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22
Design and Simulation of Time-Pulse Coded
Optoelectronic Neural Elements and Devices
Vladimir G. Krasilenko, Aleksandr I. Nikolskyy and Alexander A. Lazarev
Vinnitsa Social Economy Institute of University “Ukraine”,
Vinnitsa National Technical University
Ukraine
1. Introduction
Creation of intellectual systems is impossible without creation of proper tools, proper micro-
and macroelement bases (Krasilenko et al., 1995, a; Krasilenko & Magas, 1999). So as any
concrete technical decision is a compromise between many contradictory requirements
taking into account solvable tasks, the creation of universal, effective, neural module as a
macroelement base for neurobiologic (Krasilenko et al., 2002, a; Krasilenko et al. , 2001, a) is,
probably, the future task. At the same time, searches for ways of creation of multifunction
devices which work on new mathematical, logical, hybrid, neural, neural-fuzzy bases and
others like that, especially on the basis of the biologically explained conceptions, will always
be actual (Krasilenko et al., 2002, a; Levin, 1990, a; Shimbirev, 1990, a), because just life and
time choose the most optimal solutions from all offered and existent.
The strategic direction of solution of various scientific problems, including the problem of
creation of artificial intelligence (AI) systems, human brain simulators, robotics systems,
monitoring and control systems, decision-making systems, as well as systems based on
artificial neural networks, etc., becomes fast-acting and parallel processing of large arrays
(2D) of data using non-conventional computational systems, matrix logics (multi-valued,
signed-digit, fuzzy logics, continuous, neural-fuzzy and others) and corresponding
mathematical apparatus (Krasilenko et al., 2001, a; Masahiko & Yatagai, 1997; Berger &
Collings, 1997; Krasilenko et al., 1997,a; Leondes, 1998; Krasilenko, 1988,b). For numerous
perspective realizations of optical learning neural networks (NN) with 2D structure
(Masahiko & Yatagai, 1997) of recurrent optical NN (Berger & Collings, 1997) of the
continuous logic equivalency models (CLEM) NN (Krasilenko et al. , 2001, a; Krasilenko et
al., 1997,a; Leondes, 1998), the elements of matrix logic are required. Optic and
optoelectronic technologies, methods and principles as well as corresponding element base
provide attractive alternative for 2D data processing. These technologies and methods
successfully solve problems of parallelism, input-output and interconnections. Signed-digit
number system (SDNS) are considered to be most promising and widely used nowadays,
among this systems we can find high-order systems, including the quaternion SDNS system
(Krasilenko et al., 2001, c). The architectures based on the system embrace such features as
high density of recording, they are less complicated and they contain few system
components, stages of addition, etc. Only a few of them (Huang & Itoh & Yatagai, 1999) can
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Optoelectronic Devices and Properties
be used for processing of 2D data and perform wide range of needed arithmetic and logic
operations (Guilfoyle & McCallum, 1996).
There exist a number of generalizations of continuous logic (CL) ( Levin , 1990, a ),
(Shimbirev, 1990, a; Volgin, 1986). Among them we should note sequential logic, hybrid
logic (HL), continuous discrete logic (CDL), controlled continuous logic (CCL) or predicate
selective algebra (Volgin, 1986), fuzzy logic (Zadeh, 1965). In hybrid logic the threshold and
dethreshold operations are basic, they realize transformations over continuous and discrete
variables (Shimbirev, 1990, a). Hybrid logic (HL) is basic mathematical body for analysis
and synthesis of hybrid (analog-digital) devices and systems. Functions max and min can be
realized sequentially performing threshold and dethreshold operators, i.e. by means of
hybrid logic (HL). Generalization of scalar two-valued logic on matrix case has led to
intensive development of binary images algebra (BIA) (Huang et.al., 1989) and 2D Boolean
elements for optic and optoelectronic processors (Huang & Itoh & Yatagai, 1999; Awwal &
Iftekharuddin, 1999; Krasilenko et al., 2001, c; Guilfoyle & McCallum, 1996; Krasilenko et al.
, 1988,a; Krasilenko et.al., 1991,a; Krasilenko & Dubthak, 1992). We would like to draw the
attention to the fact, that both natural neurons and their more complex physical and
mathematical models suggest discrete-analog and purely analog means for information
processing with different level of accuracy, with the possibility of rearrangement of chosen
coding system. This, in its turn, requires corresponding image neuron circuit engineering
with programmable logic operations, with transition from analog to discrete processing, to
storing etc. Thus, the search of means aimed at construction of elements, especially
universal (at least quasi-universal or multifunctional) with programmable tuning, able to
perform not only operations of two-valued logic, but other matrix (multi-valued,
continuous, neuro-fuzzy, etc.) logic operations is very actual problem(Guilfoyle &
McCallum, 1996).
