Design of sequences with good correlation properties

This thesis is dedicated to exploring sequences with good correlation properties. Periodic sequences with desirable correlation properties have numerous applications in communications. Ideally, one would like to have a set of sequences whose out-of-phase auto-correlation magnitudes and cross-correlation magnitudes are very small, preferably zero. However, theoretical bounds show that the maximum magnitudes of auto-correlation and cross-correlation of a sequence set are mutually constrained, i.e., if a set of sequences possesses good auto-correlation properties, then the cross-correlation properties are not good and vice versa. The design of sequence sets that achieve those theoretical bounds is therefore of great interest. In addition, instead of pursuing the least possible correlation values within an entire period, it is also interesting to investigate families of sequences with ideal correlation in a smaller zone around the origin. Such sequences are referred to as sequences with zero correlation zone or ZCZ sequences, which have been extensively studied due to their applications in 4G LTE and 5G NR systems, as well as quasi-synchronous code-division multiple-access communication systems. Paper I and a part of Paper II aim to construct sequence sets with low correlation within a whole period. Paper I presents a construction of sequence sets that meets the Sarwate bound. The construction builds a connection between generalised Frank sequences and combinatorial objects, circular Florentine arrays. The size of the sequence sets is determined by the existence of circular Florentine arrays of some order. Paper II further connects circular Florentine arrays to a unified construction of perfect polyphase sequences, which include generalised Frank sequences as a special case. The size of a sequence set that meets the Sarwate bound, depends on a divisor of the period of the employed sequences, as well as the existence of circular Florentine arrays. Paper III-VI and a part of Paper II are devoted to ZCZ sequences. Papers II and III propose infinite families of optimal ZCZ sequence sets with respect to some bound, which are used to eliminate interference within a single cell in a cellular network. Papers V, VI and a part of Paper II focus on constructions of multiple optimal ZCZ sequence sets with favorable inter-set cross-correlation, which can be used in multi-user communication environments to minimize inter-cell interference. In particular, Paper~II employs circular Florentine arrays and improves the number of the optimal ZCZ sequence sets with optimal inter-set cross-correlation property in some cases.Doktorgradsavhandlin

Code design and analysis for multiple access communications

This thesis explores various coding aspects of multiple access communications, mainly for spread spectrum multiaccess(SSMA) communications and collaborative coding multiaccess(CCMA) communications. Both the SSMA and CCMA techniques permit efficient simultaneous transmission by several users sharing a common channel, without subdivision in time or frequency. The general principle behind these two multiaccess schemes is that one can find sets of signals (codes) which can be combined together to form a composite signal; on reception, the individual signals in the set can each be recovered from the composite signal. For the CCMA scheme, the isolation between users is based on the code structure; for the SSMA scheme, on the other hand, the isolation between users is based on the autocorrelation functions(ACFs) and crosscorrelation functions (CCFs) of the code sequences. It is clear that, in either case, the code design is the key to the system design.For the CCMA system with a multiaccess binary adder channel, a class of superimposed codes is analyzed. It is proved that every constant weight code of weight w and maximal correlation λ corresponds to a subclass of disjunctive codes of order T 3, the out-of-phase ACFs and CCFs of the codes are constant and equal to √L. In addition, all codes of the same length are mutually orthogonal.2. Maximal length sequences (m-sequences) over Gaussian integers, suitable for use with QAM modulation, are considered. Two sub-classes of m-sequences with quasi-perfect periodic autocorrelations are obtained. The CCFs between the decimated m-sequences are studied. By applying a simple operation, it is shown that some m-sequences over rational and Gaussian integers can be transformed into perfect sequences with impulsive ACFs.3. Frank codes and Chu codes have perfect periodic ACFs and optimum periodic CCFs. In addition, it is shown that they also have very favourable nonperiodic ACFs; some new results concerning the behaviour of the nonperiodic ACFs are derived. Further, it is proved that the sets of combinedFrank/Chu codes, which contain a larger number of codes than either of the two constituent sets, also have very good periodic CCFs. Based on Frank codes and Chu codes, two interesting classes of real-valued codes with good correlation properties are defined. It is shown that these codes have periodic complementary properties and good periodic and nonperiodic ACF/CCFs.Finally, a hybrid CCMA/SSMA coding scheme is proposed. This new hybrid coding scheme provides a very flexible and powerful multiple accessing capability and allows simple and efficient decoding. Given an SSMA system with K users and a CCMA system with N users, where at most T users are active at any time, then the hybrid system will have K . N users with at most T.K users active at any time. The hybrid CCMA/SSMA coding scheme is superior to the individual CCMA system or SSMA system in terms of information rate, number of users, decoding complexity and external interference rejection capability

