B.J. Falkowski

Nanyang Technological University, Tumasik, Singapore

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Publications (273)62.45 Total impact

  • Cicilia C. Lozano · Bogdan J. Falkowski · T. łuba
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    ABSTRACT: A polynomial expansion based on a fixed polarity quaternary linearly independent (FPQLI) transform is presented. The FPQLI transforms built from six recursive basic transforms whose structures are directly derived from some linearly independent transforms over Galois Field(2) (GF(2)). For certain polarities the FPQLI transform for n-variable quaternary functions directly corresponds to the binary fixed polarity Reed-Muller (FPRM) transforms for 2n-variable binary functions. Due to the way the FPQLI transform for n>1 is constructed, the transform is inherently recursive and has a regular structure. Recursive equations, fast flow graph, and underlying basis functions for the transform are given. In addition, relations between different FPQLI spectral coefficient vectors are shown and applied to reduce the computational cost of obtaining the optimal FPQLI expansion. Experimental results of the FPQLI transform have been obtained for a set of quaternary test files. The results showthat for the test files, the average number of nonzero spectral coefficients of optimal FPQLI transform is 39.05% smaller than the number for optimal FPRM over GF(4).
    No preview · Article · Jan 2012 · Journal of multiple-valued logic and soft computing
  • Cheng Fu · Bogdan J. Falkowski
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    ABSTRACT: This paper introduces two new classes of recursive fast transforms over GF (3). They are based on recursive equations using Kronecker products that allows to obtain simple corresponding fast transforms and regular butterfly diagrams. The computational costs to calculate both classes of new transforms and the experimental results comparing introduced transforms with ternary Reed–Muller transform are also presented.
    No preview · Article · Nov 2011 · Journal of Circuits System and Computers
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    ABSTRACT: With the evolution of programmable structures, that become more heterogeneous, the process of mapping a design into these structures becomes more and more complex. Modern FPGA chips are equipped with embedded memory blocks that can be used to increase the implementation quality of the design. The paper presents a logic synthesis method based on balanced decomposition that uses the concept of r-admissibility to efficiently utilize possibilities provided by memory blocks embedded in modern FPGA architectures. Results presented in this paper prove the effectiveness of proposed approach.
    No preview · Article · Jan 2010 · Przeglad Elektrotechniczny
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    M. Rawski · G. Borowik · T. Luba · P. Tomaszewicz · B.J. Falkowski
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    ABSTRACT: With the evolution of programmable structures, that become more heterogeneous, the process of mapping a design into these structures becomes more and more complex. Modern FPGA chips are equipped with embedded memory blocks that can be used to increase the implementation quality of the design. The paper presents a logic synthesis method based on balanced decomposition that uses the concept of r-admissibility to efficiently utilize possibilities provided by memory blocks embedded in modern FPGA architectures. Results presented in this paper prove the effectiveness of proposed approach.
    Full-text · Conference Paper · Jun 2009
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    Grzegorz Borowik · Tadeusz Luba · Bogdan J. Falkowski
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    ABSTRACT: This paper presents a new cost-efficient realization scheme of pattern matching circuits in FPGA structures with embedded memory blocks (EMB). The general idea behind the proposed method is to implement combinational circuits using a net of finite state machines (FSM) instead. The application of functional decomposition method reduces the utilization of resources by implementing FSMs using both EMBs and LUT-based programmable logic blocks available in contemporary FPGAs. Experimental results for the proposed method are also shown. A comparison with another dedicated method yields extremely encouraging results: with a comparable number of EMBs, the number of logic cells has been reduced by 95%.
    Full-text · Conference Paper · Apr 2009
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    Cicilia C Lozano · Bogdan J Falkowski · Tadeusz Łuba
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    ABSTRACT: Classes of fastest linearly independent ternary arithmetic (FLITA) expansions have been proposed recently. They operate in arithme-tic domain and have been shown to be useful for optimization of ternary functions representation. All FLITA transforms possess fast forward and inverse transforms and therefore can be calculated by fast transform method. However, it has been shown that for ma-nipulation of large functions it is more advantageous to start from decision diagrams rather than truth vector. Hence in this paper new algorithm to obtain FLITA spectrum from ternary decision diagram is presented. It is developed based on the new notations for spectrum of an FLITA transform introduced here. The algo-rithm derives each spectral coefficient independently from each other, allowing the coefficients to be calculated in parallel manner. By starting from decision diagram, the algorithm enables the FLITA expansion to be computed for large functions for which the fast transform based algorithm may fail.
    Full-text · Article · Jan 2009
  • Cicilia C. Lozano · Bogdan J. Falkowski · T. Luba
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    ABSTRACT: New quaternary linearly independent arithmetic (QLIA) transforms are presented in this paper. The new transforms are recursive and they are classified into two classes according to their recursive equations. Fast flow graphs and relations for the transforms are presented. Computational cost for the calculation of the QLIA spectral coefficient vector is also derived. Experimental results in terms of the minimum number of nonzero spectral coefficients based on the QLIA transforms for a set of quaternary test functions are also given and compared with the corresponding numbers for quaternary fixed polarity arithmetic (QFPA) transforms. The comparison shows that for the set of quaternary test functions the average number of minimum number of nonzero spectral coefficients based on the introduced QLIA transforms is 39.28% and 16.29% smaller than that for the polarity zero and optimal polarity QFPA transforms, respectively.
