Commutative Erasure Coding via Galois Field Bit-Matrix Operations
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Solution Overview
Problem
Conventional data storage techniques in geographically diverse systems face inefficiencies in storage space conservation and resource utilization, particularly when employing erasure coding for data redundancy, as they often result in increased storage space consumption and high computational resource demands.
Innovation Solution
The implementation of commutative erasure coding using a distribution matrix expanded according to a Galois Field (GF), allowing bit-matrix operations via AND operations, which reduces the number of encoding and decoding operations and conserves storage space while maintaining data redundancy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional erasure coding is used for data redundancy in geographically diverse storage systems, then data protection is improved, but storage space consumption increases and computational resource demands increase
Solution Approach 1:
The patent changes the mathematical parameters of erasure coding by using expanded distribution matrices based on Galois Field properties, which transforms the encoding operations into commutative bit-matrix operations. This parameter change enables more efficient computation and reduced storage requirements while maintaining the same level of data protection through fewer redundant copies
Solution Approach 2:
The patent substitutes conventional computational mechanics with optimized bit-matrix operations based on Galois Field expansion. By replacing traditional erasure coding mechanics with this mathematical approach, the system achieves the same data protection function with reduced computational resource demands and storage space consumption
2Reliability
If conventional erasure coding is used for data redundancy in geographically diverse storage systems, then data protection is improved, but computational resource demands increase
Solution Approach 1:
The patent changes the computational parameters by transforming erasure coding operations into commutative bit-matrix operations using expanded distribution matrices. This parameter transformation reduces the computational complexity and resource demands while maintaining data protection integrity across geographically diverse storage systems
Solution Approach 2:
The patent performs preliminary expansion of the distribution matrix based on Galois Field properties before the actual encoding operation. This preliminary action prepares the computational structure in advance, enabling more efficient encoding and decoding operations that reduce overall computational resource demands during data protection operations
3Quantity of substance
If fewer redundant copies are used for data recovery, then storage space is conserved, but data protection capability is reduced
Solution Approach 1:
The patent changes the mathematical parameters of redundancy by using expanded distribution matrices that enable more efficient error correction codes. This allows the system to achieve the same data protection capability with fewer redundant copies, thereby conserving storage space while maintaining reliability
Solution Approach 2:
The patent creates a composite approach by combining expanded distribution matrices with bit-matrix operations based on Galois Field properties. This composite mathematical structure enables more efficient use of redundant data, allowing the system to maintain strong data protection capability while using fewer redundant copies and conserving storage space
Data Source
AI summary
Commutative coding in a geographically diverse data storage system is disclosed. Commutative coding can achieve a same result as more conventional hierarchical erasure coding of data, but can be more efficient. Commutative coding can employ Galois Field (GF) based bit-matrix operations. The bit-matrix operations can employ a reduced GF order in associated with expanding elements of input matrixes. A reduced GF order can perform matrix operations at a lower complexity, e.g., employing AND operations for a GF(2) in contrast to XOR operations for a GF(2w), where w=4, 8, 16, etc. In an aspect, commutative coding can comprise generating a second-tier coding fragment based on applying a second erasure coding scheme, via bit-matrix operations, to a first-tier encoded fragment, wherein the first-tier encoded fragment is based on an input data fragment and a first erasure coding scheme.