Good Codes Research Articles

Remote vehicle communication anti-interference design based on multipath channel equalisation suppression

In order to improve the quality of remote vehicle communication and reduce communication distortion and error, this paper proposes a remote vehicle communication anti-interference design method based on multipath channel equalisation suppression, and constructs a dynamic channel allocation model for multi-vehicle remote communication. The signal-to-interference ratio of each channel is calculated and the continuous fractional frequency method of vehicle communication signal is used for blind source separation and on this basis, feedback link is added to the output end of the communication signal. The research results show that the method has advantages of good balance performance and vehicle communication code element's output error rate is low, anti-interference ability is strong, and the quality of remote vehicle communication is improved.

The Gilbert-Varshamov Bound for Stabilizer Codes Over <inline-formula> <tex-math notation="LaTeX">$\mathbb{Z}_m$ </tex-math> </inline-formula>

Quantum codes over finite rings have received a great deal of attention in recent years. Compared with quantum codes over finite fields, a notable advantage of quantum codes over finite rings is that they can adapt to quantum physical systems of arbitrary order. Moreover, operations are much easier to execute in finite rings than they are in fields. The modulo $m$ residue class ring $\mathbb {Z}_{m}$ is the most common finite ring. This paper investigates stabilizer codes over $\mathbb {Z}_{m}$ and presents the Gilbert–Varshamov (GV) bound. The GV bound shows that surprisingly good quantum codes exist over $\mathbb {Z}_{m}$ , which makes quantum coding feasible for arbitrary quantum physical system. We also provide an enhanced version of the GV bound for non-degenerate stabilizer codes over $\mathbb {Z}_{m}$ . The enhanced GV bound has an asymptotical form and ensures the existence of asymptotically good stabilizer codes over $\mathbb {Z}_{m}$ . Finally, these two bounds are well suited for computer searching.

Codes from Surfaces with Small Picard Number

Extending work of M. Zarzar, we evaluate the potential of Goppa-type evaluation codes constructed from linear systems on projective algebraic surfaces with small Picard number. Putting this condition on the Picard number provides some control over the numbers of irreducible components of curves on the surface and hence over the minimum distance of the codes. We find that such surfaces do not automatically produce good codes; the sectional genus of the surface also has a major influence. Using that additional invariant, we derive bounds on the minimum distance under the assumption that the hyperplane section class generates the Néron--Severi group. We also give several examples of codes from such surfaces with minimum distance better than the best known bounds in Grassl's tables.

A Polynomial-Based Key Distribution Approach for Wireless Sensor Networks

Network coding is a novel concept for improving network capacity. This additional capacity may be used to increase throughput or reliability. Also in wireless networks, network coding has been proposed as a method for improving communication. The polynomial-based key predistribution scheme of Blom and Blundo et al. has been the basic ingredient for the key establishment for wireless sensor network (WSN). It is tempting to use many random and different instances of polynomial-based key predistribution scheme for various parts of the WSN to enhance the efficiency of WSN key establishment protocols. But it is not secure in general to use many instances of Blom-Blundo et al. polynomial-based key predistribution scheme in a WSN key establishment protocol. Thus the previously constructed group-based type WSN key predistribution schemes using polynomial-based key predistribution scheme are insecure. In this paper, a suitable error correction code is chosen based on codes of the type which are described as irreducible graded cyclic CCs which can algebraically be described by one-sided principal ideals in a noncommutative algebra $$A[x; \alpha ]$$ , where $$A \cong {\mathbb {F}}[x]/(x^n-1)$$ , $${\mathbb {F}}$$ is a finite field and n is the length of the code. This leads to the notion of a generator polynomial just like for cyclic block codes. Similarly, a parity check polynomial can be introduced by considering the right annihilator ideal. This way indicates that the big class of $$\sigma$$ -cyclic convolutional codes contains quite some good codes and deserves to be investigated further.

Polar Codes for Quantum Key Distribution.

