Apparatuses, systems, and methods are disclosed for stochastic linear detection. A digital signal processor determines information about a plurality of transmitted signals based on a plurality of received signals. An initialization module determines an estimator matrix and a noise shaping matrix based on channel state information that relates the transmitted signals to the received signals. A sample generation module stochastically generates a plurality of signal estimates so that each signal estimate is a sum of a fixed component and a random component. The fixed component may be based on applying the estimator matrix to a vector of the received signals, and the random component may be based on applying the noise shaping matrix to generated noise. An output module sends soft information to an error-correcting code (ECC) decoder for decoding bits carried by the transmitted signals. The soft information may be based on the plurality of signal estimates.