBaud rates with the number of simultaneous users limited by multiple access interference (MAI), determined only by the combinatorics of the code set

Security enhancement in passive optical networks through wavelength hopping and sequences cycling technique

Growth in the telecommunication industry continues to expand with requirements evolving around increased bandwidth and security. Advances in networking technologies have introduced low cost optical components that has made passive optical networks (PON) the choice for providing huge bandwidth to end users. PON are covered by established standards such as IEEE 802.3ah and ITU-T G.983.1/984.1, with star topology of broadcast and select (B&S) on shared fiber links that poses security vulnerability in terms of confidentiality and privacy;Research and reports in the literature focus around increasing cardinality via coding schemes that lack in addressing security, which was left for implementation in application layers via cryptography. This dissertation presents an approach on security in PON at the network level using slow wavelength hopping techniques and diffusion of data packets among dense wave division multiplex (DWDM). Orthogonal wavelength sequences are generated by mapping an ITU-T G694.1 based wavelength grid matrix and code matrices. The arrangement of wavelengths in the wavelength grid matrix, which can be changed frequently (i.e, hourly) serves as the first key of secure operation. Allocation of generated wavelength sequences distributed in multiple quantities to nodes based on their security level serve as second individual keys for the nodes. In addition, an improved level of security provided via the cycling order of those allocated wavelength sequences to nodes is the third key between the central office (CO) and a node. The proposed approach to PON security provides three new keys available outside the world of cryptography;Various coding techniques are used, and results show that even time spreading/wavelength hopping based on symmetric prime numbers provided the least wavelength sequences; however, it provided excellent correlation properties and level of security. A PON simulation model was implemented to investigate channel impairments in DWDM with 64 channels spaced at 25GHz carried over a 25 km ITU-T G.655 compliant shared fiber cable. Security performance evaluation included analytical studies in classical probabilities to capture the correct order of wavelength hopping sequence using exhaustive searching and reverse construction of matrices from monitored channels. Encouraging results obtained support the feasibility of this proposed technical approach for security

Overlapped CDMA system in optical packet networks : resource allocation and performance evalutation

Dans cette thèse, la performance du système CDMA à chevauchement optique (OVCDMA) au niveau de la couche de contrôle d'accès au support (MAC) et l'allocation des ressources au niveau de la couche physique (PRY) sont étudiées. Notre but est d'apporter des améliorations pour des applications à débits multiples en répondant aux exigences de délai minimum tout en garantissant la qualité de service (QoS). Nous proposons de combiner les couches PRY et MAC par une nouvelle approche d'optimisation de performance qui consolide l'efficacité potentielle des réseaux optiques. Pour atteindre notre objectif, nous réalisons plusieurs étapes d'analyse. Tout d 'abord, nous suggérons le protocole S-ALOHA/OV-CDMA optique pour sa simplicité de contrôler les transmissions optiques au niveau de la couche liaison. Le débit du réseau, la latence de transmission et la stabilité du protocole sont ensuite évalués. L'évaluation prend en considération les caractéristiques physiques du système OY-CDMA, représentées par la probabilité de paquets bien reçus. Le système classique à traitement variable du gain (YPG) du CDMA, ciblé pour les applications à débits multiples, et le protocole MAC ±round-robin¿ récepteur/émetteur (R31), initialement proposé pour les réseaux par paquets en CDMA optique sont également pris en compte. L'objectif est d ' évaluer comparativement la performance du S-ALOHA/OY-CDMA en termes de l'immunité contre l'interférence d'accès lTIultiple (MAI) et les variations des charges du trafic. Les résultats montrent que les performances peuvent varier en ce qui concerne le choix du taux de transmission et la puissance de transmission optique au niveau de la couche PRY. Ainsi, nous proposons un schéma de répartition optimale des ressources pour allouer des taux de transmission à chevauchement optique et de puissance optique de transmission dans le système OY-CDMA comme des ressources devant être optimalement et équitablement réparties entre les utilisateurs qui sont regroupés dans des classes de différentes qualités de service. La condition d'optimalité est basée sur la maximisation de la capacité par utilisateur de la couche PHY. De ce fait, un choix optimal des ressources physiques est maintenant possible, mais il n'est pas équitable entre les classes. Par conséquent, pour améliorer la performance de la couche liaison tout en éliminant le problème d'absence d'équité, nous proposons comme une approche unifiée un schéma équitable et optimal pour l'allocation des ressources fondé sur la qualité de service pour des multiplexages temporels des réseaux par paquets en CDMA à chevauchement optique. Enfin, nous combinons cette dernière approche avec le protocole MAC dans un problème d'optimisation d'allocation équitable des ressources à contrainte de délai afin de mieux améliorer le débit du réseau et le délai au niveau de la couche liaison avec allocation équitable et optimale des ressources au niveau de la couche PHY