Hamming Distance Distributions Research Articles

On the hardness of quadratic unconstrained binary optimization problems

We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments with the D-Wave Advantage 5.1 quantum annealer, solving many instances of up to 170-variable, quadratic unconstrained binary optimization problems. Our results demonstrate that the exponents characterizing the success probability of a D-Wave annealer to solve a quadratic unconstrained binary optimization correlate very well with the predictions based on the Hamming distance distributions computed for small problem instances.

A Revisit to Ordered Statistics Decoding: Distance Distribution and Decoding Rules

This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming distance from codeword estimates to the received sequence in the reprocessing stages of the OSD algorithm. We prove that the Hamming distance and weighted Hamming distance distributions can be characterized as mixture models capturing the decoding error probability and code weight enumerator. Simulation and numerical results show that our proposed statistical approaches can accurately describe the distance distributions. Based on these distributions and with the aim to reduce the decoding complexity, several techniques, including stopping rules and discarding rules, are proposed, and their decoding error performance and complexity are accordingly analyzed. Simulation results for decoding various eBCH codes demonstrate that the proposed techniques can significantly reduce the decoding complexity with a negligible loss in the decoding error performance.

Key Predistribution Schemes Based on Orthogonal Arrays with Unique Hamming Distance Distribution

With the deep study of the Hamming distances of orthogonal arrays (OAs), the application of OAs has penetrated into many fields, one of which is to construct the key predistribution schemes (KPSs) for distributed sensor networks. In this paper, we define the Hamming distance distribution (HDD) of an OA and its uniqueness. Furthermore, we present some OAs with unique HDD. In KPSs based on these OAs, the calculations of metrics for evaluating connectivity and resilience can be simplified. We also illustrate that KPSs based on them have a wider application and better connectivity and resilience than the existing ones.

Quadratic and symmetric bilinear forms over finite fields and their association schemes

Let 𝒬(m,q) and 𝒮(m,q) be the sets of quadratic forms and symmetric bilinear forms on an m-dimensional vector space over 𝔽 q , respectively. The orbits of 𝒬(m,q) and 𝒮(m,q) under a natural group action induce two translation association schemes, which are known to be dual to each other. We give explicit expressions for the eigenvalues of these association schemes in terms of linear combinations of generalised Krawtchouk polynomials, generalising earlier results for odd q to the more difficult case when q is even. We then study d-codes in these schemes, namely subsets X of 𝒬(m,q) or 𝒮(m,q) with the property that, for all distinct A,B∈X, the rank of A-B is at least d. We prove tight bounds on the size of d-codes and show that, when these bounds hold with equality, the inner distributions of the subsets are often uniquely determined by their parameters. We also discuss connections to classical error-correcting codes and show how the Hamming distance distribution of large classes of codes over 𝔽 q can be determined from the results of this paper.

Effect of pupil dilation on off-angle iris recognition

Due to the less constrained setup in standoff iris recognition systems, it is likely to capture nonideal iris images with gaze angle, pupil dilation, reflections, and occlusions. The combined effect of pupil dilation and gaze angle on iris recognition is examined. We first highlight the effects on synthetic images generated with a biometric eye model using a ray-tracing algorithm. Then, we quantify the effects of pupil dilation and gaze angle on the real frontal and off-angle images at different dilation levels. Our experiments reveal that the larger differences in dilation levels and gaze angles between the compared iris images increase the Hamming distance. Even if the linear rubber-sheet normalization helps to minimize the dilation effect in frontal images, it cannot fully eliminate it in off-angle iris images because of not only the pupil dilation and three-dimensional iris texture but also the corneal refraction distortion and limbus occlusion. We also observe that the gaze angle is the main reason for the performance degradation in steeper off-angle images, where the effect of the dilation is limited. In addition, since the iris region in off-angle and dilated iris images is smaller than that in frontal and constricted iris images, their interclass Hamming distance distribution is shifted toward the intraclass distribution, which may increase the false match rate.

A study of how gaze angle affects the performance of iris recognition

In traditional iris recognition systems, majority of researches improves the recognition performance for frontal images by ignoring the challenging issues including corneal refraction, 3D iris texture, limbus occlusion, and blur. When comparing images from the same angle such as frontal, all the challenging effects have similar distortions (i.e., corneal refraction and 3D texture) or minimal effects (i.e., limbus effect and blur) on all iris images. However, in off-angle iris recognition they have a significant negative impact on the accuracy and performance and they require additional treatments. In this paper, we first investigate how eye structures related iris recognition affects the performance of iris biometrics for different gaze angles and then quantify the effect of gaze angle on the inter-class and intra-class Hamming distance distributions. Based on our results from real images, as gaze angle of the probe image increases, the Hamming distance scores increases in intra-class distribution. We further found that average Hamming distance of the inter-class decreases as image captured from stepper angles and the distribution moves towards the intra-class distribution that causes an increment in the false-match-rate due to the existence of less area in the segmented off-angle images compared with the frontal images.

