Applying M-sequences Decimation to Generate Interleaved Sequence

Abstract—M-sequences are widely used in for many purposes, from synchronization, whitening, communications and cryptography. We analyze decimation techniques and introduce two methods to generate decimation sequences which don’t have to calculate intermediate states. Then we apply these methods to interleaved sequence as a new method to pre-calculate for set of interleaved order which is more effective in implementation. Tóm tắt—M-dãy đang được sử dụng rất rộng rãi trong nhiều lĩnh vực, từ việc đồng bộ, làm trắng thông tin, viễn thông và kỹ thuật mật mã. Chúng tôi phân tích kỹ thuật phân rã m-dãy theo bước và giới thiệu hai phương pháp sinh dãy phân rã theo bước mà không cần tính các trạng thái trung gian. Áp dụng phương pháp này vào dãy lồng ghép, ta có một phương pháp mới để tính trước tập các thứ tự lồng ghép có tính hiệu quả trong cài đặt thực tế.

The impulse response of optic flow-sensitive descending neurons to roll m-sequences

ABSTRACT When animals move through the world, their own movements generate widefield optic flow across their eyes. In insects, such widefield motion is encoded by optic lobe neurons. These lobula plate tangential cells (LPTCs) synapse with optic flow-sensitive descending neurons, which in turn project to areas that control neck, wing and leg movements. As the descending neurons play a role in sensorimotor transformation, it is important to understand their spatio-temporal response properties. Recent work shows that a relatively fast and efficient way to quantify such response properties is to use m-sequences or other white noise techniques. Therefore, here we used m-sequences to quantify the impulse responses of optic flow-sensitive descending neurons in male Eristalis tenax hoverflies. We focused on roll impulse responses as hoverflies perform exquisite head roll stabilizing reflexes, and the descending neurons respond particularly well to roll. We found that the roll impulse responses were fast, peaking after 16.5–18.0 ms. This is similar to the impulse response time to peak (18.3 ms) to widefield horizontal motion recorded in hoverfly LPTCs. We found that the roll impulse response amplitude scaled with the size of the stimulus impulse, and that its shape could be affected by the addition of constant velocity roll or lift. For example, the roll impulse response became faster and stronger with the addition of excitatory stimuli, and vice versa. We also found that the roll impulse response had a long return to baseline, which was significantly and substantially reduced by the addition of either roll or lift.

Finding Non-liner Register on Binary M-Sequence Generating Binary Multiplication Sequence

In the current time there is an important problem that is for a received linear or nonlinear binary sequence {zn} how we can find the nonlinear feedback shift register and its linear equivalent which generate this sequence. The linear orthogonal sequences, special M-Sequences, play a big role in these methods for solving this problem. In the current research trying give illuminations about the methods which are very useful for solving this problem under short sequences, and study these methods for finding the nonlinear feedback shift register of a multiplication sequence and its linear equivalent feedback shift register of a received multiplication binary sequence{zn} where the multiplication on h degrees of a binary linear sequence {an}, or finding the equivalent linear feedback shift register of {zn}, where the sequence {zn}of the form M-sequence, and these methods are very effectively. We can extend these methods for the large sequences using programming and modern computers with large memory.

Generalization of Multiplication M-Sequences over Fp and Its Reciprocal Sequences

Mp-Sequences or M-Sequence over Fp not used so much in current time as binary M-Sequences and it is pending with the difficult to construct there coders and decoders of Mp-Sequences further these reasons there is expensive values to construct them but the progress in the technical methods will be lead to fast using these sequences in different life’s ways, and these sequences give more collection of information and distribution them on the input and output links of the communication channels, building new systems with more complexity, larger period, and security. In current article we will study the construction of the multiplication Mp-Sequence {zn}and its linear equivalent, this sequences are as multiple two sequences, the first sequence{Sn}is an arbitrary Mp-Sequence and the second sequence {ζn} reciprocal sequence of the first sequence {Sn}, length of the sequence {zn}, period, orthogonal and the relations between the coefficients and roots of the characteristic polynomial of f(x) and it’s reciprocal polynomial g(x) and compare these properties with corresponding properties in M-Sequences.

Pseudo-random sequences of non-maximum length on shift registers with reducible and primitive polynomials

Inhomogeneous pseudo-random sequences of non-maximal length formed by shift registers with linear feedbacks based on a characteristic polynomial of degree n of the form ϕ(x)=ϕ1(x)ϕ2(x), where ϕ1(x) = x m1 ⊕ 1, and ϕ2(x) of degree m 2 is primitive (m 1 = 2 k , k is a positive integer, n = m 1 + m 2) are considered. Three schemes that are equivalent in terms of periodic sequence structures were considered. Of the greatest interest are the shift registers connected in an arbitrary way using a modulo-two adder, the feedbacks in which correspond to the multipliers ϕ1(x) and ϕ2(x) the polynomials ϕ(x). In this case, there is a complex process of forming output sequences, which involves both direct and inverse M-sequences. The statement about the singularity of the generated sequences at m 1 = 4 is proved, which is confirmed by their decimation with an index equal to the period of the primitive polynomial.

