Arithmetic Coding Using Multi-Time-Scale Probability Mapping
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Solution Overview
Problem
Arithmetic encoding and decoding require accurate determination of interval size information to achieve optimal coding efficiency, which is challenging due to the need for balancing computational efficiency and reliability in adapting to varying probabilities of symbols over time.
Innovation Solution
The use of a lookup table-based approach to derive interval size information by mapping combined state variable values, which represent statistics of previously encoded or decoded symbols with different adaptation time constants, allows for efficient and reliable determination of interval sizes through weighted summation and scaling operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If multiple state variable values with different adaptation time constants are used to derive interval size information, then the adaptability to changing symbol probabilities is improved, but the computational complexity increases
Solution Approach 1:
The patent combines multiple state variable values (s1, s2, ..., sN) with different adaptation time constants into a single combined state variable value Sk through weighted summation: Sk = Σ(wi * si), where wi are weighting factors. This combined value is then used to derive interval size information, merging multiple adaptive perspectives into one unified parameter that captures statistics on different time scales while simplifying subsequent processing.
Solution Approach 2:
The patent introduces a lookup table as an intermediary component that maps the combined state variable value Sk to interval size information. This lookup table pre-stores the relationship between state variables and interval sizes, allowing the system to quickly retrieve appropriate interval size values without performing complex real-time calculations, thus reducing computational complexity while maintaining adaptability.
2Productivity
If a lookup table is used to map state variable values to interval size information, then the determination of interval sizes becomes more efficient, but the memory requirements increase
Solution Approach 1:
The patent transforms the continuous state variable Sk into a discrete index by applying a floor operation: index = floor(Sk). This discretization converts the continuous parameter space into discrete bins, allowing the lookup table to store values only at these discrete points. This parameter transformation reduces the effective size of the lookup table while maintaining the ability to represent the full range of state variable values, thus reducing memory requirements.
Solution Approach 2:
The patent uses a relatively small lookup table that can be easily stored in memory, accepting some approximation in exchange for reduced memory usage. The lookup table stores pre-computed interval size information for discrete state variable values, and the system accepts that values between discrete points will be approximated to the nearest stored value. This trade-off provides efficient encoding with minimal memory overhead.
Data Source
AI summary
An arithmetic encoder for encoding a plurality of symbols having symbol values is configured to derive an interval size information for an arithmetic encoding of one or more symbol values to be encoded based on a plurality of state variable values representing statistics of a plurality of previously encoded symbol values with different adaptation time constants. The arithmetic encoder is configured to map a first state variable value, or a scaled and/or rounded version thereof, using a lookup-table and to map a second state variable value, or a scaled and/or rounded version thereof using the lookup-table, in order to obtain the interval size information describing an interval size for the arithmetic encoding of one or more symbols to be encoded. Further arithmetic encoders, arithmetic decoders, video encoders, video decoder, methods for encoding, methods for decoding and computer programs are also disclosed which are based on the same concept and on other concepts.