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Previous work has established that the digital output of a ΣΔ modulator as an A/D converter contains more information about the analog input than is extracted with conventional linear filtering. Under reasonable mathematical assumptions, optimal nonlinear decoding of the digital output can achieve significantly larger signal-to-noise ratios than linear filtering. However, the hitherto proposed decoding algorithms only demonstrate conceptual feasibility and are impractical from a computational point of view. We present a new block-based decoding algorithm that, like previous work, employs projections onto convex sets. The algorithm owes its speed to a change of projection norm, an accelerated convergence scheme, and a decimation-like subsampling; it is on the order of 104-105 times faster than one previously published algorithm for typical parameter values, and about 2-10 times slower than linear decoding. The new algorithm is applicable to all currently popular ΣΔ architectures.