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 On the Rate-Distortion Function of Sampled Cyclostationary Gaussian Processes

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 345
Author(s):  
Emeka Abakasanga ◽  
Nir Shlezinger ◽  
Ron Dabora
Keyword(s):  
Sampling Rate ◽  
Rate Distortion ◽  
Sampling Interval ◽  
Distortion Function ◽  
Wide Sense ◽  
Information Theoretic ◽  
Synchronous Sampling ◽  
Asynchronous Sampling ◽  
Two Parameters ◽  
The Relationship

Man-made communications signals are typically modelled as continuous-time (CT) wide-sense cyclostationary (WSCS) processes. As modern processing is digital, it is applied to discrete-time (DT) processes obtained by sampling the CT processes. When sampling is applied to a CT WSCS process, the statistics of the resulting DT process depends on the relationship between the sampling interval and the period of the statistics of the CT process: When these two parameters have a common integer factor, then the DT process is WSCS. This situation is referred to as synchronous sampling. When this is not the case, which is referred to as asynchronous sampling, the resulting DT process is wide-sense almost cyclostationary (WSACS). The sampled CT processes are commonly encoded using a source code to facilitate storage or transmission over wireless networks, e.g., using compress-and-forward relaying. In this work, we study the fundamental tradeoff between rate and distortion for source codes applied to sampled CT WSCS processes, characterized via the rate-distortion function (RDF). We note that while RDF characterization for the case of synchronous sampling directly follows from classic information-theoretic tools utilizing ergodicity and the law of large numbers, when sampling is asynchronous, the resulting process is not information stable. In such cases, the commonly used information-theoretic tools are inapplicable to RDF analysis, which poses a major challenge. Using the information-spectrum framework, we show that the RDF for asynchronous sampling in the low distortion regime can be expressed as the limit superior of a sequence of RDFs in which each element corresponds to the RDF of a synchronously sampled WSCS process (yet their limit is not guaranteed to exist). The resulting characterization allows us to introduce novel insights on the relationship between sampling synchronization and the RDF. For example, we demonstrate that, differently from stationary processes, small differences in the sampling rate and the sampling time offset can notably affect the RDF of sampled CT WSCS processes.

scholarly journals Calculating the Number of Cluster Heads Based on the Rate-Distortion Function in Wireless Sensor Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Mingxin Yang ◽  
Jingsha He ◽  
Yuqiang Zhang
Keyword(s):  
Wireless Sensor Networks ◽  
Energy Consumption ◽  
Sensor Networks ◽  
Data Fusion ◽  
Rate Distortion ◽  
Distortion Function ◽  
Sensor Nodes ◽  
Wireless Sensor ◽  
Wireless Sensor Nodes ◽  
Cluster Heads

Due to limited resources in wireless sensor nodes, energy efficiency is considered as one of the primary constraints in the design of the topology of wireless sensor networks (WSNs). Since data that are collected by wireless sensor nodes exhibit the characteristics of temporal association, data fusion has also become a very important means of reducing network traffic as well as eliminating data redundancy as far as data transmission is concerned. Another reason for data fusion is that, in many applications, only some of the data that are collected can meet the requirements of the sink node. In this paper, we propose a method to calculate the number of cluster heads or data aggregators during data fusion based on the rate-distortion function. In our discussion, we will first establish an energy consumption model and then describe a method for calculating the number of cluster heads from the point of view of reducing energy consumption. We will also show through theoretical analysis and experimentation that the network topology design based on the rate-distortion function is indeed more energy-efficient.

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.

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