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FixedPoint Optimization Utility for C and C++ Based Digital Signal Processing Programs
 IEEE Trans. Circuits and Systems II
, 1998
"... Fixedpoint optimization utility software is developed that can aid scaling and wordlength determination of digital signal processing algorithms written in C or C++++++. This utility consists of two programs: the range estimator and the fixedpoint simulator. The former estimates the ranges of float ..."
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Cited by 57 (3 self)
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Fixedpoint optimization utility software is developed that can aid scaling and wordlength determination of digital signal processing algorithms written in C or C++++++. This utility consists of two programs: the range estimator and the fixedpoint simulator. The former estimates the ranges of floatingpoint variables for purposes of automatic scaling, and the latter translates floatingpoint programs into fixedpoint equivalents to evaluate the fixedpoint performance by simulation. By exploiting the operator overloading characteristics of C++++++, the range estimation and the fixedpoint simulation can be conducted by simply modifying the variable declaration of the original program. This utility is easily applicable to nearly all types of digital signal processing programs including nonlinear, timevarying, multirate, and multidimensional signal processing algorithms. In addition, this software can be used to compare the fixedpoint characteristics of different implementation archite...
Effects Of Source Distributions And Correlation On Fractionally Spaced Blind Constant Modulus Algorithm Equalizers
, 1995
"... Simplicial Complex: By an abstract simplicial complex with vertices in a set V , we mean a family of finite subsets of V satisfying the condition that K is hereditary, i. e. every subset of any set in K is also in K. Subcomplex Let K and L be any two abstract simplicial complexes with vertices V an ..."
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Cited by 6 (0 self)
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Simplicial Complex: By an abstract simplicial complex with vertices in a set V , we mean a family of finite subsets of V satisfying the condition that K is hereditary, i. e. every subset of any set in K is also in K. Subcomplex Let K and L be any two abstract simplicial complexes with vertices V and W respectively. If L ae K, then L is said to be a subcomplex of K. Topological Realization Let K be an arbitrarily given abstract simplicial complex. We will construct a space P = jKj called the topological realization as follows. For each finite set F 2 K, consider the simplex oe F defined in the previous section. These simplexes foe F jF 2 Kg (without the identification introduced in studying their faces) are by definition disjoint topological spaces. Form their topological sum S = S(K) = X F2K oe F : Then S is clearly a metrizable space containing every simplex oe F as an open and closed subspace. Introduce a relation ¸ in S as follows. Let f 2 oe F and g 2 oe G be any two points in ...
Quantization Strategies For LowPower Communications
, 2001
"... Power reduction in digital communication systems can be achieved in many ways. Reduction of the wordlengths used to represent data and control variables in the digital circuits comprising a communication system is an effective strategy, as register power consumption increases with wordlength. Anothe ..."
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Cited by 6 (1 self)
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Power reduction in digital communication systems can be achieved in many ways. Reduction of the wordlengths used to represent data and control variables in the digital circuits comprising a communication system is an effective strategy, as register power consumption increases with wordlength. Another strategy is the reduction of the required data transmission rate, and hence speed of the digital circuits, by efficient source encoding. In this dissertation, applications of both of these power reduction strategies are investigated. The LMS adaptive filter, for whichamyriad of applications exists in digital communication systems, is optimized for performance with a power consumption constraint. This optimization is achieved by an analysis of the effects of wordlength reduction on both performance  transient and steadystate  as well as power consumption. Analytical formulas for the residual steadystate mean square error (MSE) due to quantization versus wordlength of data and coefficient registers are used to determine the optimal allocation of bits to data versus coefficients under a power constraint. A condition on the wordlengths is derived under which the potentially hazardous transient "slowdown" phenomenon is avoided. The algorithm is then optimized for no slowdown and minimum MSE. Numerical studies are presented for the case of LMS channel equalization. Next, source encoding byvector quantization is studied for distributed hypothesis testing environments with simple binary hypotheses. It is shown that, in some cases, lowrate quantizers exist that cause no degradation in hypothesis testing performance. These cases are, however, uncommon. For the majority of cases, in which quantiza...
Secure Adaptive Filtering
, 2010
"... In an increasingly connected world, the protection of digital data when it is processed by other parties has arisen as a major concern for the general public, and an important topic of research. The field of Signal Processing in the Encrypted Domain has emerged in order to provide efficient and secu ..."
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Cited by 3 (1 self)
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In an increasingly connected world, the protection of digital data when it is processed by other parties has arisen as a major concern for the general public, and an important topic of research. The field of Signal Processing in the Encrypted Domain has emerged in order to provide efficient and secure solutions for preserving privacy of signals that are processed by untrusted agents. In this work, we study the privacy problem of adaptive filtering, one of the most important and ubiquitous blocks in signal processing nowadays. We present several use cases for adaptive signal processing, studying their privacy characteristics, constraints and requirements, that differ in several aspects from those of the already tackled linear filtering and classification problems. We show the impossibility of using a strategy based solely on current homomorphic encryption systems, and we propose several novel secure protocols for a privacypreserving execution of the LMS (Least Mean Squares) algorithm, combining different SPED techniques, and paying special attention to the error analysis of the finiteprecision implementations. We seek the best tradeoffs in terms of error, computational complexity and used bandwidth, showing a comparison among the different alternatives in these terms, and we provide the experimental results of a prototype implementation of
Incremental Communication for Multilayer Neural Networks: Error Analysis
, 1995
"... Artificial neural networks (ANNs) involve a large amount of internode communications. To reduce the communication cost as well as the time of learning process in ANNs, we earlier proposed an incremental internode communication method. In the incremental communication method, instead of communicati ..."
