Encrypting image by assembling the fractal-image addition method and the binary encoding method

The fractal-image addition method and the binary encoding method are assembled to form a hybrid method for encrypting a digital covert image. For this hybrid method, a host image is used to create an overt image with the information of the covert image. First, the fractal-image addition method is used to add some fractal images and the covert image to form an image-mixing matrix. Then, all the pixel values of the image-mixing matrix are transferred into binary data. Finally, the binary data are encoded into the host image to create an overt image. The pixels of the overt image contain eight groups of codes used for reconstructing the covert image. The eight groups of codes are identification codes, row amount codes, covert-image dimension codes, fractal-image amount codes, starting-pixel codes, character amount codes, character codes, and information codes. The overt image and the host image look almost the same for eyes. Furthermore, the covert image can be directly reconstructed from the overt image without using the host image. The most important feature is that the reconstructed covert image is identical to the original covert image, i.e. there is no distortion in the decoding work.     

Hybrid encoding method by assembling the magic-matrix scrambling method and the binary encoding method in image hiding

The magic-matrix scrambling method and the binary encoding method are combined to form a hybrid encoding method for hiding digital covert images. For this hybrid encoding method, a covert image is encoded into a host image to form an overt image. First, the magic-matrix scrambling method is used to rearrange all the pixels of the covert image by using a specified magic matrix modified from a magic square to form a scrambled matrix. Then, all the pixels of the scrambled matrix are denoted by binary data. Finally, the binary data are encoded into the host image to form the overt image. The pixels of the overt image contain nine groups of codes used for decoding the covert image, i.e. identification codes, covert-image dimension codes, scrambling-time codes, magic-square dimension codes, corner codes, shifting codes, arrangement codes, graylevel codes, and information codes. The overt image and the host image look almost the same for eyes. Furthermore, the covert image can be decoded directly from the overt image without using the host image. The most important feature is that the decoded covert image is identical to the original covert image, i.e. there is no distortion in the decoding work.     

On the Existence of XOR-Based Codes for Private Information Retrieval with Private Side Information

We consider the problem of Private Information Retrieval with Private Side Information (PIR-PSI), wherein the privacy of the demand and the side information are jointly preserved. Although the capacity of the PIR-PSI setting is known, we observe that the underlying capacity-achieving code construction uses Maximum Distance Separable (MDS) codes therefore contributing to high computational complexity when retrieving the demand. Pointing at this drawback of MDS-based PIR-PSI codes, we propose XOR-based PIR-PSI codes for a simple yet non-trivial setting of two non-colluding databases and two side information files at the user. Although our codes offer substantial reduction in complexity when compared to MDS-based codes, the code-rate marginally falls short of the capacity of the PIR-PSI setting. Nevertheless, we show that our code-rate is strictly higher than that of XOR-based codes for PIR with no side information. As a result, our codes can be useful when privately downloading a file especially after having downloaded a few other messages privately from the same database at an earlier time-instant.     

Non-Malleable Code in the Split-State Model

Non-malleable codes are a natural relaxation of error correction and error detection codes applicable in scenarios where error-correction or error-detection is impossible. Over the last decade, non-malleable codes have been studied for a wide variety of tampering families. Among the most well studied of these is the split-state family of tampering channels, where the codeword is split into two or more parts and each part is tampered with independently. We survey various constructions and applications of non-malleable codes in the split-state model.     

Systematic Encoding and Shortening of PAC Codes

Polarization adjusted convolutional (PAC) codes are a class of codes that combine channel polarization with convolutional coding. PAC codes are of interest for their high performance. This paper presents a systematic encoding and shortening method for PAC codes. Systematic encoding is important for lowering the bit-error rate (BER) of PAC codes. Shortening is important for adjusting the block length of PAC codes. It is shown that systematic encoding and shortening of PAC codes can be carried out in a unified framework.     

Fortran codes for the correlation functions of hard sphere fluids

Our Fortran codes for hard sphere fluids and their mixtures for the correlation functions that arise from the Percus–Yevick theory and the Verlet–Weis semi-empirical correction have proven useful during a period of nearly four decades and continue to be useful. In order to make these codes even more widely available, a brief summary is presented here and listings of these codes are given in the electronically accessible Supplementary Material to this paper.     

MC computer simulations of the preferential sputtering of Si-Ge alloys

Abstract

The ability of MC codes to predict the preferential sputtering of compound targets is investigated. The DYNA and TRIDYN codes are run for 3 keV Ar ⁺ bombardment of a SiGe binary target. The preferential sputtering of Si and Ge, the depth dependence of the sputter cross-section and the relocation operators are calculated. Difficulties arise in trying to reproduce the experimentally reported absence of preferentiality in the sputtered flux. The models used for the surface barriers, as well as the barrier heights, influences strongly the predicted quantities. A spherical surface barrier predicts much closer to stoichiometric fluxes than a planar barrier. Different codes give different collisional diffusivities for the target species in the bulk. The need for further experiments is stressed if some guidance in the choice of input parameters in the codes is desired.     

