Combinatorial Signal Coding Using Low-Precision Factorial Estimates
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Solution Overview
Problem
Existing methods for Factorial Pulse Coding of vectors, such as those used in speech, audio, and image processing, face significant complexity issues when dealing with large values of vector length and unit pulses, particularly in mobile handheld devices, due to high computational and memory requirements for calculating factorial combinations.
Innovation Solution
A method and apparatus that utilize low-resolution approximations of factorial combinations, denoted as F′(n, d), which are sufficient to generate valid codewords, reducing computational complexity by replacing multi-precision operations with low-precision additions and subtractions, and using small amounts of table memory, while ensuring the resulting codewords are uniquely decodable.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If exact factorial combinations F(n,d) are calculated using prior art methods, then coding precision is maintained, but computational complexity and memory requirements become unreasonably high for large n and m values
Solution Approach 1:
The patent uses low-precision approximations F'(n,d) instead of exact factorial combinations, sacrificing some precision for dramatically reduced computational complexity. The approximation uses simple lookup tables with pre-computed values rather than calculating full factorial combinations, making the system feasible for mobile devices.
Solution Approach 2:
The patent changes the precision parameter of the combinatorial calculation from high precision (exact F(n,d)) to low precision (approximation F'(n,d)). This parameter change allows using simpler data types and fewer computational resources while maintaining sufficient coding performance for practical applications.
2Loss of time
If lookup tables for all factorial combinations are pre-computed and stored, then computation time is reduced, but memory requirements become unreasonably large for large n and m values
Solution Approach 1:
The patent extracts only the essential information needed for approximation from the full factorial combination calculations. Instead of storing complete F(n,d) values, it stores simplified approximation data in lookup tables that capture the dominant trends while using minimal memory.
Solution Approach 2:
The patent segments the combinatorial calculation into manageable parts using approximation formulas that break down F(n,d) into components that can be pre-computed and stored efficiently. This allows creating compact lookup tables that cover the required range without storing every possible combination.
3Measurement precision
If multi-precision multiply/divide routines are used to calculate F(n,d), then calculation accuracy is maintained, but the number of MAC operations and computational resources required increase significantly
Solution Approach 1:
The patent replaces expensive multi-precision arithmetic operations with cheaper low-precision approximations using lookup tables and simple arithmetic. This substitution maintains sufficient accuracy for coding applications while dramatically improving computational efficiency for mobile device implementation.
Data Source
AI summary
The invention utilizes low complexity estimates of complex functions to perform combinatorial coding of signal vectors. The invention disregards the accuracy of such functions as long as certain sufficient properties are maintained. The invention in turn may reduce computational complexity of certain coding and decoding operations by two orders of magnitude or more for a given signal vector input.