Combinatorial Signal Coding with Piecewise Function Approximation
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Solution Overview
Problem
Existing digital communication systems face challenges in managing computational complexity and memory requirements, particularly in mobile devices, when using combinatorial coding methods for encoding and decoding vectors, especially with larger vector lengths and pulse counts.
Innovation Solution
The implementation of a combinatorial function generator that uses a piecewise approximation of combinatorial functions based on a linear combination of basis functions to reduce the computational burden, allowing for efficient encoding and decoding of signals by generating a code word or portion of a code word, which is then used to form packets for transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If exact combinatorial functions are used for encoding and decoding vectors, then coding precision is improved, but computational complexity and memory requirements increase significantly
Solution Approach 1:
The patent segments the combinatorial function calculation into multiple stages: pre-computing factorials and their inverses during system initialization, storing them in lookup tables, and then using these pre-computed values during runtime encoding and decoding operations. This segmentation separates the computationally intensive parts from the runtime operations, reducing real-time computational complexity while maintaining coding precision.
Solution Approach 2:
The patent performs preliminary computation of combinatorial values (factorials and their inverses) during system initialization or offline processing, storing results in lookup tables. This preliminary action eliminates the need for complex real-time combinatorial calculations during encoding and decoding, significantly reducing runtime computational complexity while preserving exact coding precision through stored values.
2Measurement precision
If exact combinatorial functions are used for encoding and decoding vectors, then coding precision is improved, but memory requirements increase significantly
Solution Approach 1:
The patent segments memory usage into two parts: a compact lookup table storing pre-computed factorial and inverse factorial values during initialization, and minimal runtime memory for storing the vector and code word. This segmentation reduces overall memory requirements compared to storing entire combinatorial function tables, while maintaining coding precision through the compact pre-computed values.
Solution Approach 2:
The patent performs preliminary computation and storage of combinatorial values in compact lookup tables during system initialization. This preliminary action reduces runtime memory requirements by eliminating the need for large combinatorial function tables during actual encoding and decoding operations, while preserving coding precision through the pre-stored exact values.
3Productivity
If combinatorial coding is implemented in resource-constrained devices, then bandwidth utilization is improved, but device complexity increases
Solution Approach 1:
The patent segments the combinatorial coding implementation into an initialization phase that pre-computes and stores factorial values, and a runtime phase that uses these pre-computed values for efficient encoding and decoding. This segmentation allows resource-constrained devices to achieve improved bandwidth utilization through efficient combinatorial coding while reducing device complexity by eliminating complex real-time combinatorial calculations.
Solution Approach 2:
The patent performs preliminary computation of combinatorial values during system initialization, storing results in compact lookup tables. This preliminary action enables resource-constrained devices to implement combinatorial coding with improved bandwidth utilization while minimizing device complexity, as the computationally intensive parts are completed once during initialization rather than repeatedly during operation.
Data Source
AI summary
A method and apparatus are for performing one of encoding and decoding a code word that is used to communicate a portion of a signal. For encoding, at least a portion of a code word is encoded from a signal based value using an approximation of a combinatorial function, wherein the signal based value represents one or more aspects of a signal. For decoding, at least a portion of a code word is decoded to a signal based value using an approximation of a combinatorial function, wherein the signal based value represents one or more aspects of a signal. The approximation of the combinatorial function is based on a linear combination of a set of basis functions.