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Error Recovery Properties and Soft Decoding of QuasiArithmetic Codes
, 2008
"... This paper first introduces a new set of aggregated state models for softinput decoding of quasi arithmetic (QA) codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding perfor ..."
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Cited by 4 (0 self)
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This paper first introduces a new set of aggregated state models for softinput decoding of quasi arithmetic (QA) codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding performance and complexity. It is shown that closetooptimal decoding performance can be obtained with low values of the aggregation parameter, that is, with a complexity which is significantly reduced with respect to optimal QA bit/symbol models. The choice of the aggregation parameter depends on the synchronization recovery properties of the QA codes. This paper thus describes a method to estimate the probability mass function (PMF) of the gain/loss of symbols following a single bit error (i.e., of the difference between the number of encoded and decoded symbols). The entropy of the gain/loss turns out to be the average amount of information conveyed by a length constraint on both the optimal and aggregated state models. This quantity allows us to choose the value of the aggregation parameter that will lead to closetooptimal decoding performance. It is shown that the optimum position for the length constraint is not the last time instant of the decoding process. This observation leads to the introduction of a new technique for robust decoding of QA codes with redundancy which turns out to outperform techniques based on the concept of forbidden symbol.
A SignalFlowGraph Approach to Online Gradient Calculation
 Neural Computation
, 2000
"... A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple oneinput, on ..."
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Cited by 2 (0 self)
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A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple oneinput, oneoutput transformation, as in an electrical circuit. Even if graph representations are popular in the neural network community, they are often used for qualitative description rather than for rigorous representation and computational purposes. In this article, a method for both online and batchbackward gradient computation of a system output or cost function with respect to system parameters is derived by the SFG representation theory and its known properties. The system can be any causal, in general nonlinear and timevariant, dynamic system represented by an SFG, in particular any feedforward, timedelay, or recurrent neural network. In this work, we use discretetime notation, but the same theory holds for the continuoustime case. The gradient is obtained in a straightforward way by the analysis of two SFGs, the original one and its adjoint (obtained from the first by simple transformations), without the complex chain rule expansions of derivatives usually employed. This method can be used for sensitivity analysis and for learning both offline and online. Online learning is particularly important since it is required by many real applications, such as digital signal processing, system identification and control, channel equalization, and predistortion. 1
doi:10.1155/2008/752840 Research Article Error Recovery Properties and Soft Decoding of QuasiArithmetic Codes
, 2007
"... This paper first introduces a new set of aggregated state models for softinput decoding of quasi arithmetic (QA) codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding perfor ..."
Abstract
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This paper first introduces a new set of aggregated state models for softinput decoding of quasi arithmetic (QA) codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding performance and complexity. It is shown that closetooptimal decoding performance can be obtained with low values of the aggregation parameter, that is, with a complexity which is significantly reduced with respect to optimal QA bit/symbol models. The choice of the aggregation parameter depends on the synchronization recovery properties of the QA codes. This paper thus describes a method to estimate the probability mass function (PMF) of the gain/loss of symbols following a single bit error (i.e., of the difference between the number of encoded and decoded symbols). The entropy of the gain/loss turns out to be the average amount of information conveyed by a length constraint on both the optimal and aggregated state models. This quantity allows us to choose the value of the aggregation parameter that will lead to closetooptimal decoding performance. It is shown that the optimum position for the length constraint is not the last time instant of the decoding process. This observation leads to the introduction of a new technique for robust decoding of QA codes with redundancy which turns out to outperform techniques based on the concept of forbidden symbol. Copyright © 2008 Simon Malinowski et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
Using the Fourier Transform to Compute the Weight Distribution of a Binary Linear Block Code
"... ..."
LETTER Communicated by Andrew Back A SignalFlowGraph Approach to Online Gradient Calculation
"... A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple oneinput, on ..."
