Digital transmission using highspeed medium will require highspeed microelectronic implementation of adaptive equalizers, encoders, and other associated signal processing algorithms. highspeed implementation of these algorithms is often difficult, since the recursive portion of these algorithms contain nonlinear operations (such as the quantization operation). Examples of such algorithms include differential pulse code modulation (DPCM), adaptive DPCM (ADPCM), and decision feedback equalizers (DFE's). The internal feedback or recursion in these algorithms makes it difficult to implement recursive systems concurrently using either pipelining or parallelism. In the past, look-ahead computation techniques were successfully applied to create necessary concurrency in linear recursive and some nonlinear recursive operations (such as the add-compare-select operation). This paper proposes novel computation approaches and extends the look-ahead technique to pipeline the feedback loops containing finite-level quantizers. Approaches to pipeline piecewise-linear recursive systems are also presented. The new architectures proposed in this paper are suitable for realtime highspeed implementation of quantizer loop operations where the levels of quantizer and the order of the loops are small.