Design and performance analysis of various one dimensional codes using different data formats for OCDMA system

In this paper, the design, implementation and performance analysis of various one dimensional codes in an OCDMA system for different data formats is presented. A number of different codes are used with optical CDMA to improve its error performance. Here, three such codes, optical orthogonal codes (OOC), Walsh Hadamard codes and zero cross-correlation (ZCC) codes have been compared using different data formats, NRZ raised cosine, NRZ rectangular, RZ raised cosine and RZ rectangular. It is found that NRZ raised cosine has the best system performance for all the codes used. After that, the three codes have been compared in terms of the BER, eye diagrams and received optical power using NRZ raised cosine modulation format. It is analyzed that ZCC codes have zero cross-correlation property. The simulation results revealed that ZCC codes can provide a better BER compared to the OOC and Walsh Hadamard codes and it is most suitable to be employed in the OCDMA systems.     

Simple family of nonadditive quantum codes

Most known quantum codes are additive, meaning the code can be described as the simultaneous eigenspace of an Abelian subgroup of the Pauli group. While in some scenarios such codes are strictly suboptimal, very little is understood about how to construct nonadditive codes with good performance. Here we present a family of distance 2 nonadditive quantum codes for all odd block lengths n, that has a particularly simple form. Our codes detect single qubit errors (or correct single qubit erasures) while encoding a higher dimensional space than is possible with an additive code or, for n> or =11, any previous codes. We exhibit the encoding circuits and automorphism group for our codes as well.     

Encrypted optical memory system using three-dimensional keys in the Fresnel domain

An encrypted optical memory system using double random phase codes in the Fresnel domain is proposed. In this system, two random phase codes and their positions form three-dimensional keys for encryption of images and are used as keys to recover the original data. The third dimension is the positions of the codes, which can have as many as three degrees of freedom. Original images encrypted by use of the two phase codes located in the Fresnel domain are stored holographically in a photorefractive material. We demonstrate in preliminary experiments encryption and decryption of optical memory in a LiNbO(3) :Fe photorefractive crystal by use of angular multiplexing.     

Performance characteristics and weight distribution analysis of turbo product code with Reed-Muller component codes

In this paper, we present simulation results for Reed-Muller (RM) turbo codes over AWGN and Rayleigh fading channels. We also compare the simulation results of turbo product codes and block turbo codes with RM component codes over an AWGN channel. We show that minimum distance is not important as far as the BER performance of long codes is concerned. The weight distribution of RM codes of different lengths and turbo product codes with first-order RM component codes are obtained and analyzed for their good performance. We show that the weight distribution asymptotically approaches that of random coding as the code length increases.     

Implementation of LT codes based on chaos

Fountain codes provide an efficient way to transfer information over erasure channels like the Internet. LT codes are the first codes fully realizing the digital fountain concept. They are asymptotically optimal rateless erasure codes with highly efficient encoding and decoding algorithms. In theory, for each encoding symbol of LT codes, its degree is randomly chosen according to a predetermined degree distribution, and its neighbours used to generate that encoding symbol are chosen uniformly at random. Practical implementation of LT codes usually realizes the randomness through pseudo-randomness number generator like linear congruential method. This paper applies the pseudo-randomness of chaotic sequence in the implementation of LT codes. Two Kent chaotic maps are used to determine the degree and neighbour（s） of each encoding symbol. It is shown that the implemented LT codes based on chaos perform better than the LT codes implemented by the traditional pseudo-randomness number generator.     

Theory of quantum error correction for general noise

A measure of quality of an error-correcting code is the maximum number of errors that it is able to correct. We show that a suitable notion of "number of errors" e makes sense for any quantum or classical system in the presence of arbitrary interactions. Thus, e-error-correcting codes protect information without requiring the usual assumptions of independence. We prove the existence of large codes for both quantum and classical information. By viewing error-correcting codes as subsystems, we relate codes to irreducible representations of operator algebras and show that noiseless subsystems are infinite-distance error-correcting codes.     