Automatic identification number generation circuit using nmos pair current mismatch

This paper presents a uniquely distributed identification number generation circuit based on process variation. The developed circuit utilizes current mismatch in an NMOS pair for unique ID output. To evaluate the output 1/0 probability-uniformity and process dependence, we fabricated a prototype in two different 0.18-µm standard CMOS technologies. We tested 382 chips and calculated the hamming distances between each chip. The results show the hamming distance distribution agrees with theoretical binominal distribution in mean and skewness. However, the distribution is a little wider than the theoretical one. We investigated the reason for the difference and found that circuit layout irregularity causes degradation in standard deviation and kurtosis. When the bits at both ends are excluded, the ID outputs agree with theoretical statistics. The results show the circuit architecture generates a unique and process-independent ID.

Biometrics based key management of double random phase encoding scheme using error control codes

In this paper, an optical security system has been proposed in which key of the double random phase encoding technique is linked to the biometrics of the user to make it user specific. The error in recognition due to the biometric variation is corrected by encoding the key using the BCH code. A user specific shuffling key is used to increase the separation between genuine and impostor Hamming distance distribution. This shuffling key is then further secured using the RSA public key encryption to enhance the security of the system. XOR operation is performed between the encoded key and the feature vector obtained from the biometrics. The RSA encoded shuffling key and the data obtained from the XOR operation are stored into a token. The main advantage of the present technique is that the key retrieval is possible only in the simultaneous presence of the token and the biometrics of the user which not only authenticates the presence of the original input but also secures the key of the system. Computational experiments showed the effectiveness of the proposed technique for key retrieval in the decryption process by using the live biometrics of the user.

Design of Quasi-Cyclic Cycle LDPC Codes over GF(q)

Quasi-cyclic (QC) low-density parity-check (LDPC) codes have several appealing properties regarding decoding, storage requirements and encoding aspects. In this paper, we focus on the QC LDPC codes over GF(q) whose parity-check matrices have fixed column weight j=2. By investigating two subgraphs in the Tanner graphs of the corresponding base matrices, we derive two upper bounds on the minimum Hamming distance for this class of codes. In addition, a method is proposed to construct QC LDPC codes over GF(q), which have good Hamming distance distributions. Simulations show that our designed codes have good performance.

Designing a genome-based HIV incidence assay with high sensitivity and specificity

Considerable inaccuracy in estimates of HIV incidence has been a serious obstacle to the development of efficient HIV/AIDS prevention and interventions. Accurately distinguishing recent or incident infections from chronic infections enables one to monitor epidemics and evaluate the impact of HIV prevention/intervention trials. However, serological testing has not been able to realize these promises due to a number of critical limitations. Our study is to design a novel scheme of identifying incident infections in a highly accurate manner, based on the characteristics of HIV gene diversification within an infected individual. We perform a comprehensive meta-analysis on 5596 full envelope HIV genes generated by single genome amplification-direct sequencing from 182 incident and 43 chronic cases. We devise a binary classification test based on the tail characteristics of the Hamming distance distribution of sequences. We identify a clear signature of incident infections, the presence of closely related strains in the sampled HIV envelope gene sequences in each HIV-infected patient, in both single-variant and multivariant transmissions. The sequence similarity used as a biomarker is found to have high specificity and sensitivity, greater than 95%, and is robust to viral and host-specific factors such as the clade of the viral strain, viral load, and the length and location of sequences in the HIV envelope gene. Because of rapid and continuing improvements in sequencing technology and cost, sequence-based incidence assays hold great promise as a means of quantifying HIV incidence from a single blood test.

Learning by random walks in the weight space of the Ising perceptron

Several variants of a stochastic local search process for constructing the synaptic weights of anIsing perceptron are studied. In this process, binary patterns are sequentially presented tothe Ising perceptron and are then learned as the synaptic weight configuration is modifiedthrough a chain of single- or double-weight flips within the compatible weight configurationspace of the earlier learned patterns. This process is able to reach a storage capacity ofα≈0.63 for patternlength N = 101 and α≈0.41 forN = 1001. If inaddition a relearning process is exploited, the learning performance is further improved to a storage capacityof α≈0.80 for N = 101 and α≈0.42 for N = 1001. We found that, for a given learning task, the solutions constructed by the random walk learningprocess are separated by a typical Hamming distance, which decreases with the constraint densityα of the learning task;at a fixed value of α, the width of the Hamming distance distribution decreases withN.

The Best Bits in an Iris Code

Iris biometric systems apply filters to iris images to extract information about iris texture. Daugman's approach maps the filter output to a binary iris code. The fractional Hamming distance between two iris codes is computed and decisions about the identity of a person are based on the computed distance. The fractional Hamming distance weights all bits in an iris code equally. However, not all the bits in an iris code are equally useful. Our research is the first to present experiments documenting that some bits are more consistent than others. Different regions of the iris are compared to evaluate their relative consistency, and contrary to some previous research, we find that the middle bands of the iris are more consistent than the inner bands. The inconsistent-bit phenomenon is evident across genders and different filter types. Possible causes of inconsistencies, such as segmentation, alignment issues, and different filters are investigated. The inconsistencies are largely due to the coarse quantization of the phase response. Masking iris code bits corresponding to complex filter responses near the axes of the complex plane improves the separation between the match and nonmatch Hamming distance distributions.

