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Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
Bayesian network based modeling and reliability analysis of quantum cellular
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Bayesian network based modeling and reliability analysis of quantum cellular

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  1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN INTERNATIONAL JOURNAL OF ELECTRONICS AND 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMECOMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)ISSN 0976 – 6464(Print)ISSN 0976 – 6472(Online)Volume 4, Issue 1, January- February (2013), pp. 131-145 IJECET© IAEME: www.iaeme.com/ijecet.aspJournal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEMEwww.jifactor.com BAYESIAN NETWORK BASED MODELING AND RELIABILITY ANALYSIS OF QUANTUM CELLULAR AUTOMATA CIRCUITS Dr.E.N.Ganesh Professor ECE Dept, Rajalakshmi Institute of Technology,Chennai – 600124 TamilNadu, India Email: enganesh50@yahoo.co.in ABSTRACT Quantum cellular automata (QCA) is a new technology in nanometer scale as one of the alternatives to nano cmos technology, QCA technology has large potential in terms of high space density and power dissipation with the development of faster computers with lower power consumption. This paper considers the problem of reliability analysis of Simple QCA circuits at layout level like QCA latches and NOT circuit. The tool used to tackle this problem is Bayesian networks (BN) that derive from convergence of statistics and Artificial Intelligence (AI). It consists of the representation of probabilistic causal relation between variables of a system. Using this we have transformed QCA circuit in to Bayesian framework to find the probability of getting correct output in terms of its polarization with respect to its input configuration and temperature. Reliability analysis also discussed for finding the defective cells in QCA circuit. This will increase overall efficiency of circuit and hence speed of the circuit with lower power consumption. Keywords: BN – Bayesian network, Quantum cellular automata, Reliability, Conditional probability, Join probability distribution 1. INTRODUCTION This paper considers the problem of reliability analysis of QCA circuit organized in parallel and/or in serial given the reliability of the Input cells. The mathematical tool used to tackle this problem is Bayesian networks. Reliability analysis of systems is very important in order to be able to deliver errorless QCA cell at the output. A given QCA system is often composed of many cells organized in serial and parallel, whose failure of one cell in serial 131
  2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMEmay cause the failure of the whole system or at least reduce its performance. In terms ofreliability there are two types of organizations of cells, organization in serial and organizationin parallel. These organizations impact on the reliability of the resulting circuit. If a circuitconsists of n cells Ci, i=1,…n in serial, the system will be performing well if and only if eachcomponent is performing well, so if Pi , is the reliability of the ith component, then thereliability of the system Ps is given by Ps = ∏i = 1 to n Pi (1)On the contrary if a system consists of n cells Ci, i=1,…n in parallel, the system will performwell if at least one of these cells perform well, so if Pi is the reliability of the ith component,then the reliability of the system Pp is given by Pp = 1 - ∏i = 1 to n ( 1 - pi) (2)Eq. (1) and (2) constitute the fundamental relations for computing the reliability of a QCAcircuit because any system will consist of cells or groups of cells in serial and/or in parallel.Quantum-dot Cellular Automata (QCA) is an emerging technology that offers a revolutionaryapproach to computing at nano-level [1][2]. A dot can be visualized as well. Once electronsare trapped inside the dot, it requires higher energy for electron to escape. The fundamentalunit of QCA is QCA cell created with four quantum Dots positioned at the vertices of asquare. [2] [3.]. Fig 1.a and 1.b below shows quantum cells with electrons occupyingopposite vertices. 1.a P = +1 (Binary 1) 1.b P = -1 (Binary0) Fig1 QCA cells with four Quantum dots. [1][3][4][5] This interaction forces between the neighboring cells able to synchronize their polarization.Therefore an array of QCA cells acts as wire and is able to transmit information from one endto another [6] [7][8][9][10]. Figure 2 and 3 Majority functions of QCA Cell. Fig 2.and 3 Majority AND, OR gate [3] [4][5][6] 132