Code design and analysis for multiple access communications

This thesis explores various coding aspects of multiple access communications, mainly for spread spectrum multiaccess(SSMA) communications and collaborative coding multiaccess(CCMA) communications. Both the SSMA and CCMA techniques permit efficient simultaneous transmission by several users sharing a common channel, without subdivision in time or frequency. The general principle behind these two multiaccess schemes is that one can find sets of signals (codes) which can be combined together to form a composite signal; on reception, the individual signals in the set can each be recovered from the composite signal. For the CCMA scheme, the isolation between users is based on the code structure; for the SSMA scheme, on the other hand, the isolation between users is based on the autocorrelation functions(ACFs) and crosscorrelation functions (CCFs) of the code sequences. It is clear that, in either case, the code design is the key to the system design.For the CCMA system with a multiaccess binary adder channel, a class of superimposed codes is analyzed. It is proved that every constant weight code of weight w and maximal correlation λ corresponds to a subclass of disjunctive codes of order T 3, the out-of-phase ACFs and CCFs of the codes are constant and equal to √L. In addition, all codes of the same length are mutually orthogonal.2. Maximal length sequences (m-sequences) over Gaussian integers, suitable for use with QAM modulation, are considered. Two sub-classes of m-sequences with quasi-perfect periodic autocorrelations are obtained. The CCFs between the decimated m-sequences are studied. By applying a simple operation, it is shown that some m-sequences over rational and Gaussian integers can be transformed into perfect sequences with impulsive ACFs.3. Frank codes and Chu codes have perfect periodic ACFs and optimum periodic CCFs. In addition, it is shown that they also have very favourable nonperiodic ACFs; some new results concerning the behaviour of the nonperiodic ACFs are derived. Further, it is proved that the sets of combinedFrank/Chu codes, which contain a larger number of codes than either of the two constituent sets, also have very good periodic CCFs. Based on Frank codes and Chu codes, two interesting classes of real-valued codes with good correlation properties are defined. It is shown that these codes have periodic complementary properties and good periodic and nonperiodic ACF/CCFs.Finally, a hybrid CCMA/SSMA coding scheme is proposed. This new hybrid coding scheme provides a very flexible and powerful multiple accessing capability and allows simple and efficient decoding. Given an SSMA system with K users and a CCMA system with N users, where at most T users are active at any time, then the hybrid system will have K . N users with at most T.K users active at any time. The hybrid CCMA/SSMA coding scheme is superior to the individual CCMA system or SSMA system in terms of information rate, number of users, decoding complexity and external interference rejection capability

Modernized eLoran: The Case for Completely Changing Chains, Rates, and Phase Codes

