Determining the Minimum Iteration Period of an Algorithm1

Abstract — Digital signal processing algorithms are repetitive in nature. These algorithms are described by iterative data-flow graphs where nodes represent computations and edges represent communications. For all data-flow graphs, there exists a fundamental lower bound on the iteration period referred to as the iteration bound. Determining the iteration bound for signal processing algorithms described by iterative data-flow graphs is an important problem. In this paper we review two existing algorithms for determination of the iteration bound. Then we propose another novel method based on the minimum cycle mean algorithm to determine the iteration bound with a lower polynomial time complexity than the two existing techniques. It is convenient to represent many multi-rate signal processing algorithms by multi-rate data-flow graphs. The iteration bound of a multi-rate data-flow graph (MRDFG) can be determined by considering the single-rate data-flow graph (SRDFG) equivalent of the MRDFG. However, the equivalent single-rate data-flow graph contains many redundant nodes and edges. The iteration bound of the MRDFG can be determined faster if these redundancies in the equivalent SRDFG are first removed. A previous approach has considered elimination of edge redundancy. In this paper we present an approach to eliminate node redundancy in the MRDFG. We combine elimination of node and edge redundancies to propose a novel algorithm for faster determination of the iteration bound of the MRDFG.