Received Signal Error Correction Using Monomial Trace Coefficients
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Solution Overview
Problem
Existing error correction systems for received signals are complex and energy-intensive due to the need for multiple non-zero terms in trace polynomials, leading to increased hardware complexity and energy consumption.
Innovation Solution
A method and system that utilize monomial trace coefficients by determining a target degree, selecting a primitive polynomial with specific criteria, generating syndromes, and calculating monomial trace coefficients to generate an error correction value for correcting errors at a unit position of a received signal.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If trace mapping values are computed via trace polynomial with multiple non-zero terms, then error correction capability is achieved, but hardware complexity increases
Solution Approach 1:
The patent extracts only the necessary monomial trace coefficient from the trace polynomial computation. Instead of computing all trace mapping values with multiple non-zero terms, the invention identifies and uses only the essential monomial coefficient, thereby reducing hardware complexity while maintaining error correction capability.
Solution Approach 2:
The patent replaces complex, multi-term trace polynomial computation with a simpler, single monomial trace coefficient calculation. This substitution uses a cheaper computational approach that achieves the same error correction function with reduced hardware resources.
2Reliability
If trace mapping values are computed via trace polynomial with multiple non-zero terms, then error correction capability is achieved, but energy consumption increases
Solution Approach 1:
The patent extracts only the necessary monomial trace coefficient from the trace polynomial computation. Instead of computing all trace mapping values with multiple non-zero terms, the invention identifies and uses only the essential monomial coefficient, thereby reducing energy consumption while maintaining error correction capability.
Solution Approach 2:
The patent performs only the partial computation necessary to obtain the monomial trace coefficient, rather than fully computing all trace mapping values. This partial action approach reduces energy consumption by avoiding unnecessary computational steps while still achieving the required error correction capability.
Data Source
AI summary
A method for correcting an error of a received signal is provided. The method includes: determining a target degree based upon a length of the received signal; obtaining plural primitive polynomials each having a degree equal to the target degree; selecting one of the primitive polynomials as a target polynomial; defining plural syndromes according to the received signal; generating a group of product values based on the syndromes; obtaining plural coefficient polynomials based on the product values; obtaining monomial trace coefficients based on the coefficient polynomials; generating an error correction value based on the monomial trace coefficients; and correcting the error based on the error correction value.