FEC and CRC Decoder Polynomial Selection for Low-Complexity ECC
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing semiconductor memory devices face challenges in correcting errors due to increased operating speeds and data volumes, necessitating efficient error correction codes that reduce calculation complexity while maintaining error correction capabilities.
Innovation Solution
An error correction code circuit utilizing a Galois field GF(2m) with optimized generator polynomials for both forward error correction (FEC) and cyclic redundancy check (CRC) decoders, reducing calculation complexity by selecting primitive polynomials that minimize logic gate counts and optimizing encoding/decoding operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional error correction codes are used to correct errors in semiconductor memory devices, then error correction capability is maintained, but calculation complexity increases and manufacturing precision deteriorates
Solution Approach 1:
The patent changes the parameter of primitive polynomial selection by choosing specific primitive polynomials (e.g., x^8 + x^4 + x^3 + x + 1 for FEC and x^8 + x^7 + x^2 + x + 1 for CRC) that optimize the balance between error correction capability and calculation complexity. This parameter optimization reduces the number of logic gates required while maintaining reliable error correction for modern high-capacity memory devices.
2Reliability
If advanced error correction codes are used to handle increased data volumes, then error correction capability is improved, but manufacturing precision deteriorates due to increased device complexity
Solution Approach 1:
The patent optimizes polynomial parameters to reduce the number of logic gates required for error correction operations. By selecting specific primitive polynomials that minimize gate count while maintaining correction capability for large data volumes, the patent enables manufacturing with standard precision levels even for advanced memory capacities.
Solution Approach 2:
The patent segments the error correction function into separate FEC and CRC decoder modules, each with dedicated optimized polynomial circuits. This segmentation allows independent optimization of each module's complexity while maintaining overall error correction capability for increased data volumes.
3Reliability
If complex generator polynomials are used for both FEC and CRC decoders, then error detection and correction capability is improved, but device complexity increases
Solution Approach 1:
The patent changes the polynomial parameters by selecting specific primitive polynomials for FEC (e.g., x^8 + x^4 + x^3 + x + 1) and CRC (e.g., x^8 + x^7 + x^2 + x + 1) that provide adequate error detection and correction capability with minimized device complexity. These parameter choices reduce logic gate requirements while maintaining reliability for modern storage devices.
Solution Approach 2:
The patent segments the error correction system into distinct FEC and CRC decoder circuits, each using optimized polynomials tailored to their specific functions. This segmentation allows each module to use simplified polynomials appropriate for its purpose rather than requiring both to handle the full complexity of general error correction.
Data Source
AI summary
An error correction code circuit, an operating method thereof, and a storage device are disclosed. The error correction code circuit includes a forward error correction (FEC) decoder configured to correct an error of a codeword based on a first generator polynomial with respect to a first primitive polynomial having a calculation complexity among primitive polynomials having a leading term m on a Galois field GF(2m), and a cyclic redundancy check (CRC) decoder configured to detect an error of an error-corrected CRC codeword based on a second generator polynomial with respect to a second primitive polynomial different from the first primitive polynomial. The respective values of the coefficients of the second generator polynomial are symmetrical to each other based on the intermediate-order term.