LDPC Code Design for Distributed Storage: Balancing Repair Bandwidth, Reliability, and Storage Overhead

Abstract

Distributed storage systems suffer from significant repair traffic generated due to frequent storage node failures. This paper shows that properly designed low-density parity-check (LDPC) codes can substantially reduce the amount of required block downloads for repair thanks to the sparse nature of their factor graph representation. In particular, with a careful construction of the factor graph, both low repair-bandwidth and high reliability can be achieved for a given code rate. First, a formula for the average repair bandwidth of LDPC codes is developed. This formula is then used to establish that the minimum repair bandwidth can be achieved by forcing a regular check node degree in the factor graph.Moreover, it is shown that given a fixed code rate, the variable node degree should also be regular to yield minimum repair bandwidth, under some reasonable minimum variable node degree constraint.It is also shown that for a given repair-bandwidth requirement, LDPC codes can yield substantially higher reliability than currently utilized Reed-Solomon (RS) codes. Our reliability analysis is based on a formulation of the general equation for the mean-time-to-data-loss (MTTDL) associated with LDPC codes. The formulation reveals that the stopping number is closely related to the MTTDL. It is further shown that LDPC codes can be designed such that a small loss of repair-bandwidth optimality may be traded for a large improvement in erasure-correction capability and thus the MTTDL. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

Network environment-adaptive erasure coding scheme for decentralized ubiquitous storage

“…Table 2 lists the parameters used for simulation. These values are chosen consistent with the existing References 11,16,17 . Lastly, the desired level of durability is set to 13 nines, i.e., 𝐿𝑅 should be lower than equal to 1 × 10 −13 , which is the level of durability that most practical storage systems promise.…”

“…Lastly, the desired level of durability is set to 13 nines, i.e., 𝐿𝑅 should be lower than equal to 1 × 10 −13 , which is the level of durability that most practical storage systems promise. The proposed schemes are compared against several existing methods including the Hadoop RS code 19 , Storj RS code 17 , Optimal Repair RS code 10 , and LDPC code 11 . Figure 4 depicts the comparison of 𝐿𝑅 between EAPA and other schemes under different 𝜆 with 𝛽 set to 2 (except for ORCPA), which is commonly used by most erasure codes-based storage systems (# denotes adaptive parameters according to the algorithm; detailed values are listed in Table 3).…”

A Reliability Model for Dependent and Distributed MDS Disk Array Units

“…We mostly focus on one dimensional MDS protection schemes in this study, however it can be shown that the model can be used to derive closed form expressions for multi dimensional MDS disk arrays [21] and code structures [22]. Furthermore, although it is out of scope of this paper, we can show that the general model proposed in this study can be used to predict reliability for non-MDS codes [23], [24], array BP-XOR codes [25], [26] as well as repair-efficient codes [27], [28] under novel opportunistic repair mechanisms [29].…”

On the Fault Tolerant Distributed Data Caching using LDPC Codes in Cellular Networks

“…Secondly, to achieve the same level of fault tolerance, erasure codes use less storage space compared to replication [26]. The tradeoff between key criteria such as repair bandwidth, reliability, and storage overhead used in the performance evaluation process of LDPC codes is also partially analyzed in [27]. Unlike Reed-Solomon codes, it is shown that the repair bandwidth of LDPC codes does not change even if the code length increases.…”