Thesis Proposal

Total Page:16

File Type:pdf, Size:1020Kb

Thesis Proposal Towards Template Security for Iris- Based Biometric Systems by Marwa Fouad Thesis submitted to the Faculty of Graduate and Postdoctoral Studies in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Electrical & Computer Engineering School of Electrical Engineering and Computer Science University of Ottawa © Marwa Fouad, Ottawa, Canada, 2012 Abstract Personal identity refers to a set of attributes (e.g., name, social insurance number, etc.) that are associated with a person. Identity management is the process of creating, maintaining and destroying identities of individuals in a population. Biometric technologies are technologies developed to use statistical analysis of an individual’s biological or behavioral traits to determine his identity. Biometrics based authentication systems offer a reliable solution for identity management, because of their uniqueness, relative stability over time and security (among other reasons). Public acceptance of biometric systems will depend on their ability to ensure robustness, accuracy and security. Although robustness and accuracy of such systems are rapidly improving, there still remain some issues of security and balancing it with privacy. While the uniqueness of biometric traits offers a convenient and reliable means of identification, it also poses the risk of unauthorized cross-referencing among databases using the same biometric trait. There is also a high risk in case of a biometric database being compromised, since it’s not possible to revoke the biometric trait and re-issue a new one as is the case with passwords and smart keys. This unique attribute of biometric based authentication system poses a challenge that might slow down public acceptance and the use of biometrics for authentication purposes in large scale applications. In this research we investigate the vulnerabilities of biometric systems focusing on template security in iris-based biometric recognition systems. The iris has been well studied for authentication purposes and has been proven accurate in large scale applications in several airports and border crossings around the world. The most widely accepted iris recognition systems are based on Daugman’s model that creates a binary iris template. In this research we develop different systems using watermarking, bio- cryptography as well as feature transformation to achieve revocability and security of binary templates in iris based biometric authentication systems, while maintaining the performance that enables widespread application of these systems. All algorithms developed in this research are applicable on already existing biometric authentication systems and do not require redesign of these existing, well established iris-based authentication systems that use binary templates. II Acknowledgements I would like to seize this opportunity to pay tribute to all those who have contributed, one way or another, to the completion of this work, which marks another important milestone in my life. First of all, I would like to express my heartfelt thanks to Prof. Emil Petriu taking an interest in my work and having the initiative to assume a guidance role, and helping me to submit this thesis. I would also like to express my profound gratitude and great indebtedness to Prof. Abdulmotaleb El Saddik, for his benevolent supervision of my doctorate thesis. I thank him for encouraging and believing in me. His continuous support and constructive criticism, his invaluable advice, guidance, as well as his understanding were of great value to me. But most of all, I thank him for his patience with me through the highs and lows of this research time. I deeply appreciate the help and contributions received from many people during this project: I am very grateful to Prof. Jiying Zhao. Your kindness and helpfulness will forever remain imprinted in my mind. I would also like to gratefully acknowledge the contributions of Fawaz A Alsulaiman. I really appreciate your help in a field that was new to me. I dedicate this thesis to my husband, my supporting pillar, whose continual back-up and loving support was of great value in accomplishing this work. I also dedicate this thesis to my children; watching you grow is the greatest pleasure in my life and raising you has taught me so much about life and about myself. Last but not least, I wish to repay the debt of gratitude I owe my beloved parents, my mentors and teachers, my idols and my heroes; for years of encouragement and for their strong belief in me. I owe them great appreciation for what I have learned and what I have achieved. I wish you were here with me, mom, but you’re always on my mind and your love, support and wisdom are forever engraved in my heart and mind. God bless your soul and may you rest in peace. III Contents ABSTRACT ..................................................................................................................... II ACKNOWLEDGEMENTS ................................................................................................ III CONTENTS ................................................................................................................... IV LIST OF FIGURES .......................................................................................................... VII LIST OF TABLES ............................................................................................................. X LIST OF ACRONYMS ..................................................................................................... XI CHAPTER 1 INTRODUCTION ...................................................................................... 