This paper addresses the performance of polar codes in the context of the quantum key distribution (QKD) protocol. It introduces the notion of an interactive polar decoder and studies its performance. The results demonstrate that the interactive decoder is efficient in the right environment and can be used to construct good classical polar codes efficiently.

Approaching the Sustainable Development Practices in Mountain Tourism in the Romanian Carpathians

The article aims to identify the degree to which tourism managers who work in Romania in the area of the Carpathian Mountains have implemented sustainable development practices. It also assesses the quantification of their availability to be informed and to apply voluntary tools of sustainable development. Qualitative research based on the method of semi-structured in-depth interviews was conducted, with 34 managers who work in the accommodation units in the Romanian Carpathians. Results show that most managers are concerned with issues linked to sustainable evolution of the accommodation unit they manage. The researchers have noticed a low interest in sustainable evolution negatively correlated with the comfort level of the accommodation unit and competitiveness. Based on these results the authors recommend the adoption of measures that may allow sustainable development, and for the Romanian authorities to encourage the increase in the number of tourism units that can use sustainable management systems. This can be done through accessible rules, development of networks that may offer information about good practices and codes of conduct, as well as the possibility to participate in exchange programs.

Software and the Scientist: Coding and Citation Practices in Geodynamics

AbstractIn geodynamics as in other scientific areas, computation has become a core component of research, complementing field observation, laboratory analysis, experiment, and theory. Computational tools for data analysis, mapping, visualization, modeling, and simulation are essential for all aspects of the scientific workflow. Specialized scientific software is often developed by geodynamicists for their own use, and this effort represents a distinctive intellectual contribution. Drawing on a geodynamics community that focuses on developing and disseminating scientific software, we assess the current practices of software development and attribution, as well as attitudes about the need and best practices for software citation. We analyzed publications by participants in the Computational Infrastructure for Geodynamics and conducted mixed method surveys of the solid earth geophysics community. From this we learned that coding skills are typically learned informally. Participants considered good code as trusted, reusable, readable, and not overly complex and considered a good coder as one that participates in the community in an open and reasonable manor contributing to both long‐ and short‐term community projects. Participants strongly supported citing software reflected by the high rate a software package was named in the literature and the high rate of citations in the references. However, lacking are clear instructions from developers on how to cite and education of users on what to cite. In addition, citations did not always lead to discoverability of the resource. A unique identifier to the software package itself, community education, and citation tools would contribute to better attribution practices.

Narrow-Sense BCH Codes Over $ {\mathrm {GF}}(q)$ With Length $n=\frac {q^{m}-1}{q-1}$

Cyclic codes are widely employed in communication systems, storage devices, and consumer electronics, as they have efficient encoding and decoding algorithms. BCH codes, as a special subclass of cyclic codes, are in most cases among the best cyclic codes. A subclass of good BCH codes are the narrow-sense BCH codes over $ {\mathrm {GF}}(q)$ with length $n=(q^{m}-1)/(q-1)$ . Little is known about this class of BCH codes when $q>2$ . The objective of this paper is to study some of the codes within this class. In particular, the dimension, the minimum distance, and the weight distribution of some ternary BCH codes with length $n=(3^{m}-1)/2$ are determined in this paper. A class of ternary BCH codes meeting the Griesmer bound is identified. An application of some of the BCH codes in secret sharing is also investigated.

Accumulate Repeat Accumulate Check Accumulate Codes

In this paper, a novel accumulate-repeat-accumulate-check-accumulate (ARACA) code is proposed as a subclass of protograph-based low-density parity-check (LDPC) codes. The key feature of the proposed ARACA code is represented by the outer connection doping in the protograph. This feature can provide the linear minimum distance growth (LMDG) property at a good iterative decoding threshold while maintaining an efficient encoder structure. The effect of the outer connection doping on the typical minimum distance, the iterative decoding threshold, and the LMDG property is discussed and analyzed by comparing case examples and using the asymptotic protograph ensemble weight enumerator. Some good ARACA code protographs are provided for a wide range of code rates. In addition, an efficient and universal encoding procedure and the corresponding encoder structure are provided for them. The performance of the proposed ARACA code is evaluated and compared with well-known good LDPC codes. The simulation results confirm the superiority of the proposed ARACA codes in terms of encoding complexity and frame error rate performance, especially at low-rates in an ultra-reliable regime.

Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1

Fractional repetition (FR) codes are a class of distributed storage codes that replicate and distribute information data over several nodes for easy repair, as well as efficient reconstruction. In this paper, we propose three new constructions of FR codes based on relative difference sets (RDSs) with λ = 1 . Specifically, we propose new ( q 2 - 1 , q , q ) FR codes using cyclic RDS with parameters ( q + 1 , q - 1 , q , 1 ) constructed from q-ary m-sequences of period q 2 - 1 for a prime power q, ( p 2 , p , p ) FR codes using non-cyclic RDS with parameters ( p , p , p , 1 ) for an odd prime p or p = 4 and ( 4 l , 2 l , 2 l ) FR codes using non-cyclic RDS with parameters ( 2 l , 2 l , 2 l , 1 ) constructed from the Galois ring for a positive integer l. They are differentiated from the existing FR codes with respect to the constructable code parameters. It turns out that the proposed FR codes are (near) optimal for some parameters in terms of the FR capacity bound. Especially, ( 8 , 3 , 3 ) and ( 9 , 3 , 3 ) FR codes are optimal, that is, they meet the FR capacity bound for all k. To support various code parameters, we modify the proposed ( q 2 - 1 , q , q ) FR codes using decimation by a factor of the code length q 2 - 1 , which also gives us new good FR codes.

A fast intra mode decision algorithm combining neighboring information for H.264/AVC high profile

Intra coding in H.264/AVC can significantly improve the coding efficiency but at the cost of high computational complexity due to the use of rich prediction modes and rate-distortion optimization technique. To reduce the complexity, this paper proposes a fast mode decision algorithm for intra prediction in H.264/AVC high profile. The best prediction mode not only relies on the content of current block but also depends on the neighboring blocks because of the spatial continuity. Based on the reconstructed neighboring pixels, different prediction mode leads to different residual block which is the difference between the original block and predicted block. Since small residual block is advantageous to get good coding including the small distortion and few bit numbers, the feature from the residual block will be used to help do mode decision. Besides the neighboring pixels, the best modes of encoded neighboring blocks are also used to select the candidate modes. The proposed algorithm uses the sum of absolute transformed difference (SATD) to measure the residual block and uses the most probable mode to indicate the influence of the prediction modes of the neighboring blocks. Based on the statistic on mode decision accuracy, the most probable mode and the modes with the smallest residual block are considered as the candidate modes. Meanwhile, the early termination rules which can directly select only one mode are given in the proposed algorithm. Experimental results show that the proposed algorithm effectively reduces the complexity of intra prediction with slight coding performance degradation compared with the full search algorithm.

Asymptotically good quasi-cyclic codes of fractional index

Generalizing the quasi-cyclic codes of index 113 introduced by Fan et al., we study a more general class of quasi-cyclic codes of fractional index generated by pairs of polynomials. The parity check polynomial and encoder of these codes are obtained. The asymptotic behaviours of the rates and relative distances of this class of codes are studied by using a probabilistic method. We prove that, for any positive real number δ such that the asymptotic GV-bound at k+l2δ is greater than 12, the relative distance of the code is convergent to δ, while the rate is convergent to 1k+l. As a result, quasi-cyclic codes of fractional index are asymptotically good.

Maximal order codes over number fields

We present constructions of codes obtained from maximal orders over number fields. Particular cases include codes from algebraic number fields by Lenstra and Guruswami, codes from units of the ring of integers of number fields, and codes from both additive and multiplicative structures of maximal orders in central simple division algebras. The parameters of interest are the code rate and the minimum Hamming distance. An asymptotic study reveals several families of asymptotically good codes.