Abstract
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A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple oneinput, oneoutput transformation, as in an electrical circuit. Even if graph representations are popular in the neural network community, they are often used for qualitative description rather than for rigorous representation and computational purposes. In this article, a method for both online and batchbackward gradient computation of a system output or cost function with respect to system parameters is derived by the SFG representation theory and its known properties. The system can be any causal, in general nonlinear and timevariant, dynamic system represented by an SFG, in particular any feedforward, timedelay, or recurrent neural network. In this work, we use discretetime notation, but the same theory holds for the continuoustime case. The gradient is obtained in a straightforward way by the analysis of two SFGs, the original one and its adjoint (obtained from the first by simple transformations), without the complex chain rule expansions of derivatives usually employed. This method can be used for sensitivity analysis and for learning both offline and online. Online learning is particularly important since it is required by many real applications, such as digital signal processing, system identification and control, channel equalization, and predistortion. 1
AJIS Special Edition Knowledge Management December 2001 THEORY AND PRACTICE THINKING STYLES IN ENGINEERING AND SCIENCE
"... This paper describes knowledge as an element of thinking styles, which are properties of thinking collectives. According to the theory outlined here, the choice of a thinking style to solve a certain problem is relative, but once the thinking has been chosen, realism prevails. This paper also descri ..."
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This paper describes knowledge as an element of thinking styles, which are properties of thinking collectives. According to the theory outlined here, the choice of a thinking style to solve a certain problem is relative, but once the thinking has been chosen, realism prevails. This paper also describes the genesis and development of thinking styles and, with them, of facts. The theoretical concepts are illustrated with two examples of thinking styles: a description of the thinking styles of circuit theorists and circuit designers (theory vs. practice), and a comparison of the thinking styles of two closely related technical societies of the Institute of Electrical and Electronics Engineers (IEEE). Applications of the theory are also presented in this paper; they include information management, documentation tools, and writing styles, and mainly draw from the author's own experience with these topics. BACKGROUND Much has been said about the relationship between theory and practice, and it has been said by people who are both technically more experienced and philosophically better educated than I am. Nevertheless, I regularly thought and debated about the philosophical background of science for the better part of the time I spent at the Signal and Information Processing Laboratory of the Swiss Federal Institute of Technology, mainly for three reasons. One is that I soon noticed the incredible discrepancy between the ideal science producing facts and objective truths,
General Purpose Biquads Optimized for Dynamic Range and Low Noise
"... Abstract—In this paper two generalpurpose (GP) biquadratic filters are analyzed and optimized. The design equations for both filters are given, and the methods used to optimize the dynamic range and reduce the noise are described. On one example of the 2ndorder Butterworth filter, PSpice analyses ..."
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Abstract—In this paper two generalpurpose (GP) biquadratic filters are analyzed and optimized. The design equations for both filters are given, and the methods used to optimize the dynamic range and reduce the noise are described. On one example of the 2ndorder Butterworth filter, PSpice analyses were carried out, and a comparison of noise, referred to the input, is given. The dynamic range is optimized such as to have the same signal level at each amplifier output. Both optimization procedures are highly effective and can be applied to the similar filter design problems. I. II.
The serially coupled multiple ring resonator filters and Vernier effect
"... The general characteristics of serially coupled multiple ring resonator (SMRR) filters are analyzed. In this case, the ring resonators of the SMRR have identical perimeters and the coupling coefficients distribution provides passband characteristics with steeper rolloff, flatter top and greater sto ..."
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The general characteristics of serially coupled multiple ring resonator (SMRR) filters are analyzed. In this case, the ring resonators of the SMRR have identical perimeters and the coupling coefficients distribution provides passband characteristics with steeper rolloff, flatter top and greater stopband rejection than a single ring resonator. In addition, we have also designed and simulated a nonsymmetric Vernier type of SMRR filters for improving a wide free spectral range (FSR) with different ring radii. To expand the FSR of the SMRR, Vernier filters are determined by the least common multiple of the FSR of individual ring resonators. The improvement in suppression of interstitial resonances is also investigated. A novel derivation of the optical transfer functions in Zdomain of SMRR filters is expressed employing a graphical approach to ring resonators with unequal perimeters that can be represented in signal flow graph diagrams.