Optimum wordlength allocation

This paper presents an approach to the wordlength allocation and optimization problem for linear digi-tal signal processing systems implemented in Field-Programmable Gate Arrays. The proposed technique guarantees an optimum set of wordlengths for each internal variable, allowing the user to trade-o imple-mentation area for error at system outputs. Optimal-ity is guaranteed through modelling as a mixed integer linear program, constructed through novel techniques for the linearization of error and area constraints. Optimum results in this eld are valuable since they can be used to assess the eectiveness of heuristic wordlength optimization techniques. It is demon-strated that one such previously published heuristic reaches within 0:7 % of the optimum area over a range of benchmark problems.