Intra Frame Coding In Advanced Video Coding Standard (H.264) to Obtain Consistent PSNR and Reduce Bit Rate for Diagonal Down Left Mode Using Gaussian Pulse

Intra prediction process of H.264 video coding standard used to code first frame i.e. Intra frame of video to obtain good coding efficiency compare to previous video coding standard series. More benefit of intra frame coding is to reduce spatial pixel redundancy with in current frame, reduces computational complexity and provides better rate distortion performance. To code Intra frame it use existing process Rate Distortion Optimization (RDO) method. This method increases computational complexity, increases in bit rate and reduces picture quality so it is difficult to implement in real time applications, so the many researcher has been developed fast mode decision algorithm for coding of intra frame. The previous work carried on Intra frame coding in H.264 standard using fast decision mode intra prediction algorithm based on different techniques was achieved increased in bit rate, degradation of picture quality(PSNR) for different quantization parameters. Many previous approaches of fast mode decision algorithms on intra frame coding achieved only reduction of computational complexity or it save encoding time and limitation was increase in bit rate with loss of quality of picture. In order to avoid increase in bit rate and loss of picture quality a better approach was developed. In this paper developed a better approach i.e. Gaussian pulse for Intra frame coding using diagonal down left intra prediction mode to achieve higher coding efficiency in terms of PSNR and bitrate. In proposed method Gaussian pulse is multiplied with each 4x4 frequency domain coefficients of 4x4 sub macro block of macro block of current frame before quantization process. Multiplication of Gaussian pulse for each 4x4 integer transformed coefficients at macro block levels scales the information of the coefficients in a reversible manner. The resulting signal would turn abstract. Frequency samples are abstract in a known and controllable manner without intermixing of coefficients, it avoids picture getting bad hit for higher values of quantization parameters. The proposed work was implemented using MATLAB and JM 18.6 reference software. The proposed work measure the performance parameters PSNR, bit rate and compression of intra frame of yuv video sequences in QCIF resolution under different values of quantization parameter with Gaussian value for diagonal down left intra prediction mode. The simulation results of proposed algorithm are tabulated and compared with previous algorithm i.e. Tian et al method. The proposed algorithm achieved reduced in bit rate averagely 30.98% and maintain consistent picture quality for QCIF sequences compared to previous algorithm i.e. Tian et al method.

Capacity of optical communications over a lossy bosonic channel with a receiver employing the most general coherent electro-optic feedback control

We study the problem of designing optical receivers to discriminate between multiple coherent states using coherent processing receivers---i.e., one that uses arbitrary coherent feedback control and quantum-noise-limited direct detection---which was shown by Dolinar to achieve the minimum error probability in discriminating any two coherent states. We first derive and re-interpret Dolinar's binary-hypothesis minimum-probability-of-error receiver as the one that optimizes the information efficiency at each time instant, based on recursive Bayesian updates within the receiver. Using this viewpoint, we propose a natural generalization of Dolinar's receiver design to discriminate $M$ coherent states each of which could now be a codeword, i.e., a sequence of $N$ coherent states each drawn from a modulation alphabet. We analyze the channel capacity of the pure-loss optical channel with a general coherent-processing receiver in the low-photon number regime and compare it with the capacity achievable with direct detection and the Holevo limit (achieving the latter would require a quantum joint-detection receiver). We show compelling evidence that despite the optimal performance of Dolinar's receiver for the binary coherent-state hypothesis test (either in error probability or mutual information), the asymptotic communication rate achievable by such a coherent-processing receiver is only as good as direct detection. This suggests that in the infinitely-long codeword limit, all potential benefits of coherent processing at the receiver can be obtained by designing a good code and direct detection, with no feedback within the receiver.

Good Linear Codes from Quadratic Residue Codes over a Finite Non‐Chain Ring

This paper is devoted to the study of quadratics residue codes and their extended codes over a finite non-chain ring. A class of Gray maps preserving the self-duality from the ring to the finite field are introduced. Some structural properties of quadratic residue codes and their extended codes are given. As an interesting application of these families of codes, some good linear codes are obtained by a special Gray map.

Relación entre la comprensión lectora, la ortografía y el rendimiento: un estudio en Educación Primaria.

