Network coding (NC) can be applied to achieve the maximal information flow in a network. In energy-constraint wireless networks such as wireless sensor networks, applying NC can further reduce the number of wireless t...
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Network coding (NC) can be applied to achieve the maximal information flow in a network. In energy-constraint wireless networks such as wireless sensor networks, applying NC can further reduce the number of wireless transmissions and hence prolong the life time of sensor nodes. Although applying NC in wireless networks is obviously beneficial, it is possible that a malicious node (Byzantine attacker) can take advantage of the inherent vulnerability of error propagation in the NC scheme to corrupt all the information transmissions. In the NC scheme, an intermediate node linearly combines several incoming messages as its outgoing messages. Thus a data error injected in any intermediate nodes will corrupt the information reaching a destination. Recent research efforts have shown that NC can be combined with classical error control codes and cryptography for secure communications or misbehavior detections. Nevertheless, when it comes to Byzantine attacks, these results have limited effects. In this paper, a distributed algorithm is developed to effectively detect, locate, and isolate the Byzantine attackers in a wireless ad hoc network with random linear network coding (RLNC). To the best of our knowledge, our work is the first to address the problem of Byzantine failures in a wireless network with RLNC.
A major problem in communication engineering system is the transmitting of information from source to receiver over a noisy channel. To check the error in information digits many error detecting and correcting codes h...
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A major problem in communication engineering system is the transmitting of information from source to receiver over a noisy channel. To check the error in information digits many error detecting and correcting codes have been developed. The main aim of these error correcting codes is to encode the information digits and decode these digits to detect and correct the common errors in transmission. This information theory concept helps to study the information transmission in biological systems and extend the field of coding theory into the biological domain. In the cellular level, the information in DNA is transformed into proteins . The sequence of bases like Adenine (A), Thymine (T), Guanine (G) and Cytosine (C) in DNA may be considered as digital codes which transmit genetic information. This paper shows the existence of any form error detecting code in the DNA structure, by encoding the DNA sequences using Hamming code.
Let C be a binary linear block code of length n, dimension k and minimum Hamming distance d over GF(2)(n). Let d(perpendicular to) denote the minimum Hamming distance of the dual code of C over GF(2)(n). Let epsilon :...
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Let C be a binary linear block code of length n, dimension k and minimum Hamming distance d over GF(2)(n). Let d(perpendicular to) denote the minimum Hamming distance of the dual code of C over GF(2)(n). Let epsilon : GF(2)(n) bar right arrow {-1, 1}(n) be the component-wise mapping epsilon(v(i)):=(-1)(vi), for v = (v(1), v(2), ..., v(n)) is an element of GF(2)(n). Finally, for p < n, let Phi(C) be a p x n random matrix whose rows are obtained by mapping a uniformly drawn set of size p of the codewords of C under epsilon. It is shown that for d(perpendicular to) large enough and y:=p/n is an element of (0, 1) fixed, as n -> infinity the empirical spectral distribution of the Gram matrix of 1/root n Phi(C) resembles that of a random i.i.d. Rademacher matrix (i.e., the Marchenko-Pastur distribution). Moreover, an explicit asymptotic uniform bound on the distance of the empirical spectral distribution of the Gram matrix of 1/root n Phi(C) to the Marchenko-Pastur distribution as a function of y and d(perpendicular to) is presented.
We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic ...
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We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group algebra of a nilpotent group. (C) 2010 Elsevier Inc. All rights reserved.
With an ever increasing volume of digital data there is a huge increase in the demand for much faster, smaller, and denser storage technologies. Conventional 2-D (surface) storage/memory technologies may soon be repla...
