Golomb Coding for Variable-Range Numeric Data Compression
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Solution Overview
Problem
Current data compression methods, such as Huffman coding, often perform poorly when dealing with sequences of numerals with flat or skewed probability distributions, leading to inefficient coding and increased bit usage, especially when the range of values is unknown or variable.
Innovation Solution
The use of Golomb coding with a Raw Code approach, where the exponent value is encoded as a variable length code and the residual value is transmitted separately, allowing for efficient compression by treating a sequence of Golomb Codes as a single string and optimizing the transmission of exponent and residual values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Huffman coding is used for data compression, then compression is achieved for data with known probability distributions, but performance deteriorates when dealing with sequences of numerals with flat or skewed probability distributions or unknown value ranges
Solution Approach 1:
The patent applies parameter changes by transforming the data representation from direct numeral encoding to exponent-residual decomposition. By changing the parameterization of how numbers are represented (using exponent E and residual R instead of direct values), the coding scheme becomes adaptable to flat or skewed probability distributions without requiring prior knowledge of the distribution characteristics.
Solution Approach 2:
The patent segments the encoding process into two distinct parts: exponent encoding and residual encoding. This segmentation allows each component to be optimized independently - the exponent captures the magnitude information efficiently while the residual handles the variation within that magnitude, improving overall compression for diverse probability distributions.
2Productivity
If traditional compression methods are used, then coding is performed on individual values, but compression efficiency is limited when considering the sequence as a whole
Solution Approach 1:
The patent merges the encoding of exponents and residuals into a unified Golomb coding framework. By combining these elements into a single coding pass rather than treating them separately, the method achieves better compression efficiency while maintaining manageable complexity through systematic organization of the encoding steps.
3Quantity of substance
If fixed-length coding is used, then transmission is simple, but more bits are required to transmit data sequences with variable exponents and residuals
Solution Approach 1:
The patent introduces dynamic-length coding through variable-length exponent and residual representations. Instead of fixed-length codes, the encoding adapts to the actual values being transmitted, using fewer bits for common patterns and more bits only when necessary, thus reducing the average number of bits required while maintaining transmission simplicity through systematic variable-length structures.
Data Source
AI summary
Briefly, in accordance with one embodiment, a method of data compression is disclosed.