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This paper introduces a network coding-based protection scheme against single- and multiple-link failures. The proposed strategy ensures that in a connection, each node receives two copies of the same data unit: one copy on the working circuit and a second copy that can be extracted from linear combinations of data units transmitted on a shared protection path. This guarantees instantaneous recovery of data units upon the failure of a working circuit. The strategy can be implemented at an overlay layer, which makes its deployment simple and scalable. While the proposed strategy is similar in spirit to the work of Kamal in 2007 2010, there are significant differences. In particular, it provides protection against multiple-link failures. The new scheme is simpler, less expensive, and does not require the synchronization required by the original scheme. The sharing of the protection circuit by a number of connections is the key to the reduction of the cost of protection. This paper also conducts a comparison of the cost of the proposed scheme to the 1+1 and shared backup path protection (SBPP) strategies and establishes the benefits of our strategy.