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With an ever increasing volume of digital data there is a huge increase in the demand for much faster, smaller, and denser storage technologies. Conventional 2-D (surface) storage/memory technologies may soon be replaced with much faster and denser 3-D volumetric (holographic) storage technologies. Photo sensitive protein bacteriorhodopsin has been proven to have great chemical, thermal, and holographic properties and is a good choice for both associative and volumetric memories. Associative memory systems have a wide range of practical applications. However, there is a lack of a formal computational model that can be used to analyze the performance of different algorithms on architectures that support associative memory. We first address this issue by defining a new computational model on protein-based associative memory processors. We also present and analyze algorithms for several fundamental problems on this new model. Secondly, we employ balanced modulated codes in volumetric memories to reduce the bit error rate and improve fidelity. Conventional coding schemes such as 6 : 8 coding, limit the size of the page to 8 bits and achieve a code rate (utility) of only 75%. As the technology matures we need efficient algorithms to produce these codes with better utility. In this paper, 1 we address this problem and give algorithms that can generate these codes with superior utility.
A direct method is proposed to get the inverse matrix of circulant matrix that find important application in engineering, the elements of the inverse matrix are functions of zero points of the characteristic polynomia...
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A direct method is proposed to get the inverse matrix of circulant matrix that find important application in engineering, the elements of the inverse matrix are functions of zero points of the characteristic polynomial g(z) and g'(z) of circulant matrix, four examples to get the inverse matrix are presented in the paper. (C) 2011 Elsevier Inc. All rights reserved.
Recently, there were several papers on finding good linear codes. Various methods were introduced to make good linear codes. In this paper, we give a simple iterative algorithm to make good linear codes. Using our alg...
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Recently, there were several papers on finding good linear codes. Various methods were introduced to make good linear codes. In this paper, we give a simple iterative algorithm to make good linear codes. Using our algorithm we construct 86 codes which improve the minimum distance of previously best known linear codes for fixed parameters n, k.
A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a finite group. In these realizations, the group algebra is identified with the ambient space,...
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A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a finite group. In these realizations, the group algebra is identified with the ambient space, and the group elements with the coordinates of the ambient space. It is an obvious consequence of the definition that every p(r)-ary affine-invariant code of length pm, with p prime, can be realized as an ideal of the group algebra F-p(r) [(F-pm. +)], where (F-pm. +) is the underlying additive group of the field F-pm with p(m) elements. In this paper we describe all the group code structures of an affine-invariant code of length p(m) in terms of a family of maps from F-pm to the group of automorphisms of (F-pm, +). We also present a family of non-obvious group code structures in an arbitrary affine-invariant code. (C) 2010 Elsevier Inc. All rights reserved.
We quantify the error statistics and patterning effects in a 5 x 40 Gbit/s WDM RZ-OOK SMF/DCF fibre link using hybrid Raman/EDFA amplification. By extensive use of a numerical model, we determine how the error statist...
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We quantify the error statistics and patterning effects in a 5 x 40 Gbit/s WDM RZ-OOK SMF/DCF fibre link using hybrid Raman/EDFA amplification. By extensive use of a numerical model, we determine how the error statistics change with the transmission distance. This knowledge is used as a basis for a constrained coding technique in order to improve the transmission error rate. We propose an adaptive constrained code for mitigation of the patterning effects and demonstrate that this approach can substantially reduce the bit error rate (BER) even for very large values of the channel BER (BER > 10(-1)). The proposed technique can be used in combination with forward error correction schemes (FEC) to extend the range of channel BERs that an FEC scheme is effective over. (C) 2011 Elsevier B.V. All rights reserved.
We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer t >= 3 is said to be exceptional if f (x) = x(t) is ...
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We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer t >= 3 is said to be exceptional if f (x) = x(t) is APN (Almost Perfect Nonlinear) over F(2n) for infinitely many values of n. Equivalently, t is exceptional if the binary cyclic code of length 2(n) - 1 with two zeros omega, omega(t) has minimum distance 5 for infinitely many values of n. The conjecture we prove states that every exceptional number has the form 2(i) 4 + 1 or 4(i) - 2(i) + 1. (C) 2011 Elsevier Inc. All rights reserved.
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