scholarly journals On the State Approach Representations of Convolutional Codes over Rings of Modular Integers

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2962
Author(s):  
Ángel Luis Muñoz Muñoz Castañeda ◽  
Noemí DeCastro-García ◽  
Miguel V. Carriegos
Keyword(s):  
Coding Theory ◽  
Convolutional Codes ◽  
Codes Over Rings ◽  
Input State ◽  
First Order ◽  
Convolutional Coding ◽  
Artinian Rings ◽  
Base Ring ◽  
Order Representation ◽  
Classical Construction

In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers.

The Study of Coded CPM Schemes

2012 ◽  
Vol 198-199 ◽  
pp. 1408-1412
Author(s):  
Lin Bo Su ◽  
Jian Hua Chen ◽  
Ying Peng Hu
Keyword(s):  
Fading Channels ◽  
Convolutional Codes ◽  
Continuous Phase ◽  
Coded Modulation ◽  
Superior Performance ◽  
Continuous Phase Modulation ◽  
Codes Over Rings ◽  
Constant Envelope ◽  
Modulation Schemes ◽  
Serially Concatenated

Continuous Phase Modulation (CPM) schemes belong to a class of constant-envelope digital modulation schemes, the constant-envelope nature of the CPM signals makes them robust for the nonlinear and fading channels, and very useful for the satellite and/or the mobile radio channels. Comparing to PSK modulation, CPM modulation can not only provide spectral economy, but also exhibit a “coding gain”. CPM can be decomposed into a Continuous Phase Encoder (CPE) followed by a Memoryless Modulator (MM), this allows many new coded modulation schemes of combination of convolutional encoder and CPM modulator to be possible, such as serially-concatenated CPM (SC-CPM), SC-CPM with Convolutional Codes over Rings, pragmatic CPM (P-CPM), Concatenation of convolutional endocder and extended CE（CCEC）, etc. Some simulations show that these new CPM schemes can offer superior performance.

scholarly journals First-order discrete Faddeev gravity at strongly varying fields

2017 ◽  
Vol 32 (35) ◽  
pp. 1750181
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
Dimensional Space ◽  
Tetrad Field ◽  
First Order ◽  
Antiferromagnetic Structure ◽  
Riemannian Connection ◽  
Order Representation ◽  
Independent Variable ◽  
The Continuum ◽  
Elementary Area ◽  
Classical Background

We consider the Faddeev formulation of general relativity (GR), which can be characterized by a kind of d-dimensional tetrad (typically d = 10) and a non-Riemannian connection. This theory is invariant w.r.t. the global, but not local, rotations in the d-dimensional space. There can be configurations with a smooth or flat metric, but with the tetrad that changes abruptly at small distances, a kind of “antiferromagnetic” structure. Previously, we discussed a first-order representation for the Faddeev gravity, which uses the orthogonal connection in the d-dimensional space as an independent variable. Using the discrete form of this formulation, we considered the spectrum of (elementary) area. This spectrum turns out to be physically reasonable just on a classical background with large connection like rotations by [Formula: see text], that is, with such an “antiferromagnetic” structure. In the discrete first-order Faddeev gravity, we consider such a structure with periodic cells and large connection and strongly changing tetrad field inside the cell. We show that this system in the continuum limit reduces to a generalization of the Faddeev system. The action is a sum of related actions of the Faddeev type and is still reduced to the GR action.

scholarly journals Some structural properties of convolutional codes over rings

1998 ◽  
Vol 44 (2) ◽  
pp. 839-845 ◽  
Author(s):  
R. Johannesson ◽  
Zhe-Xian Wan ◽  
E. Wittenmark
Keyword(s):  
Structural Properties ◽  
Convolutional Codes ◽  
Codes Over Rings

scholarly journals Generic Noninteger Order Controller for Time-Delay Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Sami Hafsi ◽  
Sadem Ghrab ◽  
Kaouther Laabidi
Keyword(s):  
Time Delay ◽  
Stability Region ◽  
Delay Systems ◽  
Pid Controllers ◽  
Time Delay Systems ◽  
First Order ◽  
Industrial Utilization ◽  
Complete Set ◽  
Order Representation ◽  
Fractional Controller

This paper focuses on the problem of fractional controller P I stabilization for a first-order time-delay systems. For this reason, we utilize the Hermite–Biehler and Pontryagin theorems to compute the complete set of the stabilizing P I λ parameters. The widespread industrial utilization of PID controllers and the potentiality of their noninteger order representation justify a timely interest in P I λ tuning techniques. Step responses are calculated through K p , K i , l a m b d a parameters inside and outside stability region to prove the method efficiency.

Neighboring Optimal Feedback Law for Higher-Order Dynamic Systems

2002 ◽  
Vol 124 (3) ◽  
pp. 492-497 ◽  
Author(s):  
Tawiwat Veeraklaew ◽  
Sunil K. Agrawal
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Optimal Solution ◽  
Higher Order ◽  
Input State ◽  
Linear Quadratic ◽  
First Order ◽  
Optimal Feedback ◽  
Order Form ◽  
Jacobi Equations

In recent years, using tools from linear and nonlinear systems theory, it has been shown that classes of dynamic systems in first-order forms can be alternatively written in higher-order forms, i.e., as sets of higher-order differential equations. Input-state linearization is one of the most popular tools to achieve such a representation. The equations of motion of mechanical systems naturally have a second-order form, arising from the application of Newton’s laws. In the last five years, effective computational tools have been developed by the authors to compute optimal trajectories of such systems, while exploiting the inherent structure of the dynamic equations. In this paper, we address the question of computing the neighboring optimal for systems in higher-order forms. It must be pointed out that the classical solution of the neighboring optimal problem is well known only for systems in the first-order form. The main contributions of this paper are: (i) derivation of the optimal feedback law for higher-order linear quadratic terminal controller using extended Hamilton-Jacobi equations; (ii) application of the feedback law to compute the neighboring optimal solution.

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