Son numerosos los trabajos realizados para conocer relación entre la comprensión lectora, la ortografía y el rendimiento académico. La codificación y la decodificación son habilidades necesarias para el aprendizaje de la lecto-escritura en las etapas iniciales de su aprendizaje. El objetivo del estudio es comprobar las relaciones existentes entre estas variables al final de la etapa de primaria. Se evaluó la ortografía con un dictado y la comprensión con el test de compresión lectora de Ángel Lázaro. En el estudio participaron 252 alumnos con edades comprendidas entre 11 y 12 años. Para conocer estas relaciones se empleó un diseño correlacional. Se crearon tres grupos en función de los niveles de ejecución en comprensión lectora y ortografía y se realizaron diferentes contrastes. En el total de la muestra se encontraron correlaciones significativas entre el rendimiento académico y la comprensión lectora y débiles y sin significación estadística entre las medidas ortográficas y la comprensión lectora. Con respecto al solapamiento entre ambas, el análisis por grupos confirmó que una buena ejecución en comprensión lectora no asegura un desempeño adecuado en decodificación ortográfica. En la discusión se analizan estas relaciones y sus implicaciones educativas.

Empirical Research: Getting Started with Stata

AbstractThis article provides a guide to approaching empirical research work for the first time, as well as obtaining a foundation in the use of the statistical software package, Stata. The emphasis revolves around data cleaning and its importance in writing a good research essay. I also cover a basic introduction to Stata, the importance of do‐files, common data problems and good coding practice. In closing, I advise that not everything in research needs to go to plan, but that good research practice makes it easier to adapt when plans do not work out.

Good and asymptotically good quantum codes derived from algebraic geometry

In this paper, we construct several new families of quantum codes with good parameters. These new quantum codes are derived from (classical) t-point ($$t\ge 1$$t?1) algebraic geometry (AG) codes by applying the Calderbank---Shor---Steane (CSS) construction. More precisely, we construct two classical AG codes $$C_1$$C1 and $$C_2$$C2 such that $$C_1\subset C_2$$C1?C2, applying after the well-known CSS construction to $$C_1$$C1 and $$C_2$$C2. Many of these new codes have large minimum distances when compared with their code lengths as well as they also have small Singleton defects. As an example, we construct a family $${[[46, 2(t_2 - t_1), d]]}_{25}$$[[46,2(t2-t1),d]]25 of quantum codes, where $$t_1 , t_2$$t1,t2 are positive integers such that $$1

Good Code Sets from Complementary Pairs via Discrete Frequency Chips

It is shown that replacing the sinusoidal chip in Golay complementary code pairs by special classes of waveforms that satisfy two conditions, symmetry/anti-symmetry and quazi-orthogonality in the convolution sense, renders the complementary codes immune to frequency selective fading and also allows for concatenating them in time using one frequency band/channel. This results in a zero-sidelobe region around the mainlobe and an adjacent region of small cross-correlation sidelobes. The symmetry/anti-symmetry property results in the zero-sidelobe region on either side of the mainlobe, while quasi-orthogonality of the two chips keeps the adjacent region of cross-correlations small. Such codes are constructed using discrete frequency-coding waveforms (DFCW) based on linear frequency modulation (LFM) and piecewise LFM (PLFM) waveforms as chips for the complementary code pair, as they satisfy both the symmetry/anti-symmetry and quasi-orthogonality conditions. It is also shown that changing the slopes/chirp rates of the DFCW waveforms (based on LFM and PLFM waveforms) used as chips with the same complementary code pair results in good code sets with a zero-sidelobe region. It is also shown that a second good code set with a zero-sidelobe region could be constructed from the mates of the complementary code pair, while using the same DFCW waveforms as their chips. The cross-correlation between the two sets is shown to contain a zero-sidelobe region and an adjacent region of small cross-correlation sidelobes. Thus, the two sets are quasi-orthogonal and could be combined to form a good code set with twice the number of codes without affecting their cross-correlation properties. Or a better good code set with the same number codes could be constructed by choosing the best candidates form the two sets. Such code sets find utility in multiple input-multiple output (MIMO) radar applications.