Neuromodule, as it has been shown in works (Krasilenko et al., 1995, a; Krasilenko et al. ,
2001, a; Krasilenko et.al , 1995,c) can serve such macroelement basis. Functioning of neural
elements of such neuromodule must be described by future more generalized
neurobiological (Krasilenko et al., 1995, a; Krasilenko et al. , 2001, a) or the most generalized
at present time logics: continuous, hybrid, neural, fuzzy, neural-fuzzy and other logics
(Krasilenko et al., 1995,a; Krasilenko et al., 2002, a; Krasilenko et al. , 2001, a; Levin , 1990, a;
Shimbirev, 1990, a; Krasilenko et.al , 1995, c).
One of perspective directions of researches on creation of macrobase neural modules with
intelligence and quasiuniversality, and which operate on afore-mentioned new
mathematical bases, is the use of conception of time-pulse coded signals and the offered
approach to creation of different elements and structures for effective and highly productive
1D and 2D data processing (Krasilenko et.al., 2004, a; Krasilenko et.al, 2004, b; Krasilenko
et.al., 2005, a). Prospects of new optical and optoelectronic technologies (Masahiko &
Yatagai, 1997; Guilfoyle & McCallum, 1996; Baukens et.al., 1997) are limited to narrow
special processors. Therefore, to our mind, the central problem of new untraditional parallel
architecture, picture logic structures and elements creation, neurocomputers, is the problem
of logical universal and intelligence vector-matrix functional base (Krasilenko et al., 1995, a;
Krasilenko & Magas 1999; Krasilenko et.al., 2004, a; Krasilenko et.al., 2005, a; Krasilenko et.al
, 1995, c; Krasilenko et.al., 2005, b).
One of promising directions of research in this sphere is the application of time-pulse-
coding architectures (TPCA), that were considered in works (Krasilenko et.al., 1991,a;
Design and Simulation of Time-Pulse Coded Optoelectronic Neural Elements and Devices
461
Krasilenko & Dubthak, 1992; Krasilenko, 1991,b) these architectures were generalized in
(Krasilenko et al., 1995, a). The time-pulse representation of matrix continuous-logic
variables by two-level optic signals not only permits to increase functional possibilities (up
to universality), noiseproofnes, stability and decrease requirements regarding alignment
and optical system, but also simplify control circuits and adjustment circuits on required
functional performed, operation, and keep untouched the whole methodological basis of
such universal elements construction irrespective of word length of a code and type of logic.
It is shown, that it is possible to create more sophisticated problem-oriented processors, in
which the specific time-pulse coded operands are used and to use the elements of only two-
valued logic, which will realize functions of different logics, continuous etc. The two-stage
structure is used for 2D-arrays processing: at the first stage – elementwise processing; at the
second stage – overall processing. At the same time in works (Krasilenko et al., 1995, a;
Krasilenko et.al , 1995, c) little attention is paid to such non-traditional basic components of
TPCA as width-pulse, phase-pulse, photoconverters, photocurrents comparators.
Considerable results, to our mind, for creation of ANN are the development of
«equivalence» models and a proper «equivalence» paradigm (Krasilenko & Nikolskyy et.al.,
2000, a; Krasilenko & Nikolskyy et.al., 2001, d). Computer simulation results of
«equivalence» neural networks models (ENNM) have showed their efficiency and
substantial advantages: increase of capacity to (2.5 – 4.0)N; where N is neurons amount, the
possibility of spatially invariant recognition of very correlated 2D- and 1D-patterns
(Krasilenko et.al., 2008, a; Krasilenko et.al., 2009, a; Krasilenko, 2001, e; Krasilenko et.al.,
2002,b). Considerable foundation for development of the proper hardware tools and design
of the newest macroelement base was expansion of scalar neurobiologic (NBL) and creation
of mathematics of matrix neurobiologic with its base operations of the normalized
equivalences (nonequivalence) of two vectors, «equivalence» of spatial functions of 2D-
patterns, operations of autoequivalence of nonlinear transformations (Krasilenko et.al., 2009,
a; Krasilenko, 2001, e; Krasilenko et.al., 2002,b) and whole family of new «equivalence»
operations on the basis of use summarizing operations of continuous fuzzy and neuro-
fuzzy logic: fuzzy negation, t-norm and s-norm (Krasilenko et al., 2002, a).
