Analysis and Extension of Pyramid Codes Based on the Distributed Storage System

With the development of the Internet, many interconnections between goods have resulted in a massive amount of information and data. More efficient and less costly coding methods are needed to store and process this data. Reed-Solomon code has been widely favored by many users in cloud computing and distributed storage as a kind of erasure code. The Pyramid code reduces repair costs as an upgrade to the Reed-Solomon code. It simplifies computation at the cost of adding redundancy. Taking (16,12) Pyramid code as an example, although it can repair three or fewer errors, it cannot cover all cases of four errors. This paper aims to thoroughly analyze Pyramid Code by comparing it to (15,12) RS code and put an idea of adding overlapping parts into finding some solutions to cover more 4-error cases based on the idea of improving formulas of Parity3 and Parity4 by increasing overlapping part in (16,12) Pyramid code. Then this paper details the trade-off between the recovery rate of different solutions under a 4-error case and repair cost for single or double disk failure to find a better way to solve the problem.