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In this paper, we present a novel efficient algorithm for the estimation of the Channel Impulse Response (CIR) when this CIR is sparse (meaning a big number of the CIR coefficients are equal to zero) for multicarrier systems using Orthogonal Frequency-Division Multiplexing (OFDM) transmission. The derivation of this CIR estimation algorithm investigates first the sparse structure of the channel through the modeling of the sparse CIR as a Bernoulli-Gaussian process. This established modeling will allow us to exploit the relationship between the Reed-Solomon (RS) codes and the OFDM modulator to efficiently estimate the sparse CIR. To do so, we consider the pilot tones that are usually scattered among the information sequence for the synchronization or equalization purposes, as syndromes in order to estimate the sparse channel coefficients, and we prove that using our proposed algorithm, the obtained estimates are unbiased and that the estimation error is quasi-optimum. Furthermore, our proposed technique keeps valid even in the case where the pilots tones are assumed to be not uniformly placed in the transmitted sequence provided that their positions satisfy a repartition condition. Simulation results are presented to illustrate the performance of our proposed algorithm and to support our claims.