Combinatorial Signal Coding With Log-Domain Complexity Reduction
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Solution Overview
Problem
Existing Factorial Pulse Coding methods face complexity and precision issues when dealing with large vector lengths and unit pulse counts, particularly in mobile handheld devices, due to high computational and memory requirements for combinatorial calculations.
Innovation Solution
A low-complexity approach is introduced by using approximations of factorial combinations, such as logarithmic transformations and reduced precision calculations, to generate a suitable codeword that ensures unique decodability without the need for extensive multi-precision operations, utilizing functions P′(i), Q′(d), and R′(k) to reduce computational burden and memory usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If direct implementation of combinatorial function F(n,d) is used for large n and m, then coding precision is maintained, but computational complexity and memory requirements become unreasonably high
Solution Approach 1:
The patent segments the computation of F(n,d) into manageable parts by using the recurrence relation F(n,d) = F(n-1,d-1) + F(n-1,d), breaking down the large combinatorial calculation into smaller incremental steps that can be computed with limited precision arithmetic
Solution Approach 2:
The patent changes the parameter representation by working with logarithms of combinatorial values (log F(n,d)) rather than direct values, transforming the computation into addition and multiplication operations that are less demanding on computational resources while maintaining sufficient precision
2Loss of time
If lookup tables for all factorial combinations are pre-computed and stored, then computation time is reduced, but memory storage requirements become unreasonably large
Solution Approach 1:
Instead of storing complete F(n,d) values, the patent stores segmented logarithmic components that can be combined through addition, dramatically reducing storage requirements while enabling quick computation through simple arithmetic operations
Solution Approach 2:
The patent pre-computes and stores only the necessary logarithmic components of combinatorial values in lookup tables, performing preliminary preparation of data in a compressed form that can be rapidly assembled during actual coding operations
3Measurement precision
If multi-precision multiply/divide routines are employed to maintain precision, then coding accuracy is preserved, but the number of MAC operations and computational resources increase significantly
Solution Approach 1:
The patent substitutes complex multi-precision arithmetic operations with simpler operations in the logarithmic domain, replacing expensive multiply/divide routines with addition and exponentiation that can be performed with standard precision arithmetic
Solution Approach 2:
By transforming the problem into the logarithmic domain, the patent changes the mathematical parameters from direct combinatorial values to their logarithms, allowing computation to proceed with standard precision while maintaining the accuracy needed for unique decodability
Data Source
AI summary
To reduce the complexity of the encoding/decoding of pulse positions and/or pulse magnitudes associated with complex combinatorial computations, a method and structure for encoding and decoding of pulse position and/or pulse magnitudes requires fewer computations of these combinatorial functions. Adaptive switching between coding or encoding is performed in accordance with the estimated density of the plurality of occupied positions.