Multirate System Retiming via Normalization Factor Vector
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Solution Overview
Problem
Current data flow graph representations for multirate systems face complexity in optimizing clock periods due to integer linear programming requirements, leading to increased computational complexity and potential errors, especially when dealing with large system sizes.
Innovation Solution
The introduction of a normalization factor vector allows the formulation of the multirate retiming problem as a single rate system, enabling the use of linear programming and shortest path algorithms, which simplifies the optimization process and eliminates the need for integer linear programming, thereby reducing computational complexity and error prone issues.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If integer linear programming is used to optimize multirate data flow graphs, then optimization accuracy is improved, but computational complexity increases and error-prone issues arise
Solution Approach 1:
The patent introduces a normalization factor as an intermediary element that transforms the multirate data flow graph into a normalized form where all nodes operate at a common rate. This normalization factor acts as a mediator that allows the application of simpler linear programming techniques instead of requiring complex integer linear programming, thereby reducing computational complexity while maintaining optimization accuracy.
Solution Approach 2:
The patent changes the parameter representation by introducing normalization factors that transform the original multirate parameters into normalized parameters. This parameter transformation allows the optimization problem to be solved using standard linear programming rather than integer linear programming, reducing computational complexity while preserving the ability to achieve optimal solutions.
2Reliability
If multirate data flow graphs are optimized directly, then system fidelity is improved, but graph size and computational requirements increase
Solution Approach 1:
The patent applies parameter changes by normalizing the multirate graph parameters using normalization factors. This transformation allows the multirate system to be represented in a normalized form that maintains system fidelity but reduces the effective graph size for optimization purposes, making the problem more tractable without losing the essential multirate characteristics.
Data Source
AI summary
Methods and apparatuses for retiming of multirate system for clock period minimization with a polynomial time without sub-optimality. In an embodiment, a normalized factor vector for the nodes of multirate graph is introduced, allowing the formulation of the multirate graph retiming constraints to a form similar to a single rate graph. In an aspect, the retiming constraints are formulated to allowed the usage of linear programming methodology instead of integer linear programming, thus significantly reducing the complexity of the solving algorithm. The present methodology also uses multirate constraints, avoiding unfolding to single rate equivalent, thus avoiding graph size increase. In a preferred embodiment, the parameters of the multirate system are normalized to the normalized factor vector, providing efficient algorithm in term of computational time and memory usage, without any sub-optimality.