1 1.1 BIOMETRIC SECURITY ................................................................................................ 1 1.2 MOTIVATION .......................................................................................................... 7 1.3 GOALS, REQUIREMENTS AND CHALLENGES ................................................................... 9 1.4 THESIS OVERVIEW.................................................................................................. 10 1.5 CONTRIBUTIONS .................................................................................................... 11 1.6 SCHOLARLY OUTPUT ............................................................................................... 12 CHAPTER 2 FEATURE TRANSFORMATION ............................................................... 13 2.1 IRIS TEMPLATE CREATION ........................................................................................ 13 2.1.1 Iris Segmentation ...................................................................................... 17 2.1.2 Iris Normalization ...................................................................................... 18 2.1.3 Feature Encoding ...................................................................................... 19 2.1.4 Iris Code Matching .................................................................................... 20 2.1.5 Performance Evaluation ........................................................................... 22 2.2 INVERTIBLE FEATURE TRANSFORMATION .................................................................... 23 2.3 NON-INVERTIBLE FEATURE TRANSFORMATION ............................................................ 23 2.4 FEATURE TRANSFORMATION EVALUATION .................................................................. 24 2.4.1 Iris Shuffling .............................................................................................. 24 2.4.2 Iris Folding ................................................................................................. 25 2.4.3 Row Shifting and Permutation .................................................................. 26 2.4.4 Database ................................................................................................... 27 IV 2.4.5 Parameter Values...................................................................................... 28 2.4.6 Performance ............................................................................................. 28 2.4.7 Security Analysis ....................................................................................... 33 2.4.8 Conclusion................................................................................................. 34 CHAPTER 3 BIOMETRIC CRYPTOSYSTEMS ............................................................... 36 3.1 KEY-GENERATING .................................................................................................. 37 3.2 KEY-BINDING ........................................................................................................ 39 3.3 PROPOSED KEY-BINDING SYSTEM ............................................................................. 45 3.3.1 Revocability ............................................................................................... 47 3.3.2 Performance ............................................................................................. 47 3.3.3 Cyclic Redundancy Check Module ............................................................ 49 3.3.4 Security Analysis ....................................................................................... 51 3.3.5 Discussion ................................................................................................. 51 3.4 PROPOSED FUZZY VAULT SYSTEM ............................................................................. 52 3.4.1 Parameter Values.....................................................................................
Recommended publications
  • Short Low-Rate Non-Binary Turbo Codes Gianluigi Liva, Bal´Azs Matuz, Enrico Paolini, Marco Chiani
    Short Low-Rate Non-Binary Turbo Codes Gianluigi Liva, Bal´azs Matuz, Enrico Paolini, Marco Chiani Abstract—A serial concatenation of an outer non-binary turbo decoding thresholds lie within 0.5 dB from the Shannon code with different inner binary codes is introduced and an- limit in the coherent case, for a wide range of coding rates 1 alyzed. The turbo code is based on memory- time-variant (1/3 ≤ R ≤ 1/96). Remarkably, a similar result is achieved recursive convolutional codes over high order fields. The resulting codes possess low rates and capacity-approaching performance, in the noncoherent detection framework as well. thus representing an appealing solution for spread spectrum We then focus on the specific case where the inner code is communications. The performance of the scheme is investigated either an order-q Hadamard code or a first order length-q Reed- on the additive white Gaussian noise channel with coherent and Muller (RM) code, due to their simple fast Hadamard trans- noncoherent detection via density evolution analysis. The pro- form (FHT)-based decoding algorithms. The proposed scheme posed codes compare favorably w.r.t. other low rate constructions in terms of complexity/performance trade-off. Low error floors can be thus seen either as (i) a serial concatenation of an outer and performances close to the sphere packing bound are achieved Fq-based turbo code with an inner Hadamard/RM code with down to small block sizes (k = 192 information bits). antipodal signalling, or (ii) as a coded modulation Fq-based turbo/LDPC code with q-ary (bi-) orthogonal modulation.