  3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Clocking is the requirement for synchronization of information flow in QCA circuits [11][12] [13]. It requires a clock not only to synchronize and control information flow but clockactually provides power to run the circuit [14] [15]. Bayesian Networks (BN) derive from theconvergence of statistical methods that permit one to go from information (data) toknowledge (probability laws, relationship between variables,…) with Artificial Intelligence(AI) that permits computers to deal with knowledge (not only information), (see for example[16]). The terminology BN comes from Thomas Bayes’s [17] 18th century work. Its actualdevelopment is due to [17]. The main purpose of BN is to integrate uncertainty into expertsystems. BN consist in a graphical representation of the causality relation between a causeand its effects. Figure 4 show that A is the cause and B its effect. A B Fig 4 Causality representation in BNBut as relation of causality is not strict, the next step is to quantify it by giving the probabilityof occurrence of B when A is realized. So an BN consists of an oriented graph where nodesrepresent variables, and oriented arcs represent the causality relation and a set ofprobabilities. A rigorous definition of a BN is given in [18].Let us consider an acyclicoriented graph g = (v,a) where v and a represents set of nodes and the arcs in the graph. Atrial E with whom there is associated a finite probability space and given n random variables (Xi )1 < i < n, a and E defines Bayesian network, noted B = (G,P). There exists a bisectionbetween the nodes of G and var(Xi). The factorization property for this is P(X1,X2 …….Xn) = Π P ( Xi / C(Xi)) (3)Where C(Xi) depends on the set of causes(parents) of Xi. P (X1, X 2,……Xi) Eq.(3) is theprobability of simultaneous realization of variables X1, X2 ….Xi and P(X i / Yi) is theconditionality probability. The main purpose of Bayesian networks is to propagate certainknowledge of the state of one or more partitioned nodes through the network so that one shalllearn how the belief’s of the expert ion the Bayesian network will change, given B = (G,P)and set of nodes it returns to compute P ( Xi / Y i ). Using the properties of chains, treesnetworks and the properties of conditional probability, algorithms can be derived topropagate certain knowledge in term of modifying the belief. BN is completely determinedby its structure and some parameters, namely a priori probabilities of nodes without parentsand conditional probabilities of intermediate nodes for different configurations of states oftheir parents. The basic cell of the QCA circuit will be the component of which reliabilitywill be available. Clocked QCA circuits are considered here, the reliability of the cell can befound in terms of probability of getting correct output of the output cell or group of cells inthat QCA circuit. Before going in detail about reliability analysis let us deal in detail aboutsimple QCA latch and transforming the latch into Bayesian network according to [19][ 20]. 133
  4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME2. BAYESIAN MODEL OF COMPUTATIONConsider a simple QCA latch of figure 5 drawn through QCA simulator from [21]. Figure 6shows layout model Bayesian network of QCA latch from [22]. Figure 5 shows the simple QCA latch from [21] Figure 6 shows the simple Bayesian model of QCA latch.Each chance node in figure 7 represents a random variable of each cell in figure6 and directedarc represents direct causal relation with the parent nodes. A link is directed to child nodefrom the parent node. Let us consider 5 QCA cells indexed in a manner of X1, X2, X 3, X 4and X5. X1 be the input and X5 be the output cell. We use two state approximate model ofsingle QCA cell [20], Two state model can be derived from the quantum formulation basedon all possible configuration of pair of electron in a cell. [23] Each state can be observed inone of possible state logical 0 ( x0) or logical 1 ( x1). The probability of observing a state is P(Xi = xi), x denotes the states be in logical 0 or 1. Polarization of cell in terms of stateprobabilities can be found from conditional and joint probabilities. The joint probability ofobserving a set under steady state assignments for the cell can be determined from quantumwave function which is cumbersome and requires quantum wave function calculations.Instead as in [20] consider a joint wave function of two cells in terms of product of twovariables and representing the product as factored representation. By using Hocktree Fockapproximation as in [24] determine state probability, but by determining polarization as in[25] the polarization can be determined from the given equation. 134
  5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME P = (ρ1 + ρ3 ) - (ρ2 + ρ4) / (ρ1 + ρ2 + ρ3 + ρ4 ) (4)Where ρ represents the expectation values of charges of two cells, Using the above equation,Eq.(4) polarization values can be found, expected values of polarization being directlyentered in the conditional probability table of a random node or a cell and hence using Geniesoftware the joint probability distribution of the circuit can be found. Using this method it ispossible to find the probability of getting output (polarization) for a given temperature andinput being found. Consider the QCA latch in figure 6, the joint probability function isdecompose in to product of individual conditional probability functions asP ( X1, …..X5 ) = P(X5 / X4, X3). P( X4 / X3 , X2) …..P(X2 / X1) P(X1) (5)But Eq.(5) hold for linear random nodes with easy message passing technique to find jointdistribution, we have consider not a linear cell instead a tree like structure. We have used here[18] Joint tree method of message passing technique for propagating the polarizationinformation. Since we have considered as tree like structure, we used above method to formclusters, we decompose the network in to clusters that form tree structures and treat thevariable in each cluster as compound variable that is capable of passing message to itsneighbor, the above network can be clustered in to three clusters X1,X2 and X3 as onecluster, X2, X3, and X4 as second cluster and X4 and X5 as another cluster. The direct causesor parent of a node depends on inferred causal ordering. The exact message passing schemedepends on tree structure, whose nodes are clique of random variables. This tree of cliques isobtained from the initial DAG structure via a series of transformations that preserve therepresented dependencies. These transformations are constructing moral and chordal graphvia constructing triangulated undirected graph. The moral graph is obtained by consideringDAG structure to a triangulated undirected graph structure called moral graph. Chordal graphis obtained from moral graph by a process of triangulation. Triangulation is the process ofbreaking all cycles in the graph to be composition of cycles over just 3 nodes by addingadditional links. There are many possible ways for achieving this. At one extreme, we canadd edges between every pair of nodes to arrive at final graph that is complete. When wetransform DAG to junction of cliques the preservation of parameters dependencies must betaken care, here in this process automatically the dependencies are preserved. Figure 7,8, 9shows the junction of tree clique for the example considered. Figure 7 shows the moral graph of QCA Bayesian network 135
  6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Figure 8 chordal graph of QCA Bayesian network Figure 9 Junction of cliques Moral graph is obtained by drawing a line between x2 andx3, hence it forms a treestructure and using minimum elimination of clique sets and running intersection property asin [21], a three node clique set is formed which is a subtree from the tree, three set of clique isformed using intersection property, [18]a chordal graph is the triangulation process of findingjunction clique set. Finally three sets Clique x1x2x3 , x2x3x4 and x4x5 with potentialfunction as shows in the figure 9. Clique sets c1,c2 and c3 are running with intersectionproperty, a junction tree between these clique is formed by connecting each predecessor tothe present clique set. A potential function is associated with each clique set formed from theconditional probability of the variables in the set. Each potential function is determined bythe product of conditional probability functions mapped to that clique. Eq.