scholarly journals On the Asymptotic Optimality of a Low-Complexity Coding Strategy for WSS, MA, and AR Vector Sources

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1378
Author(s):  
Jesús Gutiérrez-Gutiérrez ◽  
Marta Zárraga-Rodríguez ◽  
Xabier Insausti
Keyword(s):  
Moving Average ◽  
Asymptotic Optimality ◽  
Low Complexity ◽  
Convergence Speed ◽  
Sufficient Condition ◽  
Wide Sense ◽  
Gaussian Vector ◽  
Coding Strategy

In this paper, we study the asymptotic optimality of a low-complexity coding strategy for Gaussian vector sources. Specifically, we study the convergence speed of the rate of such a coding strategy when it is used to encode the most relevant vector sources, namely wide sense stationary (WSS), moving average (MA), and autoregressive (AR) vector sources. We also study how the coding strategy considered performs when it is used to encode perturbed versions of those relevant sources. More precisely, we give a sufficient condition for such perturbed versions so that the convergence speed of the rate remains unaltered.

scholarly journals A Low-Complexity and Asymptotically Optimal Coding Strategy for Gaussian Vector Sources

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 965
Author(s):  
Marta Zárraga-Rodríguez ◽  
Jesús Gutiérrez-Gutiérrez ◽  
Xabier Insausti
Keyword(s):  
Finite Length ◽  
Correlation Matrix ◽  
Moving Average ◽  
Low Complexity ◽  
Wide Sense ◽  
Gaussian Vector ◽  
Asymptotically Optimal ◽  
Optimal Coding ◽  
Length Data ◽  
Coding Strategy

In this paper, we present a low-complexity coding strategy to encode (compress) finite-length data blocks of Gaussian vector sources. We show that for large enough data blocks of a Gaussian asymptotically wide sense stationary (AWSS) vector source, the rate of the coding strategy tends to the lowest possible rate. Besides being a low-complexity strategy it does not require the knowledge of the correlation matrix of such data blocks. We also show that this coding strategy is appropriate to encode the most relevant Gaussian vector sources, namely, wide sense stationary (WSS), moving average (MA), autoregressive (AR), and ARMA vector sources.

scholarly journals Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 719 ◽  
Author(s):  
Jesús Gutiérrez-Gutiérrez ◽  
Marta Zárraga-Rodríguez ◽  
Pedro Crespo ◽  
Xabier Insausti
Keyword(s):  
Integral Formula ◽  
Moving Average ◽  
Rate Distortion ◽  
Distortion Function ◽  
Wide Sense ◽  
Vector Process

In this paper, we obtain an integral formula for the rate distortion function (RDF) of any Gaussian asymptotically wide sense stationary (AWSS) vector process. Applying this result, we also obtain an integral formula for the RDF of Gaussian moving average (MA) vector processes and of Gaussian autoregressive MA (ARMA) AWSS vector processes.

scholarly journals A Restless Bandit Model for Resource Allocation, Competition, and Reservation

2021 ◽  
Author(s):  
Jing Fu ◽  
Bill Moran ◽  
Peter G. Taylor
Keyword(s):  
Resource Allocation ◽  
Numerical Experiments ◽  
Asymptotic Optimality ◽  
Sufficient Condition ◽  
Limited Capacity ◽  
Index Policy ◽  
Asymptotically Optimal ◽  
Restless Bandit ◽  
Simple Sufficient Condition ◽  
Resource Capacity

In “A Restless Bandit Model for Resource Allocation, Competition and Reservation,” J. Fu, B. Moran, and P. G. Taylor study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. This problem is modeled as a set of heterogeneous restless multi-armed bandit problems (RMABPs) connected by constraints imposed by resource capacity. Following Whittle’s idea of relaxing the constraints and Weber and Weiss’s proof of asymptotic optimality, the authors propose an index policy and establish conditions for it to be asymptotically optimal in a regime where both arrival rates and capacities increase. In particular, they provide a simple sufficient condition for asymptotic optimality of the policy and, in complete generality, propose a method that generates a set of candidate policies for which asymptotic optimality can be checked. Via numerical experiments, they demonstrate the effectiveness of these results even in the pre-limit case.

