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In this paper we investigate a finite temperature generalization of surveypropagation, by applying it to the problem of finite temperature decoding of abiased finite connectivity Sourlas code for temperatures lower than theNishimori temperature. We observe that the result is a shift of the location ofthe dynamical critical channel noise to larger values than the correspondingdynamical transition for belief propagation, as suggested recently byMigliorini and Saad for LDPC codes. We show how the finite temperature 1-RSB SPgives accurate results in the regime where competing approaches fail toconverge or fail to recover the retrieval state

Survey propagation at finite temperature: application to a Sourlas code as a toy model