(6) gives Productof Cond .Probability.C(x2x3) = ΠvuPa(x) ε x P ( v / Pa ( X)) (6)The joint probability distribution is given by eq.(7)P(x1…..x5) = Π c(xi) i = 1…5 (7)Now the tree structure is useful for local message passing. Given any evidence, messagesconsist of the updated probabilities of the common variables between two neighboringcliques. We used average likelihood propagation algorithm for finding expected polarizationof output cell with respect to temperature and types of input. The probabilities are propagatedthrough the junction clique by local message passing. Messages are passed from leaf clique toroot clique, then again the present clique pass message to next clique and so on. Based on thevalues of c the marginal are found z(yi) for each clique, when message passed first to secondclique, a scaling factor being sent to first clique to scale the marginal for moving to the nextclique, this way message being transmitted. 136
  7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Z(yi) = Σ c( xi) (8) Z(yi) = Zi(yi) / Zj(yi) .Zj(yi) (9)Eq. (8) gives summation of all the values of potential function to give marginal function,Eq.(9) is rescaled depending on present junction clique and next junction clique scalingfunction. Hence for each passing marginal function are rescaled and value is changed for nextclique. We used this technique for QCA latch cell for finding probability of getting correctoutput at the output cell with respect temperature and inputs. Figure 10 a. shows theprobability of getting correct output of logic 1 and logic 0 with respect to input configurations1 and 0. Figure 10.b and c shows probability of getting correct output in combinational andFlip flop QCA circuits. The output value through Bayesian network gives nearly equal tosimulated value, hence Bayesian tools can be used for modeling nano circuits.Fig.10 a. shows the Probability of getting correct output of QCA latch with respect to input 0 and 1. Fig 10.b.Probability of getting correct ouput in Comb circuits through Baeysian networks 137
  8. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Fig 10.c.Probability of getting correct ouput in Flip flops circuits through Baeysian networks2.1 Simulation ResultsThe simulated values from QCA Designer circuit is taken as input to the bayseian networkand cryogenic temperature of 10 K is assumed throughout the Bayesian network. Applyingthe algorithm and probability of getting correct output is calculated. Figure 10 a to c showsthe probability of getting correct ouput for latch, combinational and sequential circuits. It isfound that the value more or less the simulated value and the baysian algorithms used tomodel the nano cicuits for device failures. The next section discuss about the reliabilityissues of QCA circuits and therbyu the reducing the faults occuring in QCA circuits.3. RELIABILITY ANALYSIS OF BAYESIAN STRUCTURE QCA circuits are constructed by serial and parallel structures of QCA wires.Reliability analysis can be done on this circuit in order to deliver errorless QCA cells in theQCA circuit. The reliability analysis of these circuits depends on reliability of input cells sothat errorless QCA cell can be constructed. Bayesian networks used in chapter 5 are used forreliability analysis of QCA circuits. The failure of a QCA cell in QCA circuit may cause thefailure of whole system and a single defective cell in parallel may reduce the overallperformance of a QCA circuit. If a circuit consists of n cells Ci, i=1,…n in serial, the systemwill be performing well if and only if each component is performing well. So if Pi , is thereliability of the ith component, then the reliability of the system Ps is given by equation 3.1.Ps = π i =1ton Pi (3.1) On the contrary if a system consists of n cells Ci, i=1,…n in parallel, the system willperform well if at least one of these cells perform well, so if Pi is the reliability of the ithcomponent, then the reliability of the system Pp is given by equation 3.2.PP = 1 − π i =1ton (1 − Pi ) (3.2) 138
