Recursive Summation Convolution for BER Signal Analysis
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for simulating signal transmission in high-speed circuit design are computationally intensive and memory-intensive due to the need for extensive recursive convolution in statistical signaling analysis, which can be impractical for achieving statistically significant Bit Error Ratios.
Innovation Solution
A computer-implementable recursive summation algorithm that efficiently performs recursive convolution by using a tree structure and memory-efficient data structures to reduce computational and memory requirements, allowing for faster and more accurate simulation of signal transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional recursive convolution methods are used for statistical signal analysis, then measurement precision of Bit Error Ratio is improved, but computation time and memory usage increase significantly
Solution Approach 1:
The patent segments the recursive convolution process into manageable computational stages using a tree structure. Instead of performing full recursive convolution on entire long bit streams, the method divides the computation into smaller sub-problems that can be solved independently and combined, significantly reducing the computational time while maintaining statistical significance for Bit Error Ratio measurement.
Solution Approach 2:
The patent transforms the computational approach by introducing a tree structure dimension to the recursive convolution process. This dimensional change allows the computation to proceed through hierarchical levels rather than linearly through the entire signal, enabling parallel computation paths and reducing the overall computation time required for accurate BER measurement.
2Measurement precision
If traditional recursive convolution methods are used for statistical signal analysis, then measurement precision of Bit Error Ratio is improved, but memory usage increases significantly
Solution Approach 1:
The patent segments the data structures used in recursive convolution, storing intermediate results in a tree structure rather than maintaining all data in linear memory. This segmentation allows memory to be reused at different tree levels and reduces the peak memory requirement while still enabling accurate statistical signal analysis and Bit Error Ratio measurement.
Solution Approach 2:
The patent performs preliminary computation and storage of intermediate convolution results in a structured format before final BER calculation. By pre-computing and organizing results in a tree structure, the method reduces the memory needed during the final statistical analysis phase, as intermediate results are already organized and ready for combination.
3Measurement precision
If longer bit streams are simulated to achieve statistically significant BER, then measurement precision is improved, but device complexity and computation time increase
Solution Approach 1:
The patent segments long bit stream simulation into smaller manageable units processed through a tree structure. This segmentation reduces simulation complexity by breaking down the overwhelming task of processing extremely long bit streams into hierarchical sub-problems that can be solved with simpler, more manageable computational resources while still achieving statistically significant BER measurements.
Solution Approach 2:
The patent introduces a hierarchical tree dimension to organize the simulation of long bit streams, transforming the linear complexity problem into a hierarchical structure. This dimensional change allows the simulation to scale more efficiently with bit stream length, reducing device complexity while maintaining the statistical significance required for accurate BER measurement.
Data Source
AI summary
Computer-implementable recursive summation algorithms are disclosed that are useful for efficiently performing recursive convolution, such as is often required in Statistical Signal Analysis (SSA) techniques. The disclosed recursive summation algorithms can be more computationally-efficient from both a speed and memory perspective than other recursive convolution techniques known in the prior art, such as the techniques relying on Fast Fourier Transforms (FFTs).