Elements of Algebraic coding Systems is an introductory text to algebraic coding theory. In the first chapter, you''ll gain inside knowledge of coding fundamentals, which is essential for a deeper understandin...
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ISBN:
(数字)9781606505755
ISBN:
(纸本)9781606505748;9781606505755
Elements of Algebraic coding Systems is an introductory text to algebraic coding theory. In the first chapter, you''ll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams''identities based on the probability of undetected error, and two important tools for algebraic decoding—namely, the finite field Fourier transform and the Euclidean algorithm for polynomials.
An introduction is presented in which the editor discusses reports within the issue on topics including data analysis of qualitative research, blind coding by multiple coders, and conventional humanist qualitative res...
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An introduction is presented in which the editor discusses reports within the issue on topics including data analysis of qualitative research, blind coding by multiple coders, and conventional humanist qualitative research.
Conventional communication networks route data packets in a store-and-forward mode. A router buffers received packets and forwards them intact towards their intended destination. Network coding (NC), however, generali...
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Conventional communication networks route data packets in a store-and-forward mode. A router buffers received packets and forwards them intact towards their intended destination. Network coding (NC), however, generalises this method by allowing the router to perform algebraic operations on the packets before forwarding them. The purpose of NC is to improve the network performance to achieve its maximum capacity also known as max-flow min-cut bound. NC has become very well established in the field of information theory, however, practical implementations in real-world networks is yet to be explored. In this thesis, new implementations of NC are brought forward. The effect of NC on flow error control protocols and queuing over computer networks is investigated by establishing and designing a mathematical and simulation framework. One goal of such investigation is to understand how NC technique can reduce the number of packets required to acknowledge the reception of those sent over the network while error-control schemes are employed. Another goal is to control the network queuing stability by reducing the number of packets required to convey a set of information. A custom- built simulator based on SimEvents ® has been developed in order to model several scenarios within this approach. The work in this thesis is divided into two key parts. The objective of the first part is to study the performance of communication networks employing error control protocols when NC is adopted. In particular, two main Automatic Repeat reQuest (ARQ) schemes are invoked, namely the Stop-and- Wait (SW) and Selective Repeat (SR) ARQ. Results show that in unicast point-to- point communication, the proposed NC scheme offers an increase in the throughput over traditional SW ARQ between 2.5% and 50.5% at each link, with negligible decoding delay. Additionally, in a Butterfly network, SR ARQ employing NC achieves a throughput gain between 22% and 44% over traditional SR ARQ when the number of i
We study the performance of algebraic codes for multi-terminal *** thesis consists of three parts: In the rst part, we analyze the performance ofgroup codes for communications systems. We observe that although group c...
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We study the performance of algebraic codes for multi-terminal *** thesis consists of three parts: In the rst part, we analyze the performance ofgroup codes for communications systems. We observe that although group codes arenot optimal for point-to-point scenarios, they can improve the achievable rate regionfor several multi-terminal communications settings such as the Distributed Sourcecoding and Interference Channels. The gains in the rates are particularly signicantwhen the structure of the source/channel is matched to the structure of the underlyinggroup. In the second part, we study the continuous alphabet version of group/linearcodes, namely lattice codes. We show that similarly to group codes, lattice codescan improve the achievable rate region for multi-terminal problems. In the third partof the thesis, we present coding schemes based on polar codes to practically achievethe performance limits derived in the two earlier parts. We also present polar codingschemes to achieve the known achievable rate regions for multi-terminal communicationsproblems such as the Distributed Source coding, the Multiple Descriptioncoding, Broadcast Channels, Interference Channels and Multiple Access Channels
In this paper, we introduce a new Fibonacci G(p,m) matrix for the m-extension of the Fibonacci p-numbers where p (>= 0) is integer and m (> 0). Thereby, we discuss various properties of G(p,m) matrix and the cod...
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In this paper, we introduce a new Fibonacci G(p,m) matrix for the m-extension of the Fibonacci p-numbers where p (>= 0) is integer and m (> 0). Thereby, we discuss various properties of G(p,m) matrix and the coding theory followed from the G(p,m) matrix. In this paper, we establish the relations among the code elements for all values of p (nonnegative integer) and m (> 0). We also show that the relation, among the code matrix elements for all values of p and m = 1, coincides with the relation among the code matrix elements for all values of p [Basu M, Prasad B. The generalized relations among the code elements for Fibonacci coding theory. Chaos, Solitons and Fractals (2008). doi: 10.1016/***.2008.09.030]. In general, correct ability of the method increases as p increases but it is independent of m. (c) 2009 Published by Elsevier Ltd.
