Erasure Coding vs. Replication: A Quantiative Comparison Presented By Mr. P. H. Chan

Background Authors: Hakim Weatherspoon and John D. Kubiatowicz from CS Division of UC Berkeley. They have launched a project called “Oceanstore”, a distributed, peer-to-peer storage server in about November 2000. This paper compares Erasure coding with replication when applied on Oceanstore.

List of sections Background Introduction System architecture of Oceanstore (very brief) Availability System Model Comparisons (Bandwidth, storage, disk seek and MTTF) Discussion

Introduction For a peer to peer system, one crucial problem is reliability. Erasure coding and Replications are two commonly used method to improve reliability of these system. With these fault resilient algorithms and a repairing algorithms, the mean time to failure (MTTF) of the system will be increased.

Introduction Generally speaking, we know that erasure code is better than replication. What is improved? How much is improved? Is it worthwhile to use erasure coding? This paper gives a quantitative approach to evaluate the performance gain of erasure code over replication based on Oceanstore.

System Architecture Data are divided in the unit of blocks. Replication/Erasure coding is applied to code the blocks into “fragments”. These fragments are distributed to the workstations in the system. Fragments belongs to the same group of blocks will not be placed in the same workstation. A central management server will constantly retrieve the fragments belongs to each data blocks.

System Architecture If there are workstation broken down, some fragments will be missing. The management server will reproduce the missing fragment and place it in other workstations. (Assumption) A dead machine will be immediately replaced by a new, blank workstation. The time period between the examinations of the same block group is called an “epoch”.

Availability Probability to have a block available in the system.

Availability With N = 1 million, M=10k. Two replicas provide 0.99 availability. Erasure coding at rate ½ (rate = original data / erasure coded data) gives 0.999999998 availability. Erasure coding improves availability.

System Model The Max. number of blocks in the system MTTF of system and MTTF of block

System Model The storage requirement The bandwidth requirement

System Model Number of disk seeks

System Model Comparing the case of using erasure code and replication, we found that the ratio of disk seeks, storage and bandwidth requirement are all equal to R*r.

Comparisons With each user writing data to the system at a rate 35MB/hr, b = 8kB, dbsz = 8kB, N=224 users, erepl = eerase = 4 months, and MTTFsystems = 1000 years, Number of replica need to sustain such MTTF is R = 22 and erasure code need r = ½ to have that MTTF. Thus, R*r = 11.

Comparisons (find MTTFblock) With R = 2, r = 32/64 and erepl = eerase = 4 months, MTTFblock of replication scheme is 74 years and that of erasure code is 1020 years. (recall)

Discussion This paper presented a quantitative approach to calculate the performance gain of using erasure code. Mapping of erasure code to data require intensive CPU time. System MTTF decrease significantly with increasing number of blocks.

Thank you.