Integrator Bound-Based Nonlinear Decoder for Delta-Sigma Modulator

A new nonlinear iterative delta-sigma decoder based on the modulator integrator bounds is presented. The proposed decoder has faster convergence and more efficient decision levels than the previously known zoomer decoder. The proposed decoder shows the best-known mean-squared error (MSE) performance, about 5.25 dB gain over the zoomer decoder. The decoder MSE bound is 0.27(d/2)²/L³, while the zoomer decoder provides claimed 0.91(d/2)²/L³, both of which obtained through numerical simulations. The differences in initial conditions and solution developments show that the proposed decoder is not a special case of the zoomer decoder. While the optimality of the zoomer decoder is based on the assumed initial condition, it is argued that the assumed condition is not optimal, since it maximizes the first quantization error and it wastes first two modulator output bits. The proposed algorithm decodes an output stream of a first-order delta-sigma modulator with a static input and an initial condition. Solution tracking behaviors, decision levels, and MSE, or signal-to-noise ratio (SNR) performances of both decoders are examined and compared to justify the claims.