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The generation of pseudorandom elements over finite fields is fundamental to the time, space and randomness complexity of randomized algorithms and data structures. We consider the problem of generating k-independent random values over a finite field F in a word RAM model equipped with constant time addition and multiplication in F, and present the first nontrivial construction of a generator that...
RS (Reed Solomon) codes have strong error correction capability. The reliability of information transmission can be improved by RS codes. It is widely used in modern communication. The blind recognition of RS codes is particularly important in the field of information interception and intelligent communication. In order to solve the blind recognition problem of the high rate RS codes, this paper presents...
In this paper, a view point of classification of linear codes based on algebraic structure and Local Cyclic Codes is presented. Linear codes are divided into two types (structural and non-structural); almost all these codes are used widely in practice. Local Cyclic Codes are described in relation with other linear codes. These codes are constructed on decompositions of polynomial ring according to...
This paper proposes a structure for a digital coder, optimizing the multiplication circuit area that leads to a substantial gain in the main circuit surface and helps future decoding. The work describes the functioning process, the technical design and tests the coder's main functions. The evolution of RS coding and the growing pallet of application domains are also briefly covered.
Error correction coding technology is a valid way to improve the reliability of communication system in which information will be distorted duo to various noises in the channel. This paper considers RS code as the error correction code, and gives the implementation of the RS encoder under CCSDS standard. The implementation of the parallel multiplier with constant coefficients under the natural base...
This paper presents an algorithmic procedure for determining the cryptographic key properties and hence matching with the required complexity and strength to assure a more reliable and secure designs of cryptographic systems. The designed algorithm is capable to provide the cryptographic key structure based on optimum solution approach. Using the Hardware Description Language (HDL), Verilog, the key...
In this article we describe two alternative order-preserving encryption schemes. First scheme is based on arithmetic coding and the second scheme uses sequence of matrices for data encrypting. In the beginning of this paper we briefly describe previous related work published in recent time. Then we propose alternative variants of OPE and consider them in details. We examine drawbacks of these schemes...
We introduce a probabilistically complete algorithm for solving a visibility-based pursuit-evasion problem in two-dimensional polygonal environments with multiple pursuers. The inputs for our algorithm are an environment and the initial positions of the pursuers. The output is a joint strategy for the pursuers that guarantees that the evader has been captured. We create a Sample-Generated Pursuit-Evasion...
In the new IEEE 802.11ah standard, a CRC code of 4 parity bits provides error detection for the SIG field of length 36 or 48 bits, giving rise to a significant performance penalty, which may be acceptable if there is an additional 32-bit Frame Check Sequence check on the payload in layer 2. However, in 802.11ah, there exist new Medium Access Control (MAC) control frames which are Null Data Packets...
With RFID-tags becoming a part of our everyday lives, the need for (ultra-)lightweight implementations of cryptographic algorithms are a major challenge for researchers and engineers alike. While purpose-built algorithms offer low hardware-footprint, their usage is often impeded by the need to comply with standards, most notably the Advanced Encryption Standard (AES). We take on this challenge by...
A Hardware-In-the-Loop (HIL) simulation system of the Diesel Generator Set (DGS), which can be used to develop and debug electronic speed governors, is developed in this paper. In the HIL simulation system, the physical diesel is replaced with its mathematical model. And the electronic speed governor, electric actuator and speed pickup are physically installed in the HIL simulation system. A DC LVDT...
In this paper, we consider the non-convex optimal power flow (OPF) problem. We apply the recently proposed continuous-time gradient dynamics approach to solve OPFs and study their convergence properties. This approach is appealing because it has a naturally distributed structure. We numerically show, for a three-bus OPF example, that the gradient dynamics locally converges to a saddle point (the primal...
We develop and analyze a new family of pseudorandom generators for polynomial threshold functions with respect to the Gaussian distribution. In particular, for any fixed degree we develop a generator whose seed length is subpolynomial in the error parameter, epsilon. We get particularly nice results for degree 1 and degree 2 threshold functions, in which cases our seed length is O(log(n) + log^{3/2}(1/epsilon))...
Furthering the study of cryptography in constant parallel time, we give new evidence for the security of Gold Reich's candidate pseudorandom generator with near-optimal, polynomial stretch. Our evidence consists both of security against sub exponential-time linear attacks as well as sub exponential-time attacks using SDP hierarchies such as Sherali-Adams+ and Lasserre/Parrilo. More specifically, instantiating...
This paper presents a practical extension to the classical gradient-based extremum seeking control for the case when the disturbances responsible for the changes in the extremum of a related performance function can be measured. The additional information is used to improve accuracy, convergence speed and robustness of the underlying ESC scheme. Based on the disturbance measurements a map between...
We give a length-efficient puncturing of Reed-Muller codes which preserves its distance properties. Formally, for the Reed-Muller code encoding n-variate degree-d polynomials over F_q with q gtrsim d/delta, we present an explicit (multi)-set S subseteq F_q^n of size N=mathrm {poly}(n^d/delta) such that every nonzero polynomial vanishes on at most delta N points in S. Equivalently, we give an explicit...
We consider the problem of noncoherent error correction in multiple-source multicast networks. We show that a distributed network error-correcting code can be designed as a subcode of a Gabidulin code. This allows the destination nodes to utilize any decoder designed using rank-metric. We show that this achieves the full capacity region of any network with up to three messages, with optimal scaling...
This paper presents a novel encoding algorithm for QC-LDPC codes constructed from Reed-Solomon codes. The encoding is performed in the transform domain via Galois Fourier transformation. Message bits are encoded in sections corresponding to sub-matrices of the parity-check matrix in the transform domain. Because of the structure of the parity-check matrices of these LDPC codes, the encoding can be...
Cyclic redundancy codes are often used in communications protocols to detect and correct random bit errors that may occur due to noise in the channel. Checksums are also often used for a similar purpose, often within the same protocol stack. This paper examines the interaction between the use of CRCs and checksums in the ANSI C12.21 protocol and finds that the use of the checksum improves the net...
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