A polynomial time algorithm for solving the word-length optimization problem

Trading off accuracy to the system costs is popularly addressed as the word-length optimization (WLO) problem. Owing to its NP-hard nature, this problem is solved using combinatorial heuristics. In this paper, a novel approach is taken by relaxing the integer constraints on the optimization variables and obtain an alternate noise-budgeting problem. This approach uses the quantization noise power introduced into the system due to fixed-point word-lengths as optimization variables instead of using the actual integer valued fixed-point word-lengths. The noise-budgeting problem is proved to be convex in the rounding mode quantization case and can therefore be solved using analytical convex optimization solvers. An algorithm with linear time complexity is provided in order to realize the actual fixed-point word-lengths from the noise budgets obtained by solving the convex noise-budgeting problem.