Permutation Code Indexing via Prime Factor Decomposition
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Solution Overview
Problem
The complexity of indexing and inverse operations in permutation codes for vector quantization leads to high computational costs due to division operations and framing issues, limiting the applicability of permutation codes to low dimensions and bit rates.
Innovation Solution
The method involves pre-recording representations of exponents for prime numbers and decomposing factorial values into powers of prime factors, allowing for the replacement of division calculations with subtraction and simplifying the calculation of combinatorial expressions, thereby reducing the complexity of indexing and decoding operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If permutation codes are used for vector quantization, then coding efficiency is improved, but computational complexity increases due to division operations
Solution Approach 1:
The patent pre-calculates and stores factorial values and their prime factor decompositions in lookup tables before actual coding operations. This preliminary preparation eliminates the need for complex division operations during real-time indexing, as the pre-stored factorials can be directly used in combinatorial calculations through simple multiplication and table lookup operations.
Solution Approach 2:
The patent replaces the mechanical division operation with a combination of multiplication and lookup table access. Instead of performing division to calculate combinatorial expressions, the method uses pre-stored factorial values and their prime factor decompositions, substituting complex arithmetic operations with simpler multiplication and memory access operations.
2Loss of information
If permutation codes are used for vector quantization, then compression performance is improved, but indexing operation complexity increases
Solution Approach 1:
The patent pre-calculates the prime factor decompositions of factorial values and stores them in lookup tables before indexing operations. This preliminary preparation allows the indexing process to use simple multiplication of pre-stored values rather than performing complex combinatorial calculations with divisions, significantly reducing indexing complexity while maintaining compression performance.
Solution Approach 2:
The patent creates and stores copies of factorial values and their prime factor decompositions in lookup tables. These pre-computed copies are then reused during indexing operations, eliminating the need to recalculate complex combinatorial expressions and reducing the computational burden of indexing while preserving the accuracy required for compression performance.
3Measurement precision
If unstructured vector quantizers are used, then vector quantization performance approaches rate-distortion bound, but complexity grows exponentially with dimension
Solution Approach 1:
The patent changes the parameter representation from storing complete factorial values to storing their prime factor decompositions. This parameter transformation allows for more efficient computation of combinatorial expressions, as the decomposed form enables multiplication-based calculations rather than division-based ones, reducing complexity while maintaining the precision needed for high-dimensional vector quantization performance.
Data Source
Figure 1A~1B
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AI summary
The invention relates to the encoding/decoding of digital signals, especially using permutation codes involving a calculation of combinatorial expressions. According to the invention, the combinatorial expressions are represented by prime factor power decompositions, and determined by a preliminary reading of pre-recorded representations of decompositions of selected integers.