Binary Alexis sequences with perfect correlation

Binary Alexis (1986) sequences are useful signals for fast start-up equalization, channel estimation, synchronization, or ranging. The aperiodic autocorrelation functions of Alexis sequences vanish in a broad window region when correlated using additional binary preamble and postamble sequences. Originally, Alexis sequences were found by computer search. Two methods are presented by which such sequences can be constructed for any length N=p^a and N=2(p^a+1), where p, is an odd prime and a=1, 2, 3     

Binary sequences with low aperiodic autocorrelation for synchronization purposes

An evolutionary algorithm is used to find three sets of binary sequences of length 49-100 suitable for the synchronization of digital communication systems. Optimization of the sets are done by taking into consideration the type of preamble used in data frames and the phase-lock mechanism of the communication system. The preamble is assumed to be either a pseudonoise (PN) sequence or a sequence of 1s. There may or may not be phase ambiguity in detection. With this categorization, the first set of binary sequences is optimized with respect to aperiodic autocorrelation which corresponds to the random (PN) preamble without phase ambiguity case. The second and third sets are optimized with respect to a modified aperiodic autocorrelation for different figures of merit corresponding to the predetermined preamble (sequence of 1s) with and without phase ambiguity cases.     

基于RSA模数的一类新型广义割圆序列的迹表示

针对最近研究的周期为pq（两个不同的大素数的乘积）的一类广义割圆序列，通过计算该序列的离散傅里叶变换系数，从而确定了该序列的Mattson-Solomon多项式，并由此得到了序列的迹表示形式.     

Binary convolutional codes with application to magnetic recording

Calderbank, Heegard, and Ozarow [1] have suggested a method of designing codes for channels with intersymbol interference, such as the magnetic recording channel. These codes are designed to exploit intersymbol interference. The standard method is to minimize intersymbol interference by constraining the input to the channel using run-length limited sequences. Calderbank, Heegard, and Ozarow considered an idealized model of an intersymbol interference channel that leads to the problem of designing codes for a partial response channel with transfer function(1 - D^{N}) /2, where the channel inputs are constrained to bepm 1. This problem is considered here. Channel inputs are generated using a nontrivial coset of a binary convolutional code. The coset is chosen to limit the zero-run length of the output of the channel and so maintain clock synchronization. The minimum squared Euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code which we call the magnitude code. An interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic.     

混沌二进制序列构成的安全性研究

由混沌映射驱动得到的伪随机二进制序列应确保有足够的比特安全性。信息有规律地泄漏,会导致有可能利用有限长度的输出序列完全地破译混沌驱动序列,并恢复有限长度的初始密钥,重建全部的输出序列。     

Polyphase sequences with low autocorrelation

Low autocorrelation for sequences is usually described in terms of low base energy, i.e., the sum of the sidelobe energies, or the maximum modulus of its autocorrelations, a Barker sequence occurring when this value is /spl les/ 1. We describe first an algorithm applying stochastic methods and calculus to the problem of finding polyphase sequences that are good local minima for the base energy. Starting from these, a second algorithm uses calculus to locate sequences that are local minima for the maximum modulus on autocorrelations. In our tabulation of smallest base energies found at various lengths, statistical evidence suggests we have good candidates for global minima or ground states up to length 45. We extend the list of known polyphase Barker sequences to length 63.     

The Subsequence Weight Distribution of Summed Maximum Length Digital Sequences

The statistics of the weight distribution of subsequences of digital sequences called hybrid-sum sequences, formed from the modulo-two sum of several maximum length sequences, are analyzed. The results indicate that a relation exists between the statistics of the weight distribution of the subsequences and the characteristic polynomials of the component maximum length sequences. An analysis procedure is developed for identifying a large group of sequences with good statistical properties for applications requiring the generation of analog pseudorandom noise by filtering digital sequences. Using the analysis approach, the filtering process is approximated by the convolution of the sequence with a sum of unit-step functions. The first five moments of the resulting weighttuples are used to characterize the statistics of the filtered sequence. The analysis reveals that the statistics of the signals generated with the hybrid-sum generator are potentially superior for many applications to the statistics of signals generated with single maximum length sequence generators. Furthermore, fewer calculations are required to evaluate the statistics of a large group of hybrid-sum generators than are required to evaluate the statistics of the same size group of approximately equivalent maximum length sequences. Efficient algorithms that may be used to evaluate the statistics of hybrid-sum sequences are indicated, and example calculations are given.     