Binary encoding method to encrypt Fourier-transformed information of digital images

An encoding method is used to encrypt the Fourier-transformed information of a hidden (covert) digital image in an overt image, while the Fourier-transformed information must be encoded with binary codes. All of the pixels in an overt image are classified into five groups that are called identification, type, tracing, dimension, and information codes. Identification codes are used to judge if the overt image contains codes that belong to the proposed encoding method or not; type codes are used to judge the encoding type; tracing codes are used to judge the encoding trace; dimension codes are used to judge the size of the hidden information; and information codes are used to decode the hidden information. Applying the proposed encoding method is rather easy, and host images corresponding to overt images are not needed for decoding work. The experiment has demonstrated four types of encoding for the proposed encoding method to reconstruct covert images without any distortion or only with a little distortion.     

On the Construction of Asymmetric Quantum Codes

Several families of good nonbinary asymmetric quantum codes are constructed in this paper. These new quantum codes are derived from the Calderbank-Shor-Steane (CSS) construction as well as the Hermitian construction applied respectively to two classical nested Bose-Chaudhuri-Hocquenghem (BCH) codes where one of them are additionally Euclidean (Hermitian) dual-containing. The asymmetric codes constructed here have parameters better than the ones available in the literature.     

A new family of two-dimensional codes for optical CDMA systems

The design of a new family of two-dimensional single pulse per column codes for optical code division multiple access (OCDMA) networks is reported. The 1-D modified pseudo-noise codes have been known to be orthogonal and their generation and system design based on these codes is rather simple. But their performance is limited due to the bandwidth constraints if the code length increases. Hence, using these 1-D modified pseudo-noise codes, modified 2-D pseudo-noise matrix codes (MPMCs) are generated. The system performance is evaluated for two, three and four simultaneous users using the link with all the sources responsible for degradation included: attenuation, chromatic dispersion, non-linear refractive effects, non-linear scattering and four-wave mixing. The effect of the non-linear and lossy dispersive medium over the system performance is shown by plotting the BER with respect to the link length for the systems designed using encoders/decoders base on 1-D modified pseudo-noise codes and our MPMCs. The performance is compared for the two types of codes by finding the crosstalk due to interfering users simultaneously operating in the network.     

Random and guided generation of coherent two-dimensional codes

Two-dimensional codes play a central role for many optical applications. Such codes are distributions of weighted points; a code is good if its autocorrelation closely approximates a multiple of the δ-function. This paper treats coherent codes with weights +1 and -1, shows their significant improvement compared with the incoherent codes which have only weights of +1, and outlines a method of generating good incoherent codes which is more efficient than random generation.     

CRC-Aided Adaptive BP Decoding of PAC Codes

Although long polar codes with successive cancellation decoding can asymptotically achieve channel capacity, the performance of short blocklength polar codes is far from optimal. Recently, Arıkan proposed employing a convolutional pre-transformation before the polarization network, called polarization-adjusted convolutional (PAC) codes. In this paper, we focus on improving the performance of short PAC codes concatenated with a cyclic redundancy check (CRC) outer code, CRC-PAC codes, since error detection capability is essential in practical applications, such as the polar coding scheme for the control channel. We propose an enhanced adaptive belief propagation (ABP) decoding algorithm with the assistance of CRC bits for PAC codes. We also derive joint parity-check matrices of CRC-PAC codes suitable for iterative BP decoding. The proposed CRC-aided ABP (CA-ABP) decoding can effectively improve error performance when partial CRC bits are used in the decoding. Meanwhile, the error detection ability can still be guaranteed by the remaining CRC bits and adaptive decoding parameters. Moreover, compared with the conventional CRC-aided list (CA-List) decoding, our proposed scheme can significantly reduce computational complexity, to achieve a better trade-off between the performance and complexity for short PAC codes.     

Error Probability Mitigation in Quantum Reading Using Classical Codes

A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the ensemble of channels. Classical and quantum codes can be envisioned for this goal. The aim of this paper is to present a simple but fruitful protocol for this task using classical error-correcting codes. Three families of codes are considered: Reed–Solomon codes, BCH codes, and Reed–Muller codes. In conjunction with the use of codes, we also analyze the role of the receiver. In particular, heterodyne and Dolinar receivers are taken into consideration. The encoding and measurement schemes are connected by the probing step. As probes, we consider coherent states. In such a simple manner, interesting results are obtained. As we show, there is a threshold below which using codes surpass optimal and sophisticated schemes for any fixed rate and code. BCH codes in conjunction with Dolinar receiver turn out to be the optimal strategy for error mitigation in quantum reading.     

一类基于级联结构的量子好码

借助经典级联码的思想，详细阐述了通过适当选择量子码作为外码和内码，构造一般意义量子级联码的过程.在此基础上，通过选择量子RS码作为外码，一组特殊结构的量子码作为内码，具体构造出了一类量子级联码，证明了其是量子好码.在量子纠错码领域中，这是首次利用经典坏码构造出量子好码.