  9. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMEEquation 1 and 2 constitute the fundamental relations for computing the reliability of a QCAcircuit because any system will consists of cells or groups of cells in serial and/or in parallelmanner. Consider a simple QCA latch of figure 11 drawn through QCAdesigner tool. AllQCA circuits are transformed into Bayesian framework and simulated using Genie software.Each cell in the QCA circuit is a node in Bayesian network. Each chance node hasConditional probability table through which joint probability of entire circuit is found. Figure 11.a QCA latch circuit drawn. Figure 11.b Bayesian using QCA designer representation Each chance node in figure 11 represents a random variable of each cell and directed arcrepresents direct causal relation with parent nodes. The structure of the resulting BN for QCAlatch cell for reliability analysis consists of three groups of nodes, let Nc be the node withoutparent say X1 Nint is the intermediate nodes consists of Nint,s serial intermediated node andNpar,s parallel intermediate node. Here X3 and X4 are parallel intermediate nodes with X1 as aparent node. X3 with X4, X2 with X4 are serial intermediate node and destination node as Nout(X5). Figure 12 shows the framed Bayesian structure for reliability analysis. Figure 12 reliability analysis of QCA Latch using Bayesian network 139
  10. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME The transformation of QCA latch Bayesian structure to reliability analysis is byconsidering each cell or node as serial or parallel (assuming all cells are in clock zone). Thisanalysis is useful to study the cell failure in terms of polarization and to identify the correctQCA cell for the circuit failure. Once defined the structure of the BN, its parameters must bedetermined: the parameters to be entered in to the Bayesian network are priori probabilities ofstates of nodes without parents, that is nodes of type Nc and the conditional probabilities ofintermediate nodes, that is nodes of type Nint,s and Nint,p, knowing some configurations of thestates of their parents. Though more than two states can be considered for each node, here itis considered that each node has only two states: failure (F) or no failure (NF). Thegeneralization to more than two states would not be very difficult. The parameters of the BNconsist of two types:1. A priori probabilities of basic components given by their reliability or the complement oftheir reliability.2. Conditional probabilities of the intermediate nodes given the configurations of theirparents. A priori probabilities of nodes of type Nc are fully determined by the reliability of thecorresponding components.4.0 RELIABILITY ALGORITHM OF QCA CIRCUITS. If nc is the basic cell of Nc and pi is the reliability of the component Nc,P ( N ci = NF ) = Pi and iP ( N = F ) = 1 − Pi , i = 1....nc c (4.1)Similarly for Nint,p and Nint,s Parameters can be defined asP ( N int, p = NF / C ( N int, p )) = 0UN ∈ C ( N int, p ), N = Failure (4.2)ElseP ( N int, p = NF / C ( N int, p )) = 1 (4.3)and P ( N int, p = F / C ( N int, p )) = 1UN ∈ C ( N int, p ), N = Failure (4.4)ElseP ( N int, p = F / C ( N int, p )) = 0 (4.5)P ( N int, s = NF / C ( N int, s )) = 1UN ∈ C ( N int, s ), N = NoFailure (4.6)ElseP ( N int, s = NF / C ( N int, s )) = 0 (4.7)AndP ( N int, s = F / C ( N int, s )) = 1UN ∈ C ( N int, s ), N = NoFailure (4.8)ElseP ( N int, s = F / C ( N int, s )) = 1 (4.9) Equations 6.3 to 6.11 gives conditional probability defined for intermediate nodes with conditionsfailure (F) and no- failure (NF). The polarization is defined for each cell, for exampleP (Ci = NF ) = 0.9 (4.10)P (Ci = F ) = 0.1, i = 1....4. 140
  11. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMEFull polarization value (logic 1) is 0.9 to +1 and -0.9 to -1, partially polarized values are 0.5to 0.8 or -0.5 to 0-0.8, and logic 0 polarization values are -0.5 to + 0.5. Let X1 cell be the Ncnode, interaction between X2 and X4 be G1 as intermediate node, interaction between X3and X4 be G2, second node be either G1 or G2 of Nint,p, third intermediate node be Nint,sand finally destination or output node Nout. Now the Bayesian network defined over QCAlatch according to above statements as shown in figure 13, assume logic 1 as input decisionand searching for utility at the output node in terms of its probability. Figure 13 a Decision and utility nodes for evaluating logic1 probability at the output node which is 0.832 with intermediate node CPT is shown in table 4.1. Table 4.1 Intermediate node G1 node CPT Table 4.1 shows the intermediate CPT table, if the entries in the CPT are changed slightlyfrom 0.9 to 0.6 less polarized that leads to decrease the probability then intermediated nodeshas to be checked. Next is to examine the cell which is less polarized by G1 or G2 nodes. Figure 14 Decision and utility nodes for evaluating logic1 probability at the output node which is 0.822, decreased than in figure 13. 141