    No preview · Article · Jan 2009
  • Cicilia C. Lozano · Bogdan J. Falkowski · Tadeusz Luba
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    ABSTRACT: A fixed polarity quaternary linearly independent (FPQLI) transform is introduced in this paper where the basic transforms are derived from the recursive structure of some linearly independent transforms over Galois Field (2) (GF(2)). For some polarities the FPQLI transform for n-variable quaternary functions directly corresponds to the binary fixed polarity Reed-Muller (FPRM) transforms for 2n-variable binary functions. In this paper, the fast flow graph and recursive equations for the FPQLI transform are given together with the underlying basis functions. Formulae for converting the FPQLI spectral coefficient vector from one polarity to another are also given and used to generate a recursive algorithm to obtain the optimal FPQLI expansion with reduced computational cost. Experimental results of the FPQLI transform have been obtained for a set of quaternary test files. Comparison of the obtained results with FPRM over GF(4) as well as the existing recursive quaternary linearly independent transforms show the advantage of applying the concept of fixed polarity to the basic transforms for function minimization in terms of smaller number of nonzero spectral coefficients.
    No preview · Conference Paper · Jan 2009
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    Bogdan J. Falkowski · Sujit Kumar Sahoo · T. Luba
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    ABSTRACT: This paper presents two novel methods for compression of fluorescent dye cell images. The compression methods achieve high compression ratio by pseudo-quantizing the pixel gray levels according to image statistics and extracting and saving the useful regions of the image. The proposed algorithms produce a better compression over the existing lossless image formats in the case of fluorescent dye cell images and this idea of compression can be further extended to other images.
    Full-text · Article · Jan 2009
  • Cheng Fu · Bogdan J. Falkowski
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    ABSTRACT: New linearly independent quaternary transforms over Ga- lois Field (4) called Generalized Fixed Polarity Helix trans- forms are introduced here. Their definitions based on recur- sive equations are described. Various properties of quater- nary helix transform matrices, their mutual relations as well as their butterfly diagrams and computational costs versus quaternary Reed-Muller transform are also discussed.
    No preview · Article · Jan 2009
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    Cicilia C Lozano · Bogdan J Falkowski · Tadeusz Łuba
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    ABSTRACT: Two classes of fixed polarity linearly independent arithmetic trans-forms (FPQLIA) for quaternary functions are introduced in this paper. These transforms are Kronecker-based and therefore can be calculated efficiently by fast transforms. Their basic definitions and fast flow graphs are shown. Relations between the different FPQLIA transforms are also presented and an algorithm for the optimization of FPQLIA is described which utilizes the given rela-tion to reduce the computational cost. Experimental results for the transforms in terms of the number of nonzero spectral coefficients in the optimal FPQLIA transforms have also been given for several quaternary test functions and compared to the corresponding num-bers for the optimal fixed polarity quaternary arithmetic (FPQA) transforms. The results show that for the set of quaternary test functions the numbers for FPQLIA transforms are on average 32% smaller than the ones for the FPQA transforms.
    Full-text · Article · Jan 2009
  • Tao Fang · Cheng Fu · Bogdan J. Falkowski · Bang Wang
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    ABSTRACT: High dynamic range (HDR) images require a higher number of bits per color channel than traditional images. This brings about problems to storage and transmission, especially in distributed wireless sensor networks in which transmission capability and energy consumption are critical issues. The paper proposes a structure of compressing multiple dynamic range images, which is called multiple dynamic range (MDR) coding. MDR imaging system is attractive due to the capability of reconstructing lower dynamic range images from partial bitstream. MDR coding shows its advantages in terms of energy efficiency in distributed wireless sensor networks. The efficacy of MDR coding is also illustrated by presenting the results of encoding a series of synthetic and natural MDR images.
    No preview · Article · Oct 2008
  • C. C. Lozano · B.J. Falkowski · T. Luba
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    ABSTRACT: Spectral expansions are alternative representations of logic functions/signals in which the information are redistributed and presented differently in terms of spectral coefficients. The use of spectral representations often allows certain operations or analysis to be performed more efficiently on the data. In this paper, spectral expansions for ternary functions based on new fastest linearly independent arithmetic transforms are presented and discussed. The new transforms are generalizations of some existing ternary transforms through permutation and reordering operations. They have regular structures and can be computed using fast transforms. Formulae for their fast forward and inverse transformations as well as their corresponding fast flow graphs are shown here. Computational costs and some properties of the transforms and their spectra are also given. Finally, experimental results of the transforms are presented which show that the new transforms can represent some functions more compactly than the existing transforms.
    No preview · Conference Paper · Jul 2008
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    Mariusz Rawski · Bogdan J Falkowski · Tadeusz Łuba
