A FAST BLOCK-BASED NONLINEAR DECODING ALGORITHM FOR SIGMA-DELTA MODULATORS

Previous work has established that the digital output of a Sigma Delta modulator as an A/D converter contains more information about the ana log 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 ratio s than linear filtering. However, the hitherto proposed decoding algor ithms only demonstrate conceptual feasibility and are impractical from a computational point of view. In this paper, 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 project ion norm, an accelerated convergence scheme, and a decimation-like sub sampling; it is on the order of 10(4)-10(5) times faster than one prev iously published algorithm for typical parameter values, and about 2-1 0 times slower than linear decoding. The new algorithm is applicable t o all currently popular Sigma Delta architectures.