Devices and methods of reducing quantization noise using a pyramid stream encoder are generally described. Groups of D digital symbols are iteratively computed for a digital signal such that each group of symbols minimizes a norm of a weighted residue vector. The weighted residue vector is formed by applying predetermined weighting coefficients to components of a residue vector. Each component is a difference between a sample of the digital signal and a linear combination of different groups of digital symbols with predefined filter coefficients. The norm of the weighted residue vector evaluated at a rate D times slower than a sampling rate of an output signal. The groups of D digital symbols are provided as the output signal.