    [Show full text]
  • Orthogonal Arrays and Codes
    Orthogonal Arrays & Codes Orthogonal Arrays - Redux An orthogonal array of strength t, a t-(v,k,λ)-OA, is a λvt x k array of v symbols, such that in any t columns of the array every one of the possible vt t-tuples of symbols occurs in exactly λ rows. We have previously defined an OA of strength 2. If all the rows of the OA are distinct we call it simple. If the symbol set is a finite field GF(q), the rows of an OA can be viewed as vectors of a vector space V over GF(q). If the rows form a subspace of V the OA is said to be linear. [Linear OA's are simple.] Constructions Theorem: If there exists a Hadamard matrix of order 4m, then there exists a 2-(2,4m-1,m)-OA. Pf: Let H be a standardized Hadamard matrix of order 4m. Remove the first row and take the transpose to obtain a 4m by 4m-1 array, which is a 2-(2,4m-1,m)-OA. a a a a a a a a a a b b b b 2-(2,7,2)-OA a b b a a b b a b b b b a a constructed from an b a b a b a b order 8 Hadamard b a b b a b a matrix b b a a b b a b b a b a a b Linear Constructions Theorem: Let M be an mxn matrix over Fq with the property that every t columns of M are linearly independent.
    [Show full text]
  • TC08 / 6. Hadamard Codes 3.12.07 SX
    TC08 / 6. Hadamard codes 3.12.07 SX Hadamard matrices. Paley’s construction of Hadamard matrices Hadamard codes. Decoding Hadamard codes Hadamard matrices A Hadamard matrix of order is a matrix of type whose coefficients are1 or 1 and such that . Note that this relation is equivalent to say that the rows of have norm √ and that any two distinct rows are orthogonal. Since is invertible and , we see that 2 and hence is also a Hadamard matrix. Thus is a Hadamard matrix if and only if its columns have norm √ and any two distinct columns are orthogonal. If is a Hadamard matrix of order , then det ⁄ . In particular we see that the Hadamard matrices satisfy the equality in Hadamard’s inequality: / |det| ∏∑ , which is valid for all real matrices of order . Remark. The expression / is the supremum of the value of det when runs over the real matrices such that 1. Moreover, the equality is reached if and only if is a Hadamard matrix. 3 If we change the signs of a row (column) of a Hadamard matrix, the result is clearly a Hadamard matrix. If we permute the rows (columns) of a Hadamard matrix, the result is another Hadamard matrix. Two Hadamard matrices are called equivalent (or isomorphic) if it is to go from one to the other by means of a sequence of such operations. Observe that by changing the sign of all the columns that begin with 1, and afterwards all the rows that begin with 1, we obtain an equivalent Hadamard matrix whose first row and first column only contain 1.
    [Show full text]
  • A Simple Low Rate Turbo-Like Code Design for Spread Spectrum Systems Durai Thirupathi and Keith M
    A simple low rate turbo-like code design for spread spectrum systems Durai Thirupathi and Keith M. Chugg Communication Sciences Institute Dept. of Electrical Engineering University of Southern California, Los Angeles 90089-2565 thirupat,chugg ¡ @usc.edu Abstract chine. The disadvantage of the SOTC is that the decoding com- plexity increases dramatically with decrease in code rate. On In this paper, we introduce a simple method to construct the other hand, THC, which is constructed using weaker con- very low rate recursive systematic convolutional codes from a stituent codes has slower rate of convergence which might not standard rate- ¢¤£¦¥ convolutional code. These codes in turn are be a desired property for practical applications. So, in design- used in parallel concatenation to obtain very low rate turbo like ing very low rate turbo-like codes for practical applications, one codes. The resulting codes are rate compatible and require low of the critical issues is to design strong enough constituent con- complexity decoders. Simulation results show that an additional volutional codes with decoding complexity of the overall code coding gain of 0.9 dB in additive white Gaussian noise (AWGN) being almost independent of the code rate. channel and 2 dB in Rayleigh fading channel is possible com- In this paper, we introduce a technique to construct such a pared to rate-1/3 turbo code. The low rate coding scheme in- class of low rate convolutional codes. These codes are then creases the capacity by more than 25% when applied to multi- used to build very low rate turbo codes. Since these codes are ple access environments such as Code Division Multiple Access constructed from rate- ¢¤£¦¥ parent codes, the complexity of the (CDMA).