Study the Multiplication M-sequences and Its Reciprocal Sequences

M-Sequences play a big important role, as the other binary orthogonalsequences, for collection the information on the input links and distributionthese information on the output links of the communication channelsand for building new systems with more complexity, larger period, andsecurity, through multiplication these sequences. In our article we try tostudy the construction of the multiplication sequence {zn}and its linearequivalent, this multiplication sequence is as multiple two sequences, thefirst sequence{an}is an arbitrary M-sequence and the second sequence{bn}is not completely different but is the reciprocal sequence of the firstsequence {an} that is the reciprocal sequence has characteristic polynomialg(x) is reciprocal of f(x), which is the characteristic polynomial of the firstsequence {an}, also we will study the linear equivalent of the multiplicationsequence {zn}and we will see that the length of the linear equivalent of {zn}is equal to ((deg f(x))2 - deg(f(x)).

Photogrammetry of sequence and bioherm morphology in the Paradox Formation, Utah, U.S.A.: A test of the coherence of Pennsylvanian (Moscovian) glacio-eustatic sea-level change

ABSTRACT Despite long-standing recognition of high-amplitude, high-frequency sea-level variation resulting from repeated glaciations of Gondwanaland, recorded as “cyclothems” in late Paleozoic strata worldwide, major questions remain concerning their precise timing and expression in the stratigraphic record. A deep meandering canyon in southern Utah cut by the San Juan River exposes cyclic Pennsylvanian (Moscovian) carbonate strata of the Paradox Formation of the Hermosa Group in three dimensions. These peritidally to subtidally deposited strata archive a long record of Pennsylvanian sea-level change that was important to the early development of sequence stratigraphy. Their interpretation with respect to sea level is complicated by lateral variations in sequence thickness and a lack, until recently, of precise geochronologic control. In this study, we use Structure from Motion photogrammetry (SfM) to quantify lateral stratigraphic variation in three dimensions (3D) in the inner gorge of the canyon, then integrate these data with published U-Pb geochronology and conodont biostratigraphy to assess magnitude and temporal significance of depositional cyclicity. 3D SfM models were used to precisely measure the thickness of sixteen depositional sequences in the Barker Creek and Akah intervals, which constitute the lower Paradox Formation. Bioherms ranging from 2–18 m in relief occur within five sequences, and are typically constructed by either microbialites, the sponge Chaetetes, or a mixture of both. On average, bioherms containing Chaetetes are steeper and thicker than those without them. Bioherm-generated bathymetric highs can influence overlying strata in several characteristic ways: 1) by serving as a nucleation site for bioherms in overlying sequences, 2) sequences often onlap bioherms, leading to local stratal truncations, and in some cases, 3) progradational geometries extend laterally outward from preexisting highs in underlying units. Sequence thickness can vary laterally by up to four times in areas with no obvious bioherms; sequences tend to be thickest in the vicinity of bioherms. To better understand the potential orbital significance and correlation of Paradox Formation cyclicity to an increasingly precise global record, we projected photogrammetry-generated average sequence thicknesses onto an age framework using conodont and fusulinid biostratigraphy and CA-TIMS U-Pb zircon ages for correlative strata in Eastern Europe. To mitigate the influence of local variability of accumulation rate, SfM-based average sequence thicknesses in the study area were used to construct a relative-sea-level history that can be compared to global records. While regional averaging cannot correct for the unknown durations of sequence-bounding unconformities, underfilled accommodation, or autocyclicity due to shoal migration, it does provide a more quantitative means to consider timescales of deposition and mechanisms responsible for cyclicity than is possible with a one-dimensional section or core. Paradox Formation cyclicity shares a broad similarity with the global record, suggesting coherent glacio-eustatic sea-level variation across several different tectonic regimes. If one explores a thickness to duration relationship in these sequences, it is plausible that eight thin (2–4 m) sequences in the investigated strata (S2.6–11; S3.5–6) have apparent durations ranging from 100 to 350 kyr, within the plausible range of short and long eccentricity. In contrast, four thicker (6–12 m) sequences in the middle Akah interval (S3.1–S3.4) contain deeper-water lithofacies and have apparent durations ranging from 500 to 1000 kyr, implying that they may be down-dip composites of multiple documented cyclothems in the North American Midcontinent, Urals–Donets, and South China Block successions.