CDF Approximation With Piecewise Quadratics for Entropy Coding
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Solution Overview
Problem
Current video compression technologies, such as HEVC, VVC, and EVC, separately optimize transformation, quantization, and entropy coding, which can be improved for more efficient encoding and decoding processes, especially with the integration of neural networks for end-to-end optimization.
Innovation Solution
The use of a cumulative distribution function (CDF) based on a second-order polynomial for entropy encoding and decoding, allowing for efficient parameter storage and adaptation across different platforms, with arithmetic encoding and decoding methods, and the application of look-up tables for parameter storage in fixed-point representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a CDF is obtained using a second-order polynomial approximation for entropy encoding, then the reliability and reproducibility of the encoding process is improved, but the computational complexity increases
Solution Approach 1:
The CDF approximation is divided into multiple intervals, with each interval having its own second-order polynomial parameters. This segmentation allows the complex CDF calculation to be broken down into simpler, manageable pieces that can be efficiently computed and stored in look-up tables, resolving the contradiction between reliability and computational complexity.
Solution Approach 2:
The CDF parameters are pre-calculated and stored in look-up tables before the actual encoding process. This preliminary action eliminates the need for complex real-time CDF calculations during encoding, thereby maintaining high reliability through accurate pre-computed values while significantly reducing computational complexity during the actual encoding operation.
2Adaptability or versatility
If look-up tables are used for parameter storage in fixed-point representation, then the adaptability across different platforms is improved, but the memory requirements increase
Solution Approach 1:
The CDF parameters are represented in fixed-point format rather than floating-point format. This parameter change ensures consistent representation across different hardware and software platforms without requiring platform-specific floating-point implementations, thereby improving adaptability. The fixed-point representation also reduces memory requirements compared to full-precision floating-point storage.
3Manufacturing precision
If second-order polynomial parameters are used to approximate the CDF, then the manufacturing precision of the approximation is improved, but the device complexity increases
Solution Approach 1:
The approximation is divided into multiple intervals, each with its own simplified second-order polynomial parameters. This segmentation maintains high approximation precision within each interval while reducing the overall complexity by breaking down the global approximation problem into smaller, more manageable local problems.
Solution Approach 2:
Instead of using a single complex high-precision CDF calculation that would require sophisticated computational resources, the patent uses simple second-order polynomial parameters that can be easily stored and quickly applied. These simple parameters act as disposable approximations that provide sufficient precision for practical purposes while being computationally inexpensive.
Data Source
AI summary
Methods and apparatuses are provided to approximate a cumulative distribution function (CDF) interval-wise with second order polynomials, while posing constraints on the polynomials within the intervals and/or on the boundary between the intervals. In this manner, a CDF approximation is obtained, which may be used in a variety of applications including entropy encoding and decoding of any source data. The constraints correspond to the characteristics of the CDF to be approximated.