    [Show full text]
  • Local List-Decoding of Reed-Muller Codes Over F2 Original Paper by Gopalan, Klivans, and Zuckerman [6, 7]
    Local List-Decoding of Reed-Muller Codes over F2 Original paper by Gopalan, Klivans, and Zuckerman [6, 7] Sahil Singla Manzil Zaheer Computer Science Department Electrical and Computer Engineering Carnegie Mellon University Carnegie Mellon University [email protected] [email protected] December 7, 2014 Abstract In this report we study the paper titled, \List-Decoding Reed-Muller Codes over Small Fields" by Parikshit Gopalan, Adam R. Klivans and David Zuckerman [6, 7]. The Reed-Muller codes are multivariate generalization of Reed-Solomon codes, which use polynomials in multiple variables to encode messages through functional encoding. Next, any list decoding problem for a code has two facets: Firstly, what is the max- imal radius up to which any ball of that radius contains only a constant number of codewords. Secondly, how to find these codewords in an efficient manner. The paper by GKZ presents the first local list-decoding algorithm for the r-th order Reed-Muller code RM(r; m) over F2 for r ≥ 2. Given an oracle for a received word m R : F2 ! F2, their randomized local list-decoding algorithm produces a list containing all degree r polynomials within relative distance (2−r − ) from R for any > 0 in time poly(mr; r). Since RM(r; m) has relative distance 2r, their algorithm beats the Johnson bound for r ≥ 2. Moreover, as the list size could be exponential in m at radius 2−r, their bound is optimal in the local setting. 1 Contents 1 Introduction 3 1.1 Basics of Code . .3 1.1.1 Johnson Bound .
    [Show full text]
  • TC+0 / 6. Hadamard Codes S
    TC+0 / 6. Hadamard codes S. Xambó Hadamard matrices. Paley’s construction of Hadamard matrices Hadamard codes. Decoding Hadamard codes Hadamard matrices A Hadamard matrix of order is a matrix of type whose coefficients are 1 or 1 and such that . Note that this relation is equivalent to say that the rows of have norm √ and that any two distinct rows are orthogonal. Since is invertible and we see that 2 and hence is also a Hadamard matrix. Thus is a Hadamard matrix if and only if its columns have norm √ and any two distinct columns are orthogonal. If is a Hadamard matrix of order , then det ⁄ . In particular we see that the Hadamard matrices satisfy the equality in Hadamard’s inequality: / |det| ∏∑ which is valid for all real matrices of order . Remark. The expression / is the supremum of the value of det when runs over the real matrices such that 1. Moreover, the equality is reached if and only if is a Hadamard matrix. 3 If we change the signs of a row (column) of a Hadamard matrix, the result is clearly a Hadamard matrix. If we permute the rows (columns) of a Hadamard matrix, the result is another Hadamard matrix. Two Hadamard matrices are called equivalent (or isomorphic) if it is possible to go from one to the other by means of a sequence of such operations. Observe that by changing the sign of all the columns that begin with 1 and afterwards of all the rows that begin with 1 we obtain an equivalent Hadamard matrix whose first row and first column only contain 1.
    [Show full text]
  • An Ultimate-Shannon-Limit-Approaching Gbps Throughput Encoder/Decoder System S
    1 An Ultimate-Shannon-Limit-Approaching Gbps Throughput Encoder/Decoder System S. Jiang, P. W. Zhang, F. C. M. Lau and C.-W. Sham Abstract—A turbo-Hadamard code (THC) is a type of low-rate component of the encoding/decoding system is fully opti- channel code with capacity approaching the ultimate Shannon mized to achieve high hardware-utilization rate. Arrange- − limit, i.e., 1.59 dB. In this paper, we investigate the hardware ment is made to ensure the data corresponding to different design of a turbo-Hadamard encoder/decoder system. The entire system has been implemented on an FPGA board. A bit error codewords are in an orderly manner such that they can be −5 rate (BER) of 10 can be achieved at Eb/N0 = 0.04 dB with received/stored/retrieved/processed efficiently at the decoder. a throughput of 3.2 Gbps or at Eb/N0 = −0.45 dB with a Last but not the least, we construct rate-adaptive THCs by throughput of 1.92 Gbps. puncturing the parity bits of the code. Sect. II briefly reviews the THC. Sect. III describes our overall design of the THC encoder/decoder system and evaluates the latency of each sub- I. INTRODUCTION decoder. Sect. IV shows the FPGA implementation results, Turbo code, low-density parity-check (LDPC) code, and including hardware utilization, throughput and bit error rate polar code are the most widely studied and implemented performance. Finally, Sect. ?? provides some concluding re- error-correction codes over the last two-and-a-half decades marks. because of their capacity-approaching capabilities [1], [2], [3], [4], [5], [6].
