Optimum wordlength allocation

This paper presents an approach to the wordlength allocation and optimization problem for linear digital 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-off implementation area for error at system outputs. Optimality 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 field are valuable since they can be used to assess the effectiveness of heuristic wordlength optimization techniques. It is demonstrated that one such previously published heuristic reaches within 0.7% of the optimum area over a range of benchmark problems.