The optimal testing in photonic switching networks using tabulation methodology

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Abstract

Optical crosstalk, a problem commonly found in Dilated Optical Multistage Interconnection Networks (DOMINs), is the outcome of undesirable coupling within a 2×2 directional coupler. As widely recognized, a switch is faulty if it causes crosstalk in excess a given threshold, the value of which can be determined according to certain criteria. Diagnosing faulty switches, which includes detection and location procedures, has become an important issue for DOMINs. The fault cluster (or test set) is an independent set of tests for diagnosing faulty switches. The test patterns (or disjoint faults) in each fault cluster can be applied in parallel during diagnosis. The fault-table method is a classical analytic and deterministic minimization method used in the circuit testing of VLSI. The method is especially efficient when tackling complicated circuits, and can be solved efficiently by modern computer technology. An algorithm that uses the tabulation method is developed to obtain the optimal fault cluster(s) for both detection and location tests. The paths of the injected signal, output signal and faulty signal throughout the network are collected to determine the conflict table. Then, the conflict table is minimized to yield the fault clusters. The fault clusters are then stored in the management system. The results can help us to diagnose faulty switches in parallel to accelerate the diagnosis. The tabulation methodology follows the same diagnostic procedure for the various infrastructures and is independent of the size of the DOMINs. Furthermore, a computer program can simulate the procedure and the results support the optimal test.

Introduction

A classic analytical and deterministic method of minimization for complicated switching functions in electronic Multistage Interconnection Networks is the fault-table method or the Quine–McCluskey method [1], [2], [3]. The tabular minimization method attempts to find a minimal form of a given set for the problems of both fault detection and fault location. The method also offers completely general processes and always yields the minimum sets of diagnostic tests for systematic simplification procedures. This paper advances the diagnosis of faulty switches in photonic switching networks using an algorithm that involves tabulation methodology. The methodology involves three steps; step 1 – construction of the conflict table, step 2 – construction of the fault-detection table (or fault-location table), and step 3 – determination of the minimal test sets (fault clusters).

2×2 directional coupler-based [4], [5], [6], [7] photonic switching is an essential synergetic approach to all optical networks as it maintains data in optical form during the switching, providing virtually unlimited communication bandwidth and transparency of data rate and encoding format. Such switches can be used to construct Dilated Optical Multistage Interconnection Networks (DOMINs) in IP over DWDM architecture, to yield all optical high-performance networks [8], [9]. The 2×2 switch element can be operated in either the Cross or Bar state by applying an appropriate control voltage to the electrode. Unfortunately, optical crosstalk is a problem in DOMINs. It is the effect of undesirable coupling (or leaks) of signals from in different paths within a directional coupler and may be caused by the parameters’ being affected by the control voltage, temperature, polarization, or aging [7], [8]. This crosstalk is the first-order crosstalk. A switch is said to be faulty if it causes crosstalk in excess of a given threshold whose value can be determined according to specific criteria. The diagnosis of photonic switching networks is an emerging and important issue in all-optical networks [10]. Nevertheless, the crosstalk in photonic switches is operational and hard to diagnose due to the small size of the switches and the difficulty in measuring the energy of light. Designing different algorithms to diagnose crosstalk faults for photonic networks of the automatic testing generation, with the current sophisticated VLSI technology [11], [12]. Although pioneering researchers have proposed many ad hoc systematic diagnosing algorithms, they have failed to predict the optimal procedure for accelerating the tests by overlapping them with computation and/or by performing that computation in parallel with the tests. The fact is that the number of unused photonic switches grows in O(N2), as the size of network increases in N×N. Intuitively, the diagnostic procedure could be accelerating the tests by overlapping the tests, referred to as disjoint faults [13].

