Optical performance monitoring covers a very wide range of measurements intended to help ensure network performance and is essential for service providers. We address the problem of solving the linearly accumulated end-to-end impairments of a special set of paths of interest in a reconfigurable all-optical network. This set of paths of interest may include all the paths between any two communicating nodes. The main focus is on the minimization of the number of monitoring devices that are required. A set of channels is injected into the network and monitored. By using the correlation in the channel quality between injected channels, a framework of algebraic performance monitoring is proposed to derive the channel quality of the paths of interest from the linear combination of the monitoring results of the injected channel. The upper bounds on the minimum number of monitoring devices required are derived and constructively achieved for a general network. For a special network in which all nodes are capable of initiating and dropping the monitoring channels, the fundamental limit on the minimum number of monitoring devices is also achieved. The proposed monitoring scheme for this kind of network can also locate at least one fault, even if multiple faults occur. We reduce the cost of monitoring by utilizing the information from the monitoring results and minimizing the number of monitoring devices.
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