We define and study parafermion stabilizer codes, which can be viewed as generalizations of Kitaev's one-dimensional (1D) model of unpaired Majorana fermions. Parafermion stabilizer codes can protect against low-w...
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We define and study parafermion stabilizer codes, which can be viewed as generalizations of Kitaev's one-dimensional (1D) model of unpaired Majorana fermions. Parafermion stabilizer codes can protect against low-weight errors acting on a small subset of parafermion modes in analogy to qudit stabilizer codes. Examples of several smallest parafermion stabilizer codes are given. A locality-preserving embedding of qudit operators into parafermion operators is established that allows one to map known qudit stabilizer codes to parafermion codes. We also present a local 2D parafermion construction that combines topological protection of Kitaev's toric code with additional protection relying on parity conservation.
A highly entangled bipartite quantum state is more advantageous for the quantum dense coding protocol than states with low entanglement. Applications of quantum channels are most likely to be commercially important on...
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A highly entangled bipartite quantum state is more advantageous for the quantum dense coding protocol than states with low entanglement. Applications of quantum channels are most likely to be commercially important only in the multiparty regime, where such a correspondence does not exist even for pure quantum states. We establish a connection between the multiparty capacity of classical information transmission in quantum dense coding and several multipartite quantum correlation measures of the shared state, used in the dense coding protocol. In particular, we show that for the noiseless channel, if multipartite quantum correlations of an arbitrary multipartite state of arbitrary number of qubits are the same as those of the corresponding generalized Greenberger-Horne-Zeilinger state, then the multipartite dense coding capability of the former is the same as or better than that of the generalized Greenberger-Horne-Zeilinger state. Interestingly, in a noisy-channel scenario, where we consider both uncorrelated and correlated noise models, the relative abilities of the quantum channels to transfer classical information can get inverted by administration of a sufficient amount of noise. When the shared state is an arbitrary multipartite mixed state, we also establish a link between the classical capacity for the noiseless case and multipartite quantum correlation measures.
Information processing with an excitable chemical medium, like the Belousov-Zhabotinsky (BZ) reaction, is typically based on information coding in the presence or absence of excitation pulses. Here we present a new co...
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Information processing with an excitable chemical medium, like the Belousov-Zhabotinsky (BZ) reaction, is typically based on information coding in the presence or absence of excitation pulses. Here we present a new concept of Boolean coding that can be applied to an oscillatory medium. A medium represents the logical TRUE state if a selected region oscillates with a high frequency. If the frequency fails below a specified value, it represents the logical FALSE state. We consider a medium composed of disks encapsulating an oscillatory mixture of reagents, as related to our recent experiments with lipid-coated BZ droplets. We demonstrate that by using specific geometrical arrangements of disks containing the oscillatory medium one can perform logical operations on variables coded in oscillation frequency. Realizations of a chemical signal diode and of a single-bit memory with oscillatory disks are also discussed.
Brain machine interfaces (BMIs) have attracted intense attention as a promising technology for directly interfacing computers or prostheses with the brain's motor and sensory areas, thereby bypassing the body. The...
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Brain machine interfaces (BMIs) have attracted intense attention as a promising technology for directly interfacing computers or prostheses with the brain's motor and sensory areas, thereby bypassing the body. The availability of multiscale neural recordings including spike trains and local field potentials (LFPs) brings potential opportunities to enhance computational modeling by enriching the characterization of the neural system state. However, heterogeneity on data type (spike timing versus continuous amplitude signals) and spatiotemporal scale complicates the model integration of multiscale neural activity. In this paper, we propose a tensor-product-kernel-based framework to integrate the multiscale activity and exploit the complementary information available in multiscale neural activity. This provides a common mathematical framework for incorporating signals from different domains. The approach is applied to the problem of neural decoding and control. For neural decoding, the framework is able to identify the nonlinear functional relationship between the multiscale neural responses and the stimuli using general purpose kernel adaptive filtering. In a sensory stimulation experiment, the tensor-product-kernel decoder outperforms decoders that use only a single neural data type. In addition, an adaptive inverse controller for delivering electrical microstimulation patterns that utilizes the tensor-product kernel achieves promising results in emulating the responses to natural stimulation.
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