Polyhedron Erasure Code for Multi-Disk Fault Tolerance
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Solution Overview
Problem
Existing erasure coding schemes provide high failure tolerance but are computationally intensive, leading to performance overhead and limitations in handling more than two disk failures while maintaining high I/O performance.
Innovation Solution
Graph-based erasure code models using polyhedrons and bitwise XOR operations for encoding and decoding data, allowing for the distribution of data and parities among different storage media to achieve higher fault tolerance with reduced computational overhead.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional erasure coding schemes (e.g., Reed-Solomon) are used to achieve high failure tolerance, then fault tolerance is improved, but computational complexity increases significantly
Solution Approach 1:
The patent changes the mathematical field parameter from Galois Field (used in Reed-Solomon codes) to Binary Field GF(2). This parameter change simplifies the computational operations from complex Galois Field multiplications to simple bitwise XOR operations, thereby reducing computational complexity while maintaining fault tolerance capabilities through the polyhedron-based erasure code structure
Solution Approach 2:
The patent substitutes the traditional Galois Field arithmetic operations with bitwise XOR operations in Binary Field. This substitution replaces complex mathematical computations with simpler bitwise operations that are more efficiently executable, reducing the computational overhead while preserving the erasure code's ability to tolerate disk failures
2Productivity
If RAID levels are used to provide high I/O performance, then productivity is improved, but failure tolerance is limited to two disks
Solution Approach 1:
The patent segments the data into multiple fragments corresponding to vertices of a polyhedron and distributes them across multiple storage devices. By using the polyhedron structure where each face represents a parity group, the system can tolerate multiple disk failures (beyond RAID's two-disk limit) while maintaining efficient parallel I/O operations through the distributed fragment structure
Solution Approach 2:
The patent transitions from the traditional two-dimensional RAID parity structure to a multi-dimensional polyhedron structure. This dimensional expansion allows the system to incorporate more parity groups and tolerate more disk failures while maintaining I/O performance through the geometric distribution of data fragments across multiple dimensions of the polyhedron
3Volume of stationary object
If the number of storage media is increased to improve capacity, then volume is improved, but the probability of failure increases without corresponding increase in parities
Solution Approach 1:
The patent creates a universal polyhedron-based erasure code structure where each face of the polyhedron represents a parity group that can protect multiple data fragments. This multi-functional structure allows the same parity mechanism to protect against multiple simultaneous failures, enabling the system to scale storage capacity while maintaining reliable protection through the geometric relationships in the polyhedron structure
Data Source
AI summary
Methods based on polyhedron models using computational operations for distributing data and parities among different data storage media. Devices, systems, and methods that split data into data strips, wherein the number of data strips equals the number of vertices of a polyhedron and respective ones of the number of the data strips correspond to respective ones of the number of vertices of the polyhedron; construct a number of parities, wherein the number of parities equals the number of faces of the polyhedron and respective ones of the number of parities correspond to respective ones of the number of parities of the polyhedron, wherein respective ones of the number of parities are constructed by computationally operating the data strips corresponding to vertices respectively associated with a face of the polyhedron corresponding to the respective parity; and distribute subsets of data strips and subsets of parities to subsets of storage media.