First deployed in the U.S. in 1957, Loran-C dominated radio-based navigation for many years. In 2000 the FAA began a significant recapitalization of Loran in the U.S.; the 2001 Volpe report on the vulnerability of the GPS reinforced the need for a revamped Loran. What emerged was an enhanced or evolved version, so called eLoran, aiming to achieve, for example, 10- 20 meter absolute positioning accuracy, RNP 0.3 mile required navigation performance, and stratum 1 time. After 10 years of development, in 2010, this U.S. e ffort was halted and the U.S. transmitters were silenced; since that time, eLoran is still being developed in Europe and deployed in Asia. Earlier this year U.S. Government interest in eLoran has again stirred (evidenced by a U.S. Army request for information and a U.S. Dept. of Transportation request for public comment); the rest of these initiated much conversation at the 2015 ION ITM. The prior U.S. (and continuing European) development of eLoran kept many of the 1950\u27s system design choices so as to be compatible with legacy Loran receivers. These include the pulse shape, groups, chains, rates, phase codes, emission delays, etc. Chosen to suit 1950\u27s technology, many of these restrictions are no longer necessary given the advances in transmitter and receiver technology (e.g. software defined radio) over the last half century. It is the opinion of these authors that as Loran, per se, no longer exists in the U.S., any re-emergence of a low frequency radio navigation system need not be held to these performance limiting constraints. In prior work these authors have promoted more significant changes to eLoran to improve system performance; specifically, single-rating all stations, reconquering the chain/rate structure within the continental U.S., and changing the phase codes. The current paper expands on these prior e fforts. Specifically, we propose putting all of the eLoran transmitters on the same repetition period and employing unique phase codes for each transmitter. To effectively choose new phase codes for eLoran, and assess their performance, we rely on the auto- and cross-correlation metrics. These metrics describe how well a receiver can both acquire and track a specific signal when contaminated by multi- path interference, the existence of other signals, and noise. While a perfect auto-correlation function, large at zero lag corresponding to the actual arrival of the signal and zero elsewhere, and a perfect cross- correlation function, zero for all lags, are preferred, it is impossible to find such codes. However, limiting the size of the window for which we require perfect auto- and cross-correlations, such codes can be found. To create such codes for eLoran we adapt results from the CDMA literature on complementary sequences and Large Area Synchronized (LAS) codes. This paper begins with a brief review of the relevant characteristics of Loran-C, including a discussion of the effects of sky wave and cross rate interference. This is followed by a survey of previously published ideas/concepts on how elements of the system could be changed so as to improve performance. Finally, details on the proposed rate/chain/phase code structure are presented. The reader should recognize that these ideas and results are not intended to define what the best eLoran system would be; rather, if eLoran soars again in the U.S., we hope to initiate a dialogue that looks beyond the decisions made in the 1950\u27s

The Proteomic Code: a molecular recognition code for proteins

<p>Abstract</p> <p>Background</p> <p>The Proteomic Code is a set of rules by which information in genetic material is transferred into the physico-chemical properties of amino acids. It determines how individual amino acids interact with each other during folding and in specific protein-protein interactions. The Proteomic Code is part of the redundant Genetic Code.</p> <p>Review</p> <p>The 25-year-old history of this concept is reviewed from the first independent suggestions by Biro and Mekler, through the works of Blalock, Root-Bernstein, Siemion, Miller and others, followed by the discovery of a Common Periodic Table of Codons and Nucleic Acids in 2003 and culminating in the recent conceptualization of partial complementary coding of interacting amino acids as well as the theory of the nucleic acid-assisted protein folding.</p> <p>Methods and conclusions</p> <p>A novel cloning method for the design and production of specific, high-affinity-reacting proteins (SHARP) is presented. This method is based on the concept of proteomic codes and is suitable for large-scale, industrial production of specifically interacting peptides.</p