    [Show full text]
  • Download Issue
    JJCIT Jordanian Journal of Computers and Information Technology (JJCIT) The Jordanian Journal of Computers and Information Technology (JJCIT) is an international journal that publishes original, high-quality and cutting edge research papers on all aspects and technologies in ICT fields. JJCIT is hosted by Princess Sumaya University for Technology (PSUT) and supported by the Scientific Research Support Fund in Jordan. Researchers have the right to read, print, distribute, search, download, copy or link to the full text of articles. JJCIT permits reproduction as long as the source is acknowledged. AIMS AND SCOPE The JJCIT aims to publish the most current developments in the form of original articles as well as review articles in all areas of Telecommunications, Computer Engineering and Information Technology and make them available to researchers worldwide. The JJCIT focuses on topics including, but not limited to: Computer Engineering & Communication Networks, Computer Science & Information Systems and Information Technology and Applications. INDEXING JJCIT is indexed in: EDITORIAL BOARD SUPPORT TEAM LANGUAGE EDITOR EDITORIAL BOARD SECRETARY Haydar Al-Momani Eyad Al-Kouz All articles in this issue are open access articles distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/). JJCIT ADDRESS WEBSITE: www.jjcit.org EMAIL: [email protected] ADDRESS: Princess Sumaya University for Technology, Khalil Saket Street, Al-Jubaiha B.O. BOX: 1438 Amman 11941 Jordan TELEPHONE: +962-6-5359949 FAX: +962-6-7295534 JJCIT EDITORIAL BOARD Ahmad Hiasat (EIC) Aboul Ella Hassanien Adil Alpkoçak Adnan Gutub Adnan Shaout Christian Boitet Gian Carlo Cardarilli Hamid Hassanpour Abdelfatah Tamimi Arafat Awajan Gheith Abandah Haytham Bani Salameh Ismail Ababneh Ismail Hmeidi João L.
    [Show full text]
  • Math 550 Coding and Cryptography Workbook J. Swarts 0121709 Ii Contents
    Math 550 Coding and Cryptography Workbook J. Swarts 0121709 ii Contents 1 Introduction and Basic Ideas 3 1.1 Introduction . 3 1.2 Terminology . 4 1.3 Basic Assumptions About the Channel . 5 2 Detecting and Correcting Errors 7 3 Linear Codes 13 3.1 Introduction . 13 3.2 The Generator and Parity Check Matrices . 16 3.3 Cosets . 20 3.3.1 Maximum Likelihood Decoding (MLD) of Linear Codes . 21 4 Bounds for Codes 25 5 Hamming Codes 31 5.1 Introduction . 31 5.2 Extended Codes . 33 6 Golay Codes 37 6.1 The Extended Golay Code : C24. ....................... 37 6.2 The Golay Code : C23.............................. 40 7 Reed-Muller Codes 43 7.1 The Reed-Muller Codes RM(1, m) ...................... 46 8 Decimal Codes 49 8.1 The ISBN Code . 49 8.2 A Single Error Correcting Decimal Code . 51 8.3 A Double Error Correcting Decimal Code . 53 iii iv CONTENTS 8.4 The Universal Product Code (UPC) . 56 8.5 US Money Order . 57 8.6 US Postal Code . 58 9 Hadamard Codes 61 9.1 Background . 61 9.2 Definition of the Codes . 66 9.3 How good are the Hadamard Codes ? . 67 10 Introduction to Cryptography 71 10.1 Basic Definitions . 71 10.2 Affine Cipher . 73 10.2.1 Cryptanalysis of the Affine Cipher . 74 10.3 Some Other Ciphers . 76 10.3.1 The Vigen`ereCipher . 76 10.3.2 Cryptanalysis of the Vigen`ereCipher : The Kasiski Examination . 77 10.3.3 The Vernam Cipher . 79 11 Public Key Cryptography 81 11.1 The Rivest-Shamir-Adleman (RSA) Cryptosystem .
