Self-Similar Lookup Table Compression for Hardware Cost Reduction
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Solution Overview
Problem
Existing methods for implementing lookup tables in hardware suffer from high hardware costs due to the exponential growth in table size at higher resolutions, and existing compression techniques either sacrifice accuracy or fail to efficiently utilize self-similarities for significant size reductions.
Innovation Solution
A method utilizing self-similarity, multilevel compression, and higher-bit compression to decompose lookup tables into smaller sub-tables, identify unique sub-tables through arithmetic right shift operations, and store these sub-tables efficiently, reducing memory requirements without sacrificing accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If lookup tables are used in hardware to store arrays of constant values for function evaluation, then function evaluation can be implemented efficiently, but hardware costs increase due to exponential growth in table size at higher resolutions
Solution Approach 1:
The lookup table is divided into multiple sub-tables based on self-similarity analysis. Each sub-table stores a portion of the original table data, and the relationship between sub-tables is captured through a compact representation (e.g., offset tables or difference tables). This segmentation allows the hardware to use multiple smaller tables instead of one large table, reducing overall hardware resource consumption while maintaining the ability to achieve high-resolution function evaluation.
Solution Approach 2:
The compression method embeds multiple levels of table representations within each other. The original lookup table is decomposed into sub-tables, which are further decomposed into even smaller sub-sub-tables, creating a nested structure. This nested arrangement allows the hardware to access different levels of detail as needed, achieving high resolution when required while using minimal hardware resources for the compressed structure.
2Area of stationary object
If existing compression techniques are applied to lookup tables, then table size is reduced, but accuracy is sacrificed
Solution Approach 1:
The compression method uses self-similarity analysis to identify patterns within the lookup table itself. By analyzing the relationships between different portions of the table and exploiting these internal patterns, the method creates a compressed representation that can be efficiently decoded to recover the original table data with full accuracy. This self-service approach ensures that no external approximation or lossy compression is needed.
Solution Approach 2:
Instead of directly storing the original lookup table, the method creates copies of portions of the table (sub-tables) and stores relationships between these copies. The compressed structure uses these copies and their relationships to reconstruct the original table exactly when needed, maintaining full accuracy while reducing storage requirements. The copying process preserves all necessary information through the self-similar relationships.
3Area of stationary object
If lookup tables are compressed to reduce hardware costs, then implementation hardware costs decrease, but decoding complexity increases
Solution Approach 1:
The compression method performs preliminary analysis of the lookup table to identify self-similar patterns and establish the compressed structure before the actual function evaluation begins. The sub-tables and their relationships are pre-computed and stored in a structured format that simplifies the decoding process. During function evaluation, the hardware simply needs to access the pre-organized compressed structure according to predetermined rules, avoiding complex real-time decoding operations.
Data Source
AI summary
A method, and system, for lossless compression of lookup tables, which uses self-similarities, multilevel compression, and higher-bit compression, and in some claims decomposition, to maximize table size savings. The techniques of this disclosure also use addition and arithmetic right shift with several small lookup tables to retrieve original data during the decoding phase. While lookup tables can hold any arbitrary data, most of the claims in this disclosure will focus on applications of lookup tables in function evaluation. Lookup tables may be used either directly for function evaluation or as parts of other table-based methods. In either case, table compression methods can be used to shrink such tables to reduce their implementation hardware costs.