scholarly journals Fast Consensus Tracking of Multiagent Systems with Diverse Communication Delays and Input Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Chun-xi Yang ◽  
Wei-xing Hong ◽  
Ling-yun Huang ◽  
Hua Wang
Keyword(s):  
Genetic Algorithm ◽  
Multiagent Systems ◽  
Frequency Domain Analysis ◽  
Convergence Speed ◽  
Sufficient Condition ◽  
Communication Delays ◽  
Tracking Problem ◽  
Consensus Tracking ◽  
Simulation Results ◽  
Input Delays

The consensus tracking problem for discrete-time multiagent systems with input and communication delays is studied. A sufficient condition is obtained over a directed graph based on the frequency-domain analysis. Furthermore, a fast decentralized consensus tracking conditions based on incrementPIDalgorithm are discussed for improving convergence speed of the multiagent systems. Based on this result, genetic algorithm is introduced to construct incrementPIDbased on genetic algorithm for obtaining optimization consensus tracking performance. Finally, a numerable example is given to compare convergence speed of three tracking algorithms in the same condition. Simulation results show the effectiveness of the proposed algorithm.

The Self-Tuning Distributed Information Fusion Kalman Filter for ARMA Signals

2011 ◽  
Vol 48-49 ◽  
pp. 1305-1309
Author(s):  
Gui Li Tao ◽  
Zi Li Deng
Keyword(s):  
Kalman Filter ◽  
System Analysis ◽  
Moving Average ◽  
Dynamic Error ◽  
Asymptotic Optimality ◽  
Correlation Method ◽  
The Self ◽  
Model Parameters ◽  
Self Tuning ◽  
Signal Filter

For the multisensor Autoregressive Moving Average (ARMA) signals with unknown model parameters and noise variances, using the Recursive Instrumental Variable (RIV) algorithm, the correlation method and the Gevers-Wouters algorithm with dead band, the fused estimators of unknown model parameters and noise variances can be obtained. Then substituting them into optimal fusion signal filter weighted by scalars, a self-tuning distributed fusion Kalman filter is presented. Using the dynamic error system analysis (DESA) method, it is rigorously proved that the self-tuning fused Kalman signal filter converges to the optimal fused Kalman signal filter, so that it has asymptotic optimality. A simulation example shows its effectiveness.

On strict stationarity and ergodicity of a non-linear ARMA model

1992 ◽  
Vol 29 (2) ◽  
pp. 363-373 ◽  
Author(s):  
Jian Liu ◽  
Ed Susko
Keyword(s):  
Moving Average ◽  
Sufficient Conditions ◽  
Arma Model ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Arma Models ◽  
Non Linear ◽  
Strict Stationarity ◽  
Necessary And Sufficient

Two recent papers by Petruccelli and Woolford (1984) and Chan et al. (1985) showed that the key element governing ergodicity of a threshold AR(1) model is the joint behavior of the two linear AR(1) pieces falling in the two boundary threshold regimes. They used essentially the necessary and sufficient conditions for ergodicity of a general Markov chain of Tweedie (1974), (1975) in a rather clever manner. However, it is difficult to extend the results to the more general threshold ARMA models. Besides, irreducibility is also required to apply Tweedie's results. In this paper, instead of pursuing the ideas in Tweedie's results, we shall develop a criterion similar in spirit to the technique used by Beneš (1967) in the context of continuous-time Markov chains. Consequently, we derive a necessary and sufficient condition for existence of a strictly stationary solution of a general non-linear ARMA model to be introduced in Section 2 of this paper. This condition is then applied to the threshold ARMA(1, q) model to yield a sufficient condition for strict stationarity which is identical to the condition given by Petruccelli and Woolford (1984) for the threshold AR(1). Hence, the conjecture that the moving average component does not affect stationarity is partially verified. Furthermore, under an additional irreducibility assumption, ergodicity of a non-linear ARMA model is established. The paper then concludes with a necessary condition for stationarity of the threshold ARMA(1, q) model.