Spatial transformation of motion and deformation fields using nonrigid registration

In this paper, we present a technique that can be used to transform the motion or deformation fields defined in the coordinate system of one subject into the coordinate system of another subject. Such a transformation accounts for the differences in the coordinate systems of the two subjects due to misalignment and size/shape variation, enabling the motion or deformation of each of the subjects to be directly quantitatively and qualitatively compared. The field transformation is performed by using a nonrigid registration algorithm to determine the intersubject coordinate system mapping from the first subject to the second subject. This fixes the relationship between the coordinate systems of the two subjects, and allows us to recover the deformation/motion vectors of the second subject for each corresponding point in the first subject. Since these vectors are still aligned with the coordinate system of the second subject, the inverse of the intersubject coordinate mapping is required to transform these vectors into the coordinate system of the first subject, and we approximate this inverse using a numerical line integral method. The accuracy of our numerical inversion technique is demonstrated using a synthetic example, after which we present applications of our method to sequences of cardiac and brain images.     

Efficient method for generating strong primes with constraint of bit length

Many methods have been proposed to generate the strong primes for the RSA public key cryptosystem. However, all of the methods are inefficient if strong primes with the constraint of bit length need to be generated. An efficient method is proposed for generating strong primes with the constraint of bit length.<>     

构造短码长不规则LDPC码

在给定长度和度数分布对情况下,不规则短码长LDPC码的性能差别很大。本文给出了一种低复杂度的基于树的贪婪搜索算法(GTS),此算法通过调整校验矩阵中环的分布情况,尽量减少短长度环,获得最大的平均最小环,从而构造性能很好的短码长不规则LDPC码。     

Binary frame synchronisation sequences for packet radio

Frame synchronisation sequences with the smallest possible correlation sidelobes are determined by exhaustive search for the case when the frame synchronisation word is preceded by specific bit synchronisation patterns. For a given length these new sequences have significantly lower sidelobes than the optimum autocorrelation sequences.     

Optimization techniques for antenna arrays

Various techniques for optimizing the performance indices of antenna arrays are discussed. In particular, methods for maximizing array directivity and signal-to-noise power ratio are reviewed. These performance indices are expressible as a ratio of two Hermitian forms, which has a certain special property to enable the facile determination of both its maximum value and the conditions under which this maximum is attained. Special maximization procedures by excitation amplitude and phase adjustments, by spacing perturbation, by phase adjustments only, and by a coordinate transformation with constraints on the array pattern are examined. For wire antennas the method of moments using a subsectioning technique can be applied to obtain numerical answers which include mutual-coupling effects. Methods for considering large arrays and for the maximization of power gain are indicated.     

Pseudorandom construction of low-density parity-check codes using linear congruential sequences

We consider maximal-length linear congruential sequences generated using a simple recursion to generate the bipartite graph of a low-density parity-check (LDPC) code. The main advantage is that the graph structure of the codes (edge connections) can be generated using a recursion, rather than having to store the graph connections in memory, which facilitates hardware implementation of the decoder. For this class of codes, sufficient conditions on the recursion parameters are derived, such that regular LDPC codes can be constructed with no cycles of length four or less. Simulation results show that these codes provide almost the same performance of a constrained pseudorandom construction that explicitly avoids cycles of length less than or equal to four.     