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    ABSTRACT: This paper presents the discussion on efficiency of different implementation methodologies of DSP algorithms targeted for modern FPGA architectures. Modern programmable structures are equipped with specialized DSP embedded blocks that allow implementing digital signal processing algorithms with use of the methodology known from digital signal processors. On the first place, however, programmable ar-chitectures give the designer the possibility to increase efficiency of designed system by exploitation of parallelism of implemented algorithms. Moreover, it is possible to apply special techniques, such as distributed arithmetic (DA) that will boost the per-formance of designed processing systems. Additionally, application of the functional decomposition based methods, known to be best suited for FPGA structures, allows utilizing possibilities of programmable technology in very high degree. The paper presents results of comparison of different design approaches in this area.
    Full-text · Article · Jul 2008
  • Bogdan J. Falkowski · Cheng Fu
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    ABSTRACT: Classification of novel fastest quaternary linearly independent transforms has been presented. They are recursively defined and have consistent formulas relating their forward and inverse transform matrices. Their transform matrices' properties and calculation example have been shown. The computational costs of the calculation for presented transforms are also discussed. The experimental results are shown and compared with the well known quaternary arithmetic transform.
    No preview · Conference Paper · Jun 2008
  • Cicilia C. Lozano · Bogdan J. Falkowski · Tadeusz Luba
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    ABSTRACT: Sixteen fastest quaternary linearly independent (FQLI) transforms are discussed in this paper. All the presented transforms can be derived using recursive equations and their inverse recursive definitions share common structure. In this paper, the fast flow graph equations and properties for the FQLI transforms are given. Based on the relationships between the spectra of the transforms, a recursive algorithm for the computation of their spectral coefficients is also proposed which reduces the total computational cost of generating their complete spectra. Experimental results for all the FQLI transforms as well as fixed polarity Reed-Muller transform over GF(4) are also given and compared in terms of the number of nonzero spectral coefficients. The comparison shows that for some quaternary functions the new FQLI transforms can give more compact representations.
    No preview · Conference Paper · Jun 2008
  • Mariusz Rawski · Tadeusz Luba · Bogdan J. Falkowski
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    ABSTRACT: The paper presents a logic synthesis method oriented towards FPGA architectures with specialized embedded memory blocks. Existing methods do not ensure effective utilization of possibilities provided by these specialized embedded modules. The presented method, based on balanced decomposition, leads to much more effective implementations of digital systems in modern FPGA structures.
    No preview · Conference Paper · Jun 2008
  • Bogdan J. Falkowski
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    ABSTRACT: In this paper, a robust phase watermarking algorithm for still images is presented where the watermark information is conveyed in the phase spectrum in the transform domain. Phase watermarking algorithm that uses multi-polarity Complex Hadamard transform is developed. The robustness of presented algorithm is investigated by its uniqueness, JPEG encoding, image resizing, dithering noise distortions, sharpening, cropping and successive watermarking.
    No preview · Conference Paper · Jan 2008
  • Cicilia C. Lozano · Bogdan J. Falkowski
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    ABSTRACT: New fastest linearly independent ternary arithmetic (LITA) transforms are presented in this paper. Fastest LITA transforms can be calculated efficiently by fast transforms and the calculation incurs low computational complexity. Formulas for the fast forward and reverse transformation of the new fastest LITA transforms are given and several of their properties are listed. A modular tree structure hardware implementation of the resulting fastest LITA polynomial expansion is also described. At the end of the paper, experimental results for the new transforms are shown.
    No preview · Conference Paper · Jan 2008
  • Mariusz Rawski · Henry Selvaraj · Bogdan J Falkowski · Tadeusz Luba
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    ABSTRACT: This chapter, taking FIR filters as an example, presents the discussion on efficiency of different implementation methodologies of DSP algorithms targeting modern FPGA architectures. Nowadays, programmable technology provides the possibility to implement digital systems with the use of specialized embedded DSP blocks. However, this technology gives the designer the possibility to increase efficiency of designed systems by exploitation of parallelisms of implemented algorithms. Moreover, it is possible to apply special techniques, such as distributed arithmetic (DA). Since in this approach, general-purpose multipliers are replaced by combinational LUT blocks, it is possible to construct digital filters of very high performance. Additionally, application of the functional decomposition-based method to LUT blocks optimization, and mapping has been investigated. The chapter presents results of the comparison of various design approaches in these areas.
    No preview · Article · Jan 2008

Publication Stats

2k Citations
62.45 Total Impact Points

Institutions

  • 1992-2012
    • Nanyang Technological University
      • School of Electrical and Electronic Engineering
      Tumasik, Singapore
  • 2009
    • Warsaw University of Technology
      • Institute of Telecommunications
      Warszawa, Masovian Voivodeship, Poland
  • 1993-2007
    • Nanyang Normal University
      Nan-yang-shih, Henan Sheng, China
  • 1990-1999
    • Portland State University
      • Department of Electrical and Computer Engineering
      Portland, Oregon, United States
  • 1997
    • University of Niš
      Nisch, Central Serbia, Serbia
  • 1989
    • University of Portland
      Portland, Oregon, United States