There are tens of different physical models of neurons (Bardachenko et.al., 2004; Krasilenko
et.al, 2002, d). But majority of them realized by simplified old mathematic models. Models
which have equivalency paradigm properties are described in works (Krasilenko et al., 2002,
a; Krasilenko et.al., 2005, a; Krasilenko et.al., 2002, e). It is possible to design such neuron
macroelement base on the basis of optical and optoelectronic technologies. The last allows to
work out the problems of coupling, density et al. But such optoelectronic models for the
equivalence paradigm, which are described in works (Krasilenko et.al., 2005, a; Krasilenko
et.al., 2002, e; Krasilenko et.al.,2009, b) have some disadvantages. Realization of normalized
equivalence or nonequivalence are considered very little, except paper (Krasilenko et. al.,
2009, c). But synthesis and design of hardware representations of normalized equivalence or
nonequivalence of two vectors (or even matrices) and their modifications (Krasilenko et al.,
2002, a) is the most actual task. In paper (Krasilenko et.al., 2009,c) an approach to realize
complement dual neuron elements - neuron equivalentor/nonequivalentor was offered.
They are one of variants of more general neuron model. We used conception of pulse-time
encoding, as in works (Krasilenko et.al., 2004, a; Krasilenko et.al, 2004, b) . Advantages of
such biologically motivated conception are pulse-time (PWM or PPM) principle of signals
and variables and operands encoding. Signals at the output of such neurons can be both
462
Optoelectronic Devices and Properties
digital and analog or hybrid, and with two complement outputs. Then they realize principle
of dualism that gives a number of advantages. Therefore, the purpose of this work is
subsequent research and perfection of such complement time-pulse coded optoelectronic
neural elements, which are named by us as the equivalentor-nonequivalentor neuron. This
conceptual approach is used for two-valued, multivalued, neural and neuro-fuzzy
continuous logics. Our second position consists in the following: the micromodel of neuron
that is the model of heteroassociative memory (HAM) can realize any operation of
neurobiologic as well as operations of discrete multivalued logic. For every input
combination (situation, state) of vector of Boolean variables there are an output variable.
Such model can operate in learning mode (tuning to necessary operations of memorizing of
input and proper output variables) and in direct mode which consists of two phases: phase
of recognition of input state and phase of forming of output signal. The traditional models
of neurons that described in work (Rudenko & Bodjanskyy, 2005) have an input vector and a
vector of weighing coefficients as a rule. In our view, the model of neuron must have not
only one vector of weighing coefficients but a few. Set of such vectors which are memorized
by a neuron will allow comparing of their closeness (remoteness), that is equivalence (
nonequivalence), for recognition of a situation at inputs.
2. Motivation and short theoretical ground
2.1 Basic neurological operations of normalized equivalence
For solution of recognition problems a number of mathematics theories and methods is
involved; the development of these theories and methods is connected with the advent of
expert and intelligence systems: theory of fuzzy sets and theory of possibilities (Zadeh,
1965), theory of neural networks (Freeman James, 1992), and other mathematics methods
(Madani, 1998). More purposefully the apparatus of algebraic and fuzzy sets of continuous
logic (CL); its derivatives and generalizations, including hybrid, fuzzy predicate logic,
neural logic etc. (Krasilenko et al., 1995, a; Levin , 1990, a; Shimbirev, 1990, a; Zhiging Wen,
1996) have become to be applied. Among non-parallel single-stage algorithms of
multialternative recognition, an important role is played by numerous versions of
algorithms, based on distances calculations (Evclidus, Mahalonobise, Hamming etc)
(Shirman, 1996). However, widely spread method, used in static recognition, cluster
analysis and other spheres, namely the method of classification by minimal space, has a
drawback, due to non-sufficient fast action of necessary space between images calculation,
vectors of large dimensions represent these images. Besides, quality of recognition, in
particular, the number of stored and correctly recognized references in neuroassociative
memory, depends greatly on chosen matrix, type, and space. In neural networks models and
recognition algorithms in hidden layers, minimal spaces (while teaching) (Leondes, 1998;
Freeman James, 1992) and criteria of maximum convergency are used as intermediate
criteria, in some new equivalence models for recognition of strongly corrected images
(Krasilenko et al. , 2001, a; Krasilenko et al., 1997,a). The interest to these new directions,
neurofuzzy models, logic-algebraic apparatus, common neurobionic principles can be
explained by the possibility to understand with their help the principles of human brain
functioning. As neurophysiological studies show, frequency-dynamic model of neuron
(FDMN), would be the most adequate (nowadays), and neurobiologic (NBL) as the most
generalized (as compared with other known logics, such as hybrid, continuous, threshold
etc.) could be used to describe the functioning of FDMN (Krasilenko et al., 1995, a;
Design and Simulation of Time-Pulse Coded Optoelectronic Neural Elements and Devices
463
