Hyper-Pyramid Integer Coding for Compact Decoding and Indexing
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Solution Overview
Problem
Existing coding methods face challenges in efficiently encoding and decoding lists of integers, particularly in terms of performance loss during decoding phases and exponential growth in code size, which limits their practical application in data compression, transmission, and indexing.
Innovation Solution
A method and system for encoding information using a hyper-pyramid structure, where a list of integers is indexed within a hyper-pyramid with a specific dimension, allowing for efficient encoding and decoding without exponential growth in code size, and enabling bijective correspondence between the encoded integer and the original list.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If traditional coding methods are used to encode lists of integers, then the encoding can be performed, but the code size grows exponentially and decoding performance is lost
Solution Approach 1:
The patent transforms the encoding problem from traditional linear coding into a geometric framework using hyper-pyramids in n-dimensional space. By representing integer lists as points in n-dimensional space and using hyper-pyramid structures to organize these points, the system achieves polynomial rather than exponential code size growth while maintaining efficient decoding through geometric relationships.
Solution Approach 2:
The patent changes the fundamental parameters of the coding system by introducing dimensionality (n-1 for lists of n integers) and using combinatorial geometry principles. This parameter transformation allows the system to achieve both compact code representation and efficient decoding by leveraging the structural properties of hyper-pyramids and their vertices.
2Ease of operation
If coding methods preserve indexing for ordering sequences, then the ordering function is improved, but the code complexity increases
Solution Approach 1:
The hyper-pyramid based coding system serves multiple functions simultaneously: it encodes integer lists, preserves indexing for ordering, enables routing in communication networks, and provides a framework for parallel algorithms. The geometric structure inherently supports ordering through vertex indexing while maintaining manageable complexity through the regularity of hyper-pyramid geometry.
Data Source
AI summary
A method and an apparatus are described for coding information, the method comprising obtaining a list of integers to be encoded; determining a hyper-pyramid having a dimension adapted to encode the list of integers, the hyper-pyramid having a plurality of vertices whose number is determined by the degree of the hyper-pyramid, which is equal to the sum of the integers of the list of integers and by the dimension of the hyper-pyramid which is equal to the number of integers of the list of integers minus one; indexing the list of integers in the hyper-pyramid using an indexing system; and providing an indication of the indexing of the list of integers in the hyper-pyramid.