Multiplicative Complementary Binary Signal-Code Constructions

There are proposed signal-code constructions consisting of two or more components shaped on a basis of binary sequences with a property of multiplicative complementariness of their matched filtering results. There are considered systematically the rules of synthesis of such binary sequences containing signal-code constructions; there are described analytically their correlation properties, their processing specificities and the structure of obtained resulting signal. On a basis of statistical model of correlated signal components and their clusterization there is shown theoretical continuity of proposed signal-code constructions and Barker’s binary sequences. There are represented the examples of shaping, processing and parameters of researched signal-code constructions. It is carried out comparative analysis of structural specificities and noise immunity of multiplicative complementary signal-code constructions with complementary sequences (Golay’s codes), i.e. signal-code constructions with property of additive complementariness, there are exposed their advantages and drawbacks regarding spectral characteristics and signal detection characteristics (errors of the first and second genus).     

Classification of Random Binary Sequences Using Walsh-Fourier Analysis

The concept of a finite binary random sequence does not seem to be covered in the classical foundations of the theory of probability. Solomonoff, Kolmogorov and Chaitin have tried to include this case by considering the lengths of programs required to generate these sequences: a longer program implying more randomness. However this definition is difficult to apply. This paper presents a straightforward procedure using Walsh functions to determine the pattern in a binary sequence. A quantitative measure of randomness has also been proposed. This has been defined as the number of independent data (via the Walsh transform) required to generate the sequence divided by the length of the sequence. However at present this classification procedure is restricted to sequences of length 2k only. When extended to infinite sequences it yields results agreeing with those by the classical probability theory.     

Binary sequences with merit factor greater than 6.34

The maximum known asymptotic merit factor for binary sequences has been stuck at a value of 6 since the 1980s. Several authors have suggested that this value cannot be improved. In this paper, we construct an infinite family of binary sequences whose asymptotic merit factor we conjecture to be greater than 6.34. We present what we believe to be compelling evidence in support of this conjecture. The numerical experimentation that led to this construction is a significant part of the story.     

Linear complexity over F/sub p/ of Sidel'nikov sequences

Helleseth, Kim, and No (2003) described the linear complexity over F/sub p/ of Sidel'nikov sequences of length p/sup m/-1 for p=3, 5, and 7. In this correspondence, the result is generalized to all odd primes.     

Error Probabilities for Binary Direct-Sequence Spread-Spectrum Communications with Random Signature Sequences

Binary direct-sequence spread-spectrum multiple-access communications, an additive white Gaussian noise channel, and a coherent correlation receiver are considered. An expression for the output of the receiver is obtained for the case of random signature sequences, and the corresponding characteristic function is determined. The expression is used to study the density function of the multiple-access interference and to determine arbitrarily tight upper and lower bounds on the average probability of error. The bounds, which are obtained without making a Gaussian approximation, are compared to results obtained using a Gaussian approximation. The effects of transmitter power, the length of the signature sequences, and the number of interfering transmitters are illustrated. Each transmitter is assumed to have the same power, although the general approach can accommodate the case of transmitters with unequal powers.     

Long Frame Sync Words for Binary PSK Telemetry

Correlation criteria have previously been established for identifying whether a given binary sequence would be a good frame sync word for phase-shift keyed telemetry. In the past, the search for a goodK-bit sync word has involved the application of these criteria to the entire set of 2^KbinaryK-tuples. It is shown that restricting this search to a much smaller subset consisting ofK-bit prefixes of pseudonoise sequences results in sync words of comparable quality, with greatly reduced computer search times for larger values ofK. As an example, this procedure is used to find good sync words of length 16-63; from a storage viewpoint, each of these sequences can be generated by a 5- or 6-bit linear feedback shift register.     

The Generation of High-Speed Binary Sequences from Interleaved Low-Speed Sequences

This paper deals with the theory of generating high-speed binary sequences by interleaving two lower speed sequences which are displaced by half a bit period with respect to each other. The interleaving can be carried out by using a high-speed switch which is clocked at twice the clock rate of the lower speed sequences or by modulo 2 addition of the displaced sequences. Starting from any binary sequence, we give a general theory for the derivation of the binary sequences which are to be interleaved to produce any required high-speed sequence. We also deal with the particular case ofm-sequences.