  12. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Table 4.1 and 4.2 gives G1 and G2 CPT, the failure of the whole system means thatcomponent X4 and cell G1 will surely fail. The element responsible for the failure of G1 is X3and X4 with 71.00% of chances against G2 with 29.00% of chances. So the system criticalelements, in terms of reliability, are G1( X3 and X4) and X4 . One can simulate many otherconfigurations to find the error occurred in terms of probability of output. Table 4.2 CPT of node G2 due to X2 and X4 QCA cells (0.71 – 1, 0.3 -0) Cell X2 Failure No - Failure Cell X4 F NF F NF Failure 1 0 0 0 No 0 1 1 1 failure Table 4.3 CPT of node G1 due to X3 and X4 QCA cells ( 0.71 -1, 0.3 -0) Cell X3 Failure No - Failure Cell X4 F NF F NF Failure 1 1 1 0 No 0 0 0 1 failure4.1 QCA NOT circuit with CLOCK Zone A QCA circuit organized in parallel is more reliable than one which is organized in serial.Serial QCA circuits require clocking for group of cells whereas a parallel QCA cell (circuitwith more layers in parallel) which has clock zones running for more no of layers. One wayto improve the reliability of a QCA circuit is to put two or more layers in parallel instead ofone layer. But this process will increase the complexity of the circuit. An example of asystem composed of QCA cells is given in Figure 6.5. The system has two main parallelbranches, one branch consisting only of the components C4 and the other one consisting ofcomponent C1 in serial with a group formed by C2 and C3 in parallel. Figure 15.QCA not circuit with serial and parallel layers a input and y output 142
  13. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME C1 C2 C3 C4Figure 16 Equivalent Component structure for reliability analysis of QCA not circuit Table 4.4 CPT of node G2 Cells c2 Failure No - Failure Cells c3 F NF F NF Failure 1 0 0 0 No 0 1 1 1 failure Table 4.5 CPT of node G1 Cells c1 Failure No - Failure Cells G2 F NF F NF Failure 1 1 1 0 No 0 0 0 1 failure Table 4.6 CPT of intermediates node. Cells c4 Failure No - Failure Cells G1 F NF F NF Failure 1 0 0 0 Nofailure 0 1 1 1 Figure 15 is QCA NOT circuit and 16 gives the reliability transformation of finding thecomponents in 15. QCA NOT circuit has two parallel branches and one loop in one of theparallel branches. As discussed in the previous section, C1 has group of cells in upper parallelarm, C2 and C3 form the smaller loop in upper parallel arms and C4 form the lower parallelarm. Let us define the components (group of cells) • C1, C2, C3 and C4 are nodes of type Nc; • G2 is a node of type Nint,s formed by regrouping the component C1 act in parallel components C2 and C3; • G1 is a node of type Nint,s formed by regrouping the component C1 and the subsystem G2; • Finally the subsystem G1 and the component C4 act in parallel on the system so that this one is a node of type Nint,p. 143
  14. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMETable 4.4, 4.5, 4.6 gives Conditional Probability of cells of G1 and G2 intermediate nodes.The failure of the whole system means that component C4 and subsystem G1 will surely fail.The element responsible for the failure of G1 is C1 with 91.74% of chances against G2 with9.17% of chances. So the system critical elements, in terms of reliability, are C1 and C4. Thegroup of cells in C1 and C4 have to be examined to find particular defect cell in terms of itsprobability of getting correct polarization or not. The same way analysis can be carried outfor QCA system to find defective cells. The reliability of QCA cell can be found using this Bayesian network of transformingQCA circuits to its Bayesian framework. The QCA latch circuit failure is due to one of theintermediate nodes as its probability decreases when it is a defect one, similarly QCA notcircuit also is used to find reliability of group of cells in serial and parallel arms. This can beextended for