Galois Field Matrix Encoding for Faster Erasure Coding
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Solution Overview
Problem
Existing erasure coding implementations in distributed storage systems are slow due to the high number of arithmetic operations required, which are proportional to the size of the data being encoded, leading to unacceptably long processing times.
Innovation Solution
The technique accelerates Galois Field arithmetic by generating a multi-element multiplication matrix from a single-element matrix and using it for encoding data, allowing for efficient encoding and storage in distributed storage systems like Elastic Cloud Storage (ECS), without relying on specific processor instruction sets.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional erasure coding implementations are used, then data protection and redundancy are achieved, but processing time and computational overhead become unacceptably long
Solution Approach 1:
The patent pre-computes multiplication matrices for Galois Field operations and stores them in lookup tables before actual encoding operations. When encoding data, the system retrieves pre-computed matrices from memory rather than performing complex arithmetic operations in real-time, significantly reducing processing time while maintaining data protection integrity
Solution Approach 2:
The patent creates simplified lookup table copies of Galois Field multiplication results that can be quickly accessed during encoding. Instead of performing full arithmetic operations, the system uses these pre-computed copies to accelerate the encoding process, achieving faster processing while preserving the mathematical correctness of erasure coding
2Quantity of substance
If the number of arithmetic operations is increased to handle larger data sizes, then encoding capacity is improved, but processing speed decreases proportionally
Solution Approach 1:
The patent segments the encoding process into distinct phases: data fragmentation into smaller units, separate multiplication operations using pre-computed matrices for each fragment, and final assembly of coded data. This segmentation allows parallel processing of multiple fragments simultaneously, improving overall processing speed while handling larger data volumes
Solution Approach 2:
The patent changes the computational parameters by transitioning from direct arithmetic operations to table-lookup operations. By representing Galois Field multiplications as simple array index operations rather than mathematical computations, the system achieves constant-time operations that do not scale with data size, maintaining processing speed regardless of data volume
Data Source
AI summary
A technique to accelerate Galois Field (GF) arithmetic. The technique, which does not rely on any specific processor instruction set, can be used to accelerate erasure coding within storage systems.