Design and performance of CDMA codes for multiuser communications

Walsh and Gold sequences are fixed power codes and are widely used in multiuser CDMA communications. Their popularity is due to the ease of implementation. Availability of these code sets is limited because of their generating kernels. Emerging radio applications like sensor networks or multiple service types in mobile and peer-to-peer communications networks might benefit from flexibilities in code lengths and possible allocation methodologies provided by large set of code libraries. Walsh codes are linear phase and zero mean with unique number of zero crossings for each sequence within the set. DC sequence is part of the Walsh code set. Although these features are quite beneficial for source coding applications, they are not essential for spread spectrum communications. By relaxing these unnecessary constraints, new sets of orthogonal binary user codes (Walsh-like) for different lengths are obtained with comparable BER performance to standard code sets in all channel conditions. Although fixed power codes are easier to implement, mathematically speaking, varying power codes offer lower inter- and intra-code correlations. With recent advances in RF power amplifier design, it might be possible to implement multiple level orthogonal spread spectrum codes for an efficient direct sequence CDMA system. A number of multiple level integer codes have been generated by brute force search method for different lengths to highlight possible BER performance improvement over binary codes. An analytical design method has been developed for multiple level (variable power) spread spectrum codes using Karhunen-Loeve Transform (KLT) technique. Eigen decomposition technique is used to generate spread spectrum basis functions that are jointly spread in time and frequency domains for a given covariance matrix or power spectral density function. Since this is a closed form solution for orthogonal code set design, many options are possible for different code lengths. Design examples and performance simulations showed that spread spectrum KLT codes outperform or closely match with the standard codes employed in present CDMA systems. Hybrid (Kronecker) codes are generated by taking Kronecker product of two spreading code families in a two-stage orthogonal transmultiplexer structure and are judiciously allocated to users such that their inter-code correlations are minimized. It is shown that, BER performance of hybrid codes with a code selection and allocation algorithm is better than the performance of standard Walsh or Gold code sets for asynchronous CDMA communications. A redundant spreading code technique is proposed utilizing multiple stage orthogonal transmultiplexer structure where each user has its own pre-multiplexer. Each data bit is redundantly spread in the pre-multiplexer stage of a user with odd number of redundancy, and at the receiver, majority logic decision is employed on the detected redundant bits to obtain overall performance improvement. Simulation results showed that redundant spreading method improves BER performance significantly at low SNR channel conditions

Framework for classifying logical operators in stabilizer codes

Entanglement, as studied in quantum information science, and non-local quantum correlations, as studied in condensed matter physics, are fundamentally akin to each other. However, their relationship is often hard to quantify due to the lack of a general approach to study both on the same footing. In particular, while entanglement and non-local correlations are properties of states, both arise from symmetries of global operators that commute with the system Hamiltonian. Here, we introduce a framework for completely classifying the local and non-local properties of all such global operators, given the Hamiltonian and a bi-partitioning of the system. This framework is limited to descriptions based on stabilizer quantum codes, but may be generalized. We illustrate the use of this framework to study entanglement and non-local correlations by analyzing global symmetries in topological order, distribution of entanglement and entanglement entropy.Comment: 20 pages, 9 figure

A NOVEL CONSTRUCTION OF VECTOR COMBINATORIAL (VC) CODE FAMILIES AND DETECTION SCHEME FOR SAC OCDMA SYSTEMS

There has been growing interests in using optical code division multiple access (OCDMA) systems for the next generation high-speed optical fiber networks. The advantage of spectral amplitude coding (SAC-OCDMA) over conventional OCDMA systems is that, when using appropriate detection technique, the multiple access interference (MAI) can totally be canceled. The motivation of this research is to develop new code families to enhance the overall performance of optical OCDMA systems. Four aspects are tackled in this research. Firstly, a comprehensive discussion takes place on all important aspects of existing codes from advantages and disadvantages point of view. Two algorithms are proposed to construct several code families namely Vector Combinatorial (VC). Secondly, a new detection technique based on exclusive-OR (XOR) logic is developed and compared to the reported detection techniques. Thirdly, a software simulation for SAC OCDMA system with the VC families using a commercial optical system, Virtual Photonic Instrument, “VPITM TransmissionMaker 7.1” is conducted. Finally, an extensive investigation to study and characterize the VC-OCDMA in local area network (LAN) is conducted. For the performance analysis, the effects of phase-induced intensity noise (PIIN), shot noise, and thermal noise are considered simultaneously. The performances of the system compared to reported systems were characterized by referring to the signal to noise ratio (SNR), the bit error rate (BER) and the effective power (Psr). Numerical results show that, an acceptable BER of 10−9 was achieved by the VC codes with 120 active users while a much better performance can be achieved when the effective received power Psr > -26 dBm. In particular, the BER can be significantly improved when the VC optimal channel spacing width is carefully selected; best performance occurs at a spacing bandwidth between 0.8 and 1 nm. The simulation results indicate that VC code has a superior performance compared to other reported codes for the same transmission quality. It is also found that for a transmitted power at 0 dBm, the BER specified by eye diagrams patterns are 10-14 and 10-5 for VC and Modified Quadratic Congruence (MQC) codes respectively

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