On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions

We investigate negacyclic and cyclic codes of length p s over the finite field F p a . Negacyclic codes of length p s are precisely the ideals of the chain ring F p a [ x ] 〈 x p s + 1 〉 . This structure is then used to obtain the Hamming distance distribution of the class of such negacyclic codes, which also provides Hamming weight distributions and enumerations of several codes. An one-to-one correspondence between negacyclic and cyclic codes is established to carry accordingly those results of negacyclic codes to cyclic codes.

Low-complexity concatenated two-state TCM schemes with near-capacity performance

This paper presents a family of concatenated two-state trellis-coded modulation (CT-TCM) schemes. Compared with the existing turbo-type bandwidth-efficient coded modulation schemes, the proposed codes have significantly reduced complexity without sacrificing performance. A joint design strategy for all component codes is established. This leads to so-called asymmetrical and time-varying trellis structures, which possess good Hamming and Euclidean distance distributions. The performance of the proposed codes is demonstrated by simulation results.

Basic Properties of Populations Generated in the Frame of One-Parameter Discrete Model of Genetic Diversity

Previously, when discussing the properties of one parameter discrete model of genetic diversity (M. Yu. Shchelkanov et al, J. Biomol. Struct. Dyn. 15, 887–894 (1998)), we took into account Hamming distance distribution only between precursor and arbitrary descendant sequences. However, really there are sets of sequence populations produced during amplification process. In the presented work we have investigated Hamming distance distributions between sequences from different descendant sets produced in the frame of one parameter discrete model. Two basic descendant generation operators (so called amplifiers) are introduced: 1) the last generation amplifier, Ḽ, which produces descendants with precursor elimination; 2) all generations amplifier, Ĝ, which produces descendants without precursor elimination. Generalization of one-parameter discrete model for the case when precursor sequences do not coincide are carried out. Using this generalization we investigate the distribution of Hamming distances between Ḽ—and Ĝ -generated sequences. Basic properties of Ḽ and Ĝ operators, Ḽ/Ĝ-choice alternative problem have been discussed. Obtained results have common theoretical significance, but they are more suitable for high level genetic diversity process (for example, HIV diversity).

The spreading of damage in the vicinity of a tricritical point: two dimensional BEG model on a honeycomb lattice

We apply the spreading of damage technique to study the critical properties of the two-dimensional S = 1 Blume-Emery-Griffith model on a honeycomb lattice in the vicinity of a tricritical line. We use Metropolis dynamics to calculate the temperature dependence of the Hamming distance as well as Hamming distance distributions along the Markov chain. We study the behavior of the spreading properties near the tricritical point and show how the spreading of damage technique may be applied to identify the tricritical point.

The spreading of damage in the Ising Ferromagnetic thin film

We study the spreading of damage in S = 1 2 Ising ferromagnetic thin films consisting of two and more monolayers. We use Metropolis dynamics to calculate the temperature dependence of the Hamming distance as well as Hamming distance distributions along the Markov chain. We suggest a new way to introduce damage to the system via the difference in the boundary conditions. We discuss the results of this new approach for the two-dimensional model. For the film with the number of layers, N, equal to 3, we display the dependence of the above quantities on the localization of the perturbation and the values of the parameters of the exchange interaction within the surfaces, between the surface and bulk spins, and within the middle layer. For the film with N ⩾ 3 we study the Hamming distance distributions along the film thickness. We discuss the behaviour of the surface and bulk spreading temperatures.

Application of the spreading of damage technique to the S=1/2 Ising thin film

We apply the spreading of the damage technique to a S=1/2 Ising ferromagnetic thin film. We use Metropolis dynamics to calculate the temperature dependence of the Hamming distance as well as the Hamming distance distributions along the Markov chain. We suggest a modification of the algorithm for calculating the Hamming distance in the case of Metropolis dynamics and we discuss the results for the two-dimensional model obtained by the modified approach. For a film with three layers we present the thermal dependences of the above quantities. We also suggest a new way to introduce damage to the system as the difference in the boundary conditions. We discuss the results of this new approach for the two-dimensional model.

Ensemble approach to simulated annealing

We present three reasons for implementing simulated annealing with an ensemble of random walkers which search the configuration space in parrallel. First, an ensemble allows the implementation of an adaptive cooling schedule because it provides good statistics for collecting thermodynamic information. This new adaptive implementation is general, simple, and, in some sense, optimal. Second, the ensemble can tell us how to optimally allocate our effort in the search for a good solution, i.e., given the total computer time available, how many members to use in the ensemble. Third, an ensemble can reveal otherwise hidden properties of the configuration space, e.g., by examining Hamming distance distributions among the ensemble members. We present numerical results on the bipartitioning of random graphs and on a graph bipartitioning problem whose static thermodynamic properties may be solved for exactly.