Krasilenko et.al, 1995, c; Antamonov, 1974; Posin, 1970). Realizations of such FDMN are
already known (Krasilenko et.al , 1995, c; Posin, 1970; Levshin, 1987) but they are rarely
used, that is connected with their electronic realizations. Only new optic and optoelectronics
technologies and their corresponding realization of neuromodules (arrays) with a great
number of FDMN and simplified parallel one-cycle inputs-outputs, efficient realizations of
interconnections by means of holograms or other optic methods are the most promising
direction, permitting to decrease considerably the size and weight parameters, at the same
time increasing the dimensions of arrays, performance and speed of data processing
(Krasilenko et al., 1995, a; Krasilenko et al. , 2001, a). Basic operation of NBL, in authors
opinion (Krasilenko et.al., 2000,b) or the set of operations may be not one, even functionally
complete operation but also optimal, basic set of operations, which is necessary for most
efficient algorithmic (and sequential in time and parallel simultaneously in space) execution
of needed transformations over information signals. We realize that on this way it is quite
impossible immediately to find out really final decision for all cases of infinite, complex and
dynamic existence of nervous system of living beings. But consideration of such
neurobiological models and their basic fundamental operations even for scalar NBL is of
gnoseological aspect, it permits still at the stages of conceptual approaches and structural-
functional and mathematical-model design rely on vitality and a ability to compete of the
suggested solutions. In many neural models (with the exception (Krasilenko et al., 1997, a))
used for optical realization of different associative devices and neural nets, only carrier
sets 2 C = { 1;
−
}
1 N and 2 C =
are used in bipolar (b) and unipolar (u) coding
u
{0, }
1 N
b
respectively. Models, proposed in (Krasilenko et al., 1997,a; Krasilenko et.al., 1996;
Krasilenko et.al., 1997,b) and called equivalental, are more general and good for
representation of bipolar and unipolar signals, including multilevel signals. The
connections, especially braking, are described more natural there. In such models, the basic
operation is a standard equivalency of vectors. The models are suitable for different
methods of weighing. Considering their prospects, in this work we will show how to build
associative (auto-associative and hetero-associative) memory of correlated 2-D images,
including multilevel (grey scale) images, based on matrix-tensor models. Functioning of
most adequate for present day, frequency-dynamic models of neurons is described by
means of mathematic apparatus of continuous logic (CL), hybrid logic, neural-fuzzy logic
and other logics, but in the long run, by means of more generalized logic – neurobiologic
(NBL) (Shimbirev, 1990, a; Krasilenko et al. , 2001, a; Antamonov, 1974), which is the
generalization of all known logics. It is impossible to find partial universal solution for all
cases of such complex, versatile, infinite and dynamic existence of nervous system of living
organisms. But gnoseological study of all known modules and taking into account the
results of neurophysiological research, providing neuroelements with adequate properties
and principles of information processing, still at the stages of conceptual approaches and
structural functional synthesis allows to hope that the suggested technical solutions will be
successfully realized and competitive. Functional and system requirements to
neuromodules are considered in a paper (Freeman James, 1992) taking into account the list
of neurons properties, some of their optoelectronic realizations, performing one of the basic
.
operations of limited difference (LD) (a.
b) have been suggested. The connections among
.
the limited difference (LD) and the basic operations are shown in works (Zadeh, 1965;
Freeman James, 1992; Shimbirev, 1990, a; Krasilenko et al., 1997,a): max(a,b), min(a,b),
464
Optoelectronic Devices and Properties
complement, functionally complete system of functions CL{ ∧ , ∨
, –}; operations of
limited sum ( ∪ ) and limited product ( × ) of neuro-fuzzy logic (Shimbirev, 1990, a),
∨
+
∨
+
operations of equivalence ( ~ ), ( ~ ), and non-equivalence ( ~/ ), ( ~/ ) of NBL (Krasilenko et al. ,
2001, a; Antamonov, 1974) from the whole set of such operations being generalizations of
XNOR and XOR of two-valued logic, permitting logically compare continuous (analog) and
multilevel normalized unipolar and bipolar signals including scalar, vector and matrix. In
the same works (Krasilenko et al. , 2001,a; Antamonov, 1974), the properties of these
operations of equivalence (non-equivalence) are shown, that is why we don't concentrate
our attention on this point, but we will use them, in case of necessity. Taking into
consideration the above-described approach, consisting in universality, let us recollect some
known facts regarding the number of functions. The number of Boolean functions of n
variables in algebra of two-valued logic (ATL), which is also Boolean algebra, equals 2
2 n . In
this ATL there are
2 n
N =
atoms, which are minterms. Functions of n variables k–valued
2
logic ( k>2) are reflections n
A → A , where A={0, 1, ... k-1}, and the number of functions
equals
n
k
N = k . Algebra, formed by set ∧ C = ⎡
⎤
∧ C = ⎡−
⎤
u
0,1
k
⎣
⎦ or
b
1,1
⎣
⎦ is called CL algebra
(ACL), and the number of CL functions, as reflections n
C → C depending on the CL
u