This study develops the deterministic diagnosing algorithm that uses the tabulation method to obtain optimal fault clusters or minimal test sets in DOMINs. This method is universal for detecting and locating the possible faulty switches. Firstly, the paths of the injected signal, output signal and faulty signal throughout the network are collected to construct the conflict table, and an algorithm is developed to minimize the table. A new fault cluster (or test set) is generated after each reduction is performed. The test patterns in each fault cluster, called disjoint faults, can be conducted in parallel during the diagnosis. Minimization continues until no conflict exists in the conflict table. The fault clusters are essentially mutually exclusive to their own test patterns. The diagnosis should be separately performed for the different fault clusters in the network. Restated, the test patterns in the same fault cluster will result in no conflict during the test, whereas any test pattern from the different fault clusters will cause conflicts. Fewer fault clusters enable faster diagnosis. Consequently, all tests for N×N DOMINs can be reduced to the number of fault clusters, given that the minimization process is complete, and especially if the DOMINs expand. The information concerning fault clusters is stored in the management system, so the faulty switches can be located quickly if a fault is detected in the switching network. This method can efficiently determine optimal fault clusters in parallel during the diagnostic process, and it will not miss any possible fault cluster. The benefit of this method a single diagnostic procedure is independent of the architecture and the size of the DOMINs. The result significantly accelerates the diagnosis by overlapping the tests, and constitutes a significant improvement over the method proposed than Hwang [13].

The rest of this paper is organized as follows. Section 2 describes the fault model and system assumptions. Section 3 discusses the specific properties of Dilated Omega Network (DON), as related to the preliminary discussions in this paper. Section 4 introduces the construction of the conflict table and the tabulation methodology algorithm. In Section 5, the tabulation method is used to find the optimal fault clusters for both fault detection and fault location procedures. Finally, conclusions and areas for future research are finally drawn in Section 6.

Section snippets

Fault models and system assumptions

A faulty switch can have four optical paths and the possible crosstalk faults in a switching element [13]. W(0,0) (or type-1) optical path and W(1,1) (or type-2) optical path faults may occur when the switch is in the Bar state; W(0,1) (or type-3) optical path and W(1,0) (or type-4) optical path faults may occur when the switch is in the Cross state.

Before the fault detection and fault location methods are considered, the system assumptions are defined as follows:

  • 1.

    A switch with crosstalk is

Dilated Omega Network

Dilated Omega Networks (DONs) belong to a class of blocking Multistage Interconnection Networks (MINs) [13], [14], [15]. An N×N DON is constructed by connecting stage i to stage (i+1) by a shuffle connection, recursively, where 0⩽i⩽log2N). The N×N DON has an asymmetrical architecture with (log2N)+1 stages and N switching elements in each stage. As in any dilated network, only half of the input terminals and output terminals will be used, and no single switching element carries over one active

Tabulation method

This section describes the tabulation method that can be applied to diagnose the crosstalk faulty switch for Dilated Optical Multistage Interconnection Networks (DOMINs). The tabulation methodology provides a systematic simplification procedure, which can be programmed to find the minimal sets of the fault cluster when the system is large. If more than two test signals or faulty signals pass through the same switch, a conflict occurs. The following definitions are used throughout this paper:

Definition

Diagnostic algorithms

The diagnostic algorithm involves two procedures – fault detection and fault location. The algorithm to find fault clusters using tabulation methodology is developed for both fault detection and fault location procedures. The fault detection procedure detects the possible crosstalk signal at output terminal. The fault location procedure locates possibly faulty switches inside the photonic switching chips.

Fault detection procedure: The possibly faulty output signal that is measured depends on

Conclusion

The methodology of tabulation has been extensively applied in VLSI testing and circuit design. However, this methodology is applied for the first time to diagnosing faulty switches of photonic switch networks. The tabulation method is a highly effective means of handling complicated circuits, and the algorithm can be efficiently implemented by a computer program. The results always reveal the optimal fault clusters or minimal test sets for detection procedure and location procedure,

Acknowledgements

We would like to thank the anonymous referees who gave precious suggestions to improve the work and this work was supported in part by the funding of Contract No. NSC 89-2213-E-155-082, Taiwan, Republic of China.

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