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Cited by 2 (1 self)
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Artificial neural networks (ANNs) involve a large amount of internode communications. To reduce the communication cost as well as the time of learning process in ANNs, we earlier proposed an incremental internode communication method. In the incremental communication method, instead of communicating the full magnitude of the output value of a node, only the increment or decrement to its previous value is sent on a communication link. In this paper, the effects of the limited precision incremental communication method on the convergence behavior and performance of multilayer neural networks are investigated. The nonlinear aspects of representing the incremental values with reduced (limited) precision for the commonly used error backpropagation training algorithm are analyzed. It is shown that the nonlinear effect of small perturbations in the input(s)/output of a node does not enforce instability. The analysis is supported by simulation studies of two problems. The simulation results ...
Analytical approach for numerical accuracy estimation of fixedpoint systems based on smooth operations
 Transactions on Circuits and Systems I
, 2012
"... Abstract—In embedded systems using fixedpoint arithmetic, converting applications into fixedpoint representations requires a fast and efficient accuracy evaluation. This paper presents a new analytical approach to determine an estimation of the numerical accuracy of a fixedpoint system, which is ..."
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Cited by 2 (1 self)
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Abstract—In embedded systems using fixedpoint arithmetic, converting applications into fixedpoint representations requires a fast and efficient accuracy evaluation. This paper presents a new analytical approach to determine an estimation of the numerical accuracy of a fixedpoint system, which is accurate and valid for all systems formulated with smooth operations (e.g. additions, subtractions, multiplications and divisions). The mathematical expression of the system output noise power is determined using matrices to obtain more compact expressions. The proposed approach is based on the determination of the timevarying impulseresponse of the system. To speedup computation of the expressions, the impulse response is modelled using a linear prediction approach. The approach is illustrated in the general case of timevarying recursive systems by the Least Mean Square (LMS) algorithm example. Experiments on various and representative applications show the fixedpoint accuracy estimation quality of the proposed approach. Moreover, the approach using the linearprediction approximation is very fast even for recursive systems. A significant speedup compared to the best known accuracy evaluation approaches is measured even for the most complex benchmarks. Index Terms—Fixedpoint arithmetic, quantization noises, adaptive filters, accuracy evaluation I.
et al
 IEEE Trans
, 1983
"... Abstract Adaptive channel equalization algorithms are commonly used in wireless communications receivers to counter intersymbol interference, multipath dispersion, and other time varying channel degradations. In this paper we obtain approximate expressions for the increase in mean square error of ..."
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Cited by 1 (1 self)
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Abstract Adaptive channel equalization algorithms are commonly used in wireless communications receivers to counter intersymbol interference, multipath dispersion, and other time varying channel degradations. In this paper we obtain approximate expressions for the increase in mean square error of the LMS adaptive algorithm when the total processing power is decreased by reducing the number of data and filter coefficient bits used by the algorithm. We also obtain expressions for the poweroptimal bitallocation factor which determines the proportion of the bits allocated to the data vs. allocated to the coefficients. Numerical studies are presented for an exponential memory IS1 channel and 4ary PSK signalling. These studies indicate that as few as 8 bits total are needed to equalize the channel and that most of these bits (6 out of 8) should be allocated to the filter coefficients. I.
Analysis of a Stabilization Technique for the FixedPoint Prewindowed RLS Algorithm
"... In this correspondence, a stable finite precision Recursive Least Squares (RLS) algorithm is derived for the prewindowed growing memory case (forgetting factor, = 1). Previously, it has been shown that the prewindowed growing memory RLS algorithm diverges under fixedpoint implementation [1, 2]. Th ..."
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Cited by 1 (0 self)
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In this correspondence, a stable finite precision Recursive Least Squares (RLS) algorithm is derived for the prewindowed growing memory case (forgetting factor, = 1). Previously, it has been shown that the prewindowed growing memory RLS algorithm diverges under fixedpoint implementation [1, 2]. The random walk phenomenon due to roundoff errors in the weight update causes the divergence of the algorithm. To overcome this effect, these roundoff errors are modeled such that their effect is incorporated into the algorithm. The steadystate behavior of this new algorithm is analyzed, and it is shown that the divergence phenomenon is actually eliminated, and the new algorithm converges. I. Introduction It has been shown that, for the prewindowed RLS algorithm ( = 1), the roundoff error associated with the weight update recursion leads to divergence as the algorithm iterates, [1, 2]. In the literature, this phenomenon has been explained as a random walk process for the weight vector [2, 7...
A Floatingpoint to Fixedpoint C Converter for Fixedpoint Digital Signal Processors
, 1997
"... An automatic scaling C program translator is developed for the efficient execution of application programs in fixedpoint digital signal processors. The program for range estimation is automatically generated by inserting codes which collect the statistics of each signal during the simulation. Wit ..."
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An automatic scaling C program translator is developed for the efficient execution of application programs in fixedpoint digital signal processors. The program for range estimation is automatically generated by inserting codes which collect the statistics of each signal during the simulation. With the range information, the number of shifts needed for the scaling is determined and the floatingpoint program is converted to a fixedpoint program by type modification, insertion of scaling codes, and using fixedpoint multiplications which are important to preserve fixedpoint accuracy. The SUIF (Stanford University Intermediate Format) system is used for parsing the original program, inserting the range estimation code, and generating the translated code. A fourth order IIR filter and an ADPCM codec are implemented on Texas Instruments' TMS320C5x as examples. The fixedpoint C codes are 5 to 14 times faster than the floatingpoint programs with acceptable finite wordlength effe...