generalizing RDP Codes Using the combinatorial Method

Summary

This paper presents a pdhlatin, which is a 2 fault tolerant level code based on the Liehamilton Latin square (chis-column Hamiltonian Latin squares) structure. By proving that it is the MDS code. In this paper, a new 2 fault tolerant hybrid coding-pimlatin based on Chis is proposed. Both of these codes have good extensibility and structural diversity. At the same time, this paper also discusses the coding reduction technology, as well as its parameter extensibility, structural variability and reliability improvement. Based on the idea of vertical reduction, this paper presents a method of constructing 2 fault-tolerant array code by using non-Hamilton Latin side.

Brief introduction

The increase in disk capacity and the increase in the size of the storage system lead to multiple failures. Therefore, multiple fault-tolerant erasure codes become popular, but the current multi-fault erasure code has some inherent limitations. Plank on Fast05 Tutorial a detailed introduction to the erasure codes of the storage system. Erasure code is a coding fault-tolerant mechanism. It will n The number of data disks encoded into m And can be fault-tolerant with arbitrary t Disk, but there is not a single n , m , t > 1 The best coding techniques in the case of consistent recognition.

Well-known multi-fault coding technology is mainly divided into three categories: Reed-solomon code, binary linear code and array code.
1. RS code is the only one applicable to any n , m (= t ) MDS code. This means optimal storage efficiency and update efficiency. However, because it uses Galois field for codec operations (although some optimization methods are proposed), computational complexity is a serious problem.
2. Binary linear code is an XOR-based encoding, which has better computational complexity, but has low storage efficiency. Figure 1 shows a 2-dimensional linear code in which the data unit < Span class= "Mi" id= "mathjax-span-9225" style= "font-family:mathjax_math-italic;" >d i j Participated in two check blocks at the same time P i And < Span class= "Mi" id= "mathjax-span-9238" style= "font-family:mathjax_math-italic;" >q i Span style= "Display:inline-block; width:0px; Height:2.456em; " > The calculation. This example illustrates the core point of the linear code: assigning data units to multiple validation groups, which means that a single data unit participates in multiple groups, guaranteeing multiple fault-tolerant features.
3. The array code organizes the data or validation units into an array. EvenOdd is the first MDS array code, and other subsequent array codes like X-code, RDP, Star-code, and so on, are similar to it.

generalizing RDP Codes Using the combinatorial Method