Numerical Erasure Coding for High-Throughput Fault Tolerance

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Solution Overview

Problem

Existing erasure coding systems, relying on Galois field arithmetic, are computationally complex and slow, limiting their deployment to archival data due to reduced throughput, making them unsuitable for high-performance data streams.

Innovation Solution

Implementing numerical operation-based erasure coding that determines the bit-width of the computing system, converts data elements into numerical representations, and uses matrix operations to generate and decode coded fragments, leveraging simple numerical operations like XOR and bit-shifting for faster processing.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If Galois field arithmetic is used for erasure coding, then data redundancy and fault tolerance are achieved, but computational complexity increases and processing speed decreases

Engineering Contradiction:

Improvedata redundancy and fault toleranceVSAvoidcomputational complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent changes the mathematical field parameter from Galois field to finite field, enabling the use of simpler numerical operations while maintaining erasure coding functionality. This parameter change allows standard arithmetic operations to replace complex Galois field arithmetic, reducing computational complexity while preserving data redundancy and fault tolerance capabilities

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent substitutes complex Galois field arithmetic operations with simpler numerical operations including addition, subtraction, multiplication, division, and bit-shifting. This substitution replaces the mechanical complexity of Galois field computations with more efficient numerical calculations that can be performed using standard computing operations

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Reliability

If Galois field arithmetic is used for erasure coding, then data redundancy is provided, but throughput of storage systems is reduced

Engineering Contradiction:

Improvedata redundancyVSAvoidthroughput

Core Design Contradiction:

ReliabilityVSProductivity

Solution Approach 1:

The patent changes the mathematical foundation from Galois field to finite field, enabling faster numerical operations. This parameter change allows the system to perform erasure coding operations with improved throughput by using standard arithmetic operations that are more efficiently implemented in hardware and software compared to Galois field arithmetic

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent substitutes Galois field arithmetic with numerical operations that can be executed more quickly using standard CPU instructions. This substitution includes using addition, subtraction, multiplication, division, and bit-shifting operations that have optimized hardware support, thereby increasing storage system throughput while maintaining data redundancy

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

3Reliability

If traditional replication is used to ensure high availability, then data safety is improved, but storage efficiency decreases

Engineering Contradiction:

Improvedata safety and high availabilityVSAvoidstorage capacity

Core Design Contradiction:

ReliabilityVSQuantity of substance

Solution Approach 1:

The patent changes the mathematical approach from traditional replication to finite field-based erasure coding. This parameter change enables the system to provide the same level of data safety and high availability as replication but with improved storage efficiency, as erasure coding can protect data with fewer redundant copies compared to traditional replication methods

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS10277253B2High performance data redundancy and fault tolerance

Publication Date: 2019.04.30 PHAZRIO INC

AI summary

One embodiment provides a system that facilitates numerical operation-based erasure coding. During operation, the system determines the bit-width of processing capability of the computing system. The system then determines, based on the bit-width, a number of bits for representing a respective data element from a data stream and a number of data elements based on a number of a dimension of a generator matrix of erasure encoding. The system then obtains the number of data elements from the data stream and converts a respective obtained data element to a corresponding numerical representation. Here, a respective obtained data element is represented by the determined number of bits. The system then generates a code word, which comprises a plurality of coded fragments, of erasure encoding from the numerical representations based on the generator matrix of the erasure encoding.