Pipelining in algorithms with quantizer loops

High-speed implementation of signal processing algorithms for digital transmission is addressed. 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). Novel computation approaches are proposed, and the look-ahead technique is extended to pipeline the feedback loops containing finite-level quantizers. Approaches to pipeline piecewise-linear recursive systems are presented. The proposed architectures are suitable for real-time high-speed implementation of quantizer loop operations where the levels of quantizer and the order of the loops are small