A method for computing likelihoods in a process for reconstructing decoded information words from a signal received on a receiver device in the form of vectors of observations after transmission of said signal using sub-channels of a wireless channel by a transmission device in the form of vectors derived from vectors of modulated symbols, said signal having been generated using a plurality of elementary coding modules, an elementary coding module being an Alamouti matrix based Differential Space Time Block Codes coder, called DSTBC coder, or an Alamouti matrix based Differential Space Frequency Block Codes coder, called DSFBC coder, the receiver device comprising at least one reception antenna, a signal decoding module, a scaling module adapted to scale observations of a vector of observations after processing by the signal decoding module to obtain a vector of scaled observations and a de-interleaving module applying a de-interleaving to the vector of scaled observations, the signal decoding module comprising elementary decoding modules, each elementary decoding module being an inverse DSTBC or inverse DSFBC module, characterized in that the method comprises applying an iterative reconstruction process, comprising in each iteration: receiving a vector of observations on each antenna, each vector of observations corresponding to a same vector of modulated symbols; determining, for each vector of observations, at least one corresponding vector of approximated scaling factors allowing obtaining a vector of scaled observations with equal noise variance; determining (75, 76, 77) for each vector of approximated scaling factors corresponding to each vector of observations, a vector of approximated scaled equivalent channel models after processing the vector of observations by the signal decoding module and the scaling module using the vector of approximated scaling factors; and, computing likelihoods in the form of values representative of joint probabilities of obtaining each vector of observations knowing a vector of modulated symbols and a model of the wireless channel using each determined vector of approximated scaling factors and each determined vector of approximated scaled equivalent channel models; wherein the determining, of one vector of approximated scaled equivalent channel models, comprises for each elementary decoding module, the sub steps of computing (761, 762) a norm, called first norm, of a couple of observations of a preceding vector of observations received on the same antenna than said vector of observations in an iteration preceding the current iteration, said couple of observations corresponding to the elementary decoding module; obtaining (763, 767) an approximated scaling factor of the vector of approximated scaling factors corresponding to the elementary decoding module; and, computing (764, 768) an approximated scaled equivalent channel model as a product of said approximated scaling factor, said first norm, a norm of channel coefficients of the model of the wireless channel corresponding to said elementary decoding module and a first predetermined parameter corresponding to said elementary decoding module. receiving a vector of observations on each antenna, each vector of observations corresponding to a same vector of modulated symbols; determining, for each vector of observations, at least one corresponding vector of approximated scaling factors allowing obtaining a vector of scaled observations with equal noise variance; determining (75, 76, 77) for each vector of approximated scaling factors corresponding to each vector of observations, a vector of approximated scaled equivalent channel models after processing the vector of observations by the signal decoding module and the scaling module using the vector of approximated scaling factors; and, computing likelihoods in the form of values representative of joint probabilities of obtaining each vector of observations knowing a vector of modulated symbols and a model of the wireless channel using each determined vector of approximated scaling factors and each determined vector of approximated scaled equivalent channel models; wherein the determining, of one vector of approximated scaled equivalent channel models, comprises for each elementary decoding module, the sub steps of computing (761, 762) a norm, called first norm, of a couple of observations of a preceding vector of observations received on the same antenna than said vector of observations in an iteration preceding the current iteration, said couple of observations corresponding to the elementary decoding module; obtaining (763, 767) an approximated scaling factor of the vector of approximated scaling factors corresponding to the elementary decoding module; and, computing (764, 768) an approximated scaled equivalent channel model as a product of said approximated scaling factor, said first norm, a norm of channel coefficients of the model of the wireless channel corresponding to said elementary decoding module and a first predetermined parameter corresponding to said elementary decoding module.