Permutation Code Encoding Using Prime Factor Decomposition
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Solution Overview
Problem
The complexity of indexing and reverse operations in permutation codes for vector quantization leads to high computational costs due to division operations and limited precision in variable framing, restricting the use of non-structured vector quantizers in real-time applications.
Innovation Solution
The method involves representing combinatorial expressions using prime factor power decompositions and pre-recording these decompositions in memory, allowing for efficient calculation of permutation codes by replacing divisions with subtractions and avoiding precision issues through pseudo-floating-point representations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If non-structured vector quantizers are used to achieve high compression performance, then the source distortion bit rate limit is approached, but the computational complexity and storage requirements increase proportionally to n^2 * M
Solution Approach 1:
The patent segments the exhaustive search process by organizing the dictionary into a hierarchical structure with codebooks at multiple levels. Instead of searching all M code vectors directly, the search is divided into stages where coarser codebooks filter candidates and finer codebooks refine the selection, reducing complexity from O(M) to O(log M) or O(sqrt M) depending on the hierarchy depth.
Solution Approach 2:
The patent employs dynamic search strategies where the search depth and precision are adapted based on the input vector characteristics and available computational resources. The hierarchical structure allows dynamic selection of search granularity, enabling real-time operation by adjusting the trade-off between compression performance and computational load.
2Measurement precision
If exhaustive search is performed to find the closest code vector, then the best match is found, but the encoding time increases significantly
Solution Approach 1:
The patent performs preliminary actions by pre-organizing the codebook into hierarchical clusters and computing distance metrics at coarser levels before detailed matching. This preliminary filtering eliminates many candidate code vectors that cannot be optimal matches, so the exhaustive search is performed only on a reduced subset, maintaining accuracy while reducing time.
Solution Approach 2:
The hierarchical structure enables skipping over large portions of the codebook that are guaranteed to be suboptimal. By evaluating coarser representations first, the system can skip entire branches of the search space that cannot contain the best match, rushing through irrelevant candidates while still finding the optimal match in the remaining subset.
3Manufacturing precision
If high-dimensional vectors are used to improve representation quality, then the source encoding performance improves, but the complexity increases exponentially with dimension
Solution Approach 1:
The patent transforms the high-dimensional search problem into a multi-level hierarchical structure where each level operates in a reduced dimensional subspace. Instead of searching the full n-dimensional space directly, the hierarchical codebooks organize code vectors into clusters that can be navigated through multiple lower-dimensional projections, effectively managing complexity while preserving representation quality.
4Quantity of substance
If permutation codes are used to reduce dictionary storage, then memory requirements decrease, but indexing and reverse operations become computationally expensive due to division operations
Solution Approach 1:
The patent replaces the mechanical division operations in permutation code indexing with algebraic computations based on pre-stored factorials and combinatorial tables. Instead of performing actual division which is computationally expensive, the system uses pre-computed factorial values and integer arithmetic operations that are much faster and can be implemented efficiently in hardware or software.
Data Source
AI summary
The invention relates to the encoding/decoding of digital signals, especially using transposition 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 whole numbers.