    [Show full text]
  • Background on Coding Theory
    6.895 PCP and Hardness of Approximation MIT, Fall 2010 Lecture 3: Coding Theory Lecturer: Dana Moshkovitz Scribe: Michael Forbes and Dana Moshkovitz 1 Motivation In the course we will make heavy use of coding theory. In this lecture we review the basic ideas and constructions. We start with two motivating examples. 1.1 Noisy Communication Alice gets a k-bit message x to send to Bob. Unfortunately, the communication channel is corrupted, and some number of bits may flip. For conceretness, say twenty percent of all bits sent on the channel may flip. Which bits are flipped is unknown, and different bits may flip for different messages sent on the channel. Can Alice still send a message that can be reliably received by Bob? We allow Alice and Bob to make any agreements prior to Alice learning about her message x. We also allow Alice to send more than k bits on the channel. The redundant bits can compesate for the bits lost due to corruption. We will see that Alice can send only n = Θ(k) bits of information about her message, such that even if twenty percent of those bits are flipped, the mistakes can be detected, and all of the original k bits can be recovered by Bob! 1.2 Equality Testing The following example is a classic example from communication complexity. Its setup and ideas are very useful for understanding PCPs. Suppose there are two players, Alice and Bob, as well as a verifier. Each player receives a private k-bit string. Alice's string is denoted x, and Bob's string is denoted y.
    [Show full text]
  • An Introduction of the Theory of Nonlinear Error-Correcting Codes
    Rochester Institute of Technology RIT Scholar Works Theses 1987 An introduction of the theory of nonlinear error-correcting codes Robert B. Nenno Follow this and additional works at: https://scholarworks.rit.edu/theses Recommended Citation Nenno, Robert B., "An introduction of the theory of nonlinear error-correcting codes" (1987). Thesis. Rochester Institute of Technology. Accessed from This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. An Introduction to the Theory of Nonlinear Error-Correcting Codes Robert B. Nenno Rochester Institute of Technology ABSTRACT Nonlinear error-correcting codes are the topic of this thesis. As a class of codes, it has been investigated far less than the class of linear error-correcting codes. While the latter have many practical advantages, it the former that contain the optimal error-correcting codes. In this project the theory (with illustrative examples) of currently known nonlinear codes is presented. Many definitions and theorems (often with their proofs) are presented thus providing the reader with the opportunity to experience the necessary level of mathematical rigor for good understanding of the subject. Also, the examples will give the reader the additional benefit of seeing how the theory can be put to use. An introduction to a technique for finding new codes via computer search is presented. Categories and Subject Descriptors: E.4 [Coding and Information Theory] For mal models of communication; H.l.l [Models and Principles] Systems and Infor mation Theory General Terms: Algorithms, Theory Additional Key Words and Phrases: Bounds on codes, designs, nongroup codes, Hadamard matrices, nonlinear error-correcting codes, uniformly packed codes October 8, 1987 TABLE OF CONTENTS Chapter 1 .
    [Show full text]
  • Coding Vs. Spreading for Narrow-Band Interference Suppression
    1 Coding vs. Spreading for Narrow-Band Interference Suppression Xiaofu Wu and Zhen Yang Abstract—The use of active narrow-band interference (NBI) suppression in spread-spectrum systems. In general, there are suppression in direct-sequence spread-spectrum (DS-SS) com- two categories for these techniques, one is based on linear munications has been extensively studied. In this paper, we signal processing techniques [3] and the other employs model- address the problem of optimum coding-spreading tradeoff for NBI suppression. With maximum likelihood decoding, we based techniques [1], including nonlinear filtering techniques first derive upper bounds on the error probability of coded and multiuser detection techniques. In [2], [4], a code-aided systems in the presence of a special class of NBI, namely, approach was proposed by Poor and Wang for NBI suppression multi-tone interference with orthogonal signatures. By employ- in direct-sequence code-division multiple-access (DS/CDMA) ing the well-developed bounding techniques, we show there is networks. This method, which is based on the minimum mean no advantage in spreading, and hence a low-rate full coding approach is always preferred. Then, we propose a practical square error (MMSE) linear detector, has been shown to out- low-rate turbo-Hadamard coding approach, in which the NBI perform all of the previous linear or nonlinear methods for NBI suppression is naturally achieved through iterative decoding. The suppression. In recent years, NBI suppression has also been proposed turbo-Hadamard coding approach employs a kind of considered in ultra-wide bandwidth (UWB) communications coded spread-spectrum signalling with time-varying spreading [5]–[9].
    [Show full text]