Minimum repair bandwidth LDPC codes for distributed storage systems

Abstract

In distributed storage systems (DSS), an optimal code design must meet the requirements of efficient local data regeneration in addition to reliable data retention. Recently, lowdensity parity-check (LDPC) codes have been proposed as a promising candidate that can secure high data rates as well as low repair bandwidth while maintaining low complexity in data reconstruction. The main objective of this study is to optimize the repair bandwidth characteristics of LDPC code families for a DSS application while meeting the data reliability requirements. First, a data access scenario in which nodes contact other available nodes randomly to download data is examined. Later, a minimum-bandwidth protocol is considered in which nodes make their selections based on the degree numbers of check nodes. Through formulating optimization problems for both protocols, a fundamental trade-off between the decoding threshold and the repair bandwidth is established for a given code rate. Finally, conclusions are confirmed by numerical results showing that irregular constructions have a large potential for establishing optimized LDPC code families for DSS applications.