Self-Tuning Information Fusion Wiener Smoother for ARMA Signals

2011 ◽  
Vol 48-49 ◽  
pp. 1018-1023
Author(s):  
Jin Fang Liu ◽  
Zi Li Deng
Keyword(s):  
Information Fusion ◽  
System Analysis ◽  
Moving Average ◽  
Dynamic Error ◽  
Asymptotic Optimality ◽  
Autoregressive Moving Average ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Self Tuning ◽  
Optimal Fusion

For the multisensor autoregressive moving average (ARMA) signals, based on the modern time series analysis method, a self-tuning information fusion Wiener smoother is presented when both model parameters and noise variances are unknown. The principle is that substituting the estimators of unknown parameters and noise variances into the corresponding optimal fusion Wiener smoother will yield a self-tuning fuser. Further, applying the dynamic error system analysis (DESA) method, it is rigorously proved that the self-tuning fused Wiener smoother converges to the optimal fused Wiener smoother in a realization, i.e. it has asymptotic optimality. A simulation example shows its effectiveness.

scholarly journals Stochastic Optimal Control for Buffer-Aided Cooperative Relaying Systems Using Nonorthogonal Multiple Access

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Zhishan Deng ◽  
Qianyun Gong ◽  
Quanzhong Li ◽  
Jiayin Qin
Keyword(s):  
Optimization Algorithm ◽  
Multiple Access ◽  
Asymptotic Optimality ◽  
Low Complexity ◽  
Base Station ◽  
Cooperative Relaying ◽  
Cell Edge ◽  
Data Buffer ◽  
Lyapunov Optimization ◽  
Cell Edge User

In this paper, a multiple-cluster downlink multiple-input single-output (MISO) nonorthogonal multiple access (NOMA) system is considered. In each cluster, there are one central user and one cell-edge user. The central user has a data buffer with finite storage units, which will decode the cell-edge user’s message and store it at the data buffer. To enhance the performance of the cell-edge user, the central user operates as a relay and helps forward the message to the cell-edge user. Our objective is to maximize the long-term average sum rates for the cell-edge users by designing the beamforming vectors and online power control, under the constraints of the data buffer causality, required information rates for central users, and transmit power at the base station and central users. Based on the current buffer state and the channel state information, we propose a low-complexity online Lyapunov optimization algorithm combined with a constrained concave-convex procedure (CCCP) to solve the causal and nonconvex problem. Furthermore, we verify the asymptotic optimality of the proposed online Lyapunov optimization algorithm. Simulation results demonstrate that our proposed scheme performs better than the greedy algorithm and the orthogonal multiple access (OMA) scheme.

On strict stationarity and ergodicity of a non-linear ARMA model

1992 ◽  
Vol 29 (02) ◽  
pp. 363-373 ◽  
Author(s):  
Jian Liu ◽  
Ed Susko
Keyword(s):  
Moving Average ◽  
Sufficient Conditions ◽  
Arma Model ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Arma Models ◽  
Non Linear ◽  
Strict Stationarity ◽  
Necessary And Sufficient

Two recent papers by Petruccelli and Woolford (1984) and Chan et al. (1985) showed that the key element governing ergodicity of a threshold AR(1) model is the joint behavior of the two linear AR(1) pieces falling in the two boundary threshold regimes. They used essentially the necessary and sufficient conditions for ergodicity of a general Markov chain of Tweedie (1974), (1975) in a rather clever manner. However, it is difficult to extend the results to the more general threshold ARMA models. Besides, irreducibility is also required to apply Tweedie's results. In this paper, instead of pursuing the ideas in Tweedie's results, we shall develop a criterion similar in spirit to the technique used by Beneš (1967) in the context of continuous-time Markov chains. Consequently, we derive a necessary and sufficient condition for existence of a strictly stationary solution of a general non-linear ARMA model to be introduced in Section 2 of this paper. This condition is then applied to the threshold ARMA(1, q) model to yield a sufficient condition for strict stationarity which is identical to the condition given by Petruccelli and Woolford (1984) for the threshold AR(1). Hence, the conjecture that the moving average component does not affect stationarity is partially verified. Furthermore, under an additional irreducibility assumption, ergodicity of a non-linear ARMA model is established. The paper then concludes with a necessary condition for stationarity of the threshold ARMA(1, q) model.

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