simulating errorless QCA systems. The extension of this work is to assume thetype of defects or device level uncertainties in QCA circuits and by using different algorithmsimulating its Bayesian framework to find defective cells in terms of its polarization.5. CONCLUSION Bayesian network can be used to find the probability based modelling of QCA cells interms of its temperature and input configurations. We have simulated the probability basedBayesian modelling of finding the correct output of simple latch circuit. We discussedreliability analysis of QCA latch and Not circuit, we found the probability decreases as wemove to higher nodes when present cell or node is a defect one, reliability of the cell can befound using this Bayesian network of transforming qca circuits to its Bayesian framework.We discussed qca latch circuit failure is due to one of the intermediate nodes as its probabilitydecreases when it is a defect one, we analysed QCA not circuit also to find reliability ofgroup of cells in serial and parallel arms. This can be extended for simulating errorless QCAsystems. We have not considered the type of defects occur for particular cell. The extensionof this work is to assume the type of defects or device level uncertainties in QCA circuits andby using different algorithm simulating its Bayesian framework.REFERENCE[1] C. Lent and P. Tougaw etal Proceeding of the IEEE, vol. 85-4, pp. 541.557, April 1997[2] K.Walus, Wei Wang and Julliaen et al, Proc IEEE Nanotechnology conf, vol 3 December2004.[3] A. Vetteth et al., Proc. IEEE Emerging Telecommunications Tech-nologies Conf., 2002[4] K.Walus, Wei Wang and Julliaen et al, Proc IEEE Nanotechnology conf, vol 3 page461-463December 2004 [5] K.Walus, Schulaf and Julliaen et al, Proc IEEE Nanotechnology conf, vol 4,page 1350-1354, 2004.[6] K.Walus, Dimitrov and Julliaen et al Proc IEEE Nanotechnology conf, vol 3,page 1435 –1439 2003[7] K.Walus, Dysart and Julliaen et al, IEEE transactions on Nanotechnology conf, vol 3, No– 2 June 2004.[8] P. D. Tougaw and C. S. Lent, J. Appl. Phys., vol. 75, no. 3, pp. 1818–1825, 1994.][9] I. Amlani et al., Appl. Phys. Lett., vol. 77, no. 5, pp. 738–740,2000.] Control input to ORgate is 1.[10] W. Porod etal Int. J. Bifurcation Chaos, vol. 7, no. 10, pp. 2199–2218, 1997. 144
  15. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME[11] I. Amlani et al, Appl. Phys. Lett., vol. 77, no. 5, pp. 738–740,2000.] Control input to ORgate is 1.[12] . Amlani et al., Science, vol. 284, pp. 289–291, 999.[13] A. Orlov et al., Appl. Phys. Lett., vol. 74, no. 19, pp. 2875–2877, 1999[14] K. Hennessy and C. S. Lent, J. Vac. Sci. Technol. B., vol. 19, no. 5, pp. 1752–1755 2001[15] K.Walus, Dysart and Julliaen et al, IEEE transactions on Nanotechnology conf, vol 3March 2004.[15 ] G. Toth, Ph.D. dissertation, Univ. Notre Dame, Notre Dame, IN, 2000[16]. Vilela Neto, Pacheco, Barbosa IEEE transaction on Computers VOL 56, pp -191 -198February 2007[17] Bayes.T., An Essay Towards Solving A Problem in the Doctrine of Chances,BIOMETRICA, 46,1958, pp. 293-298 (reprinted from an original paper of 1763).[18] Pearl J., Probabilistic Reasoning in Intelligent Systems, Margon Kaufmann,1988.[19] Barlow R Proschan, Mathematical Theory of Reliability, NASA Symposium on VLSIDesign, Coeur d’Alene, Idaho, USA, Oct. 4-5, 2005. [21] Saket Srivastava and Sanjukta Bhanja IEEE transactions on nanotechnology vol4 pp 43 – 78 2006. [22] www.qcadesigner.ca [23]. www.genie.in [24]. P. D. Tougaw and C. S. Lent, . Journal of Applied Physics, vol. 80, pp. 4722.4736, Oct 1996. [25] C. Lent and P. Tougaw, in Proceeding of the IEEE, vol. 85-4, pp. 541.557, April 1997. [26] Geza Toth, Craig S. Lent, P. Douglas Superlattices and Microstructure, Vol. 20, No. 4, 473(1996). [27] Nilesh Parihar and Dr. V. S. Chouhan, “Extraction Of QRS Complexes Using Automated Bayesian Regularization Neural Network” International Journal Of Advanced Research In Engineering & Technology (IJARET), Volume 3, Issue 2, 2012, pp. 37 - 42, Published by IAEME.[28] Er. Ravi Garg and Er. Abhijeet Kumar, “Comparasion of SNR and MSE for Various Noises Using Bayesian Framework” International journal of Electronics and Communication Engineering &Technology (IJECET), Volume 3, Issue 1, 2012, pp. 76 - 82, Published by IAEME. 145

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