Fractional Repetition Codes for Repair in Distributed Storage Systems (1010.2551v1)

Abstract: We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the concatenation of two components: an outer MDS code followed by an inner repetition code. We refer to the inner code as a Fractional Repetition code since it consists of splitting the data of each node into several packets and storing multiple replicas of each on different nodes in the system. Our model for repair is table-based, and thus, differs from the random access model adopted in the literature. We present constructions of Fractional Repetition codes based on regular graphs and Steiner systems for a large set of system parameters. The resulting codes are guaranteed to achieve the storage capacity for random access repair. The considered model motivates a new definition of capacity for distributed storage systems, that we call Fractional Repetition capacity. We provide upper bounds on this capacity while a precise expression remains an open problem.

• The paper introduces and constructs Fractional Repetition (FR) codes, a novel class of uncoded Minimum-Bandwidth Regenerating (MBR) codes using an outer MDS code and inner repetition, enabling a structured, table-driven repair.
• Specific constructions of FR codes are presented using regular graphs for efficient single-node repair and Steiner systems for handling multiple-node failures.
• The research establishes the concept of Fractional Repetition capacity and presents universally good FR code constructions capable of achieving or surpassing conventional MBR capacities in various system conditions.

Overview of Fractional Repetition Codes for Repair in Distributed Storage Systems

This paper presents a novel classification of Minimum-Bandwidth Regenerating (MBR) codes, significant for distributed storage systems (DSS), which prioritize computational efficiency through an uncoded repair mechanism. These codes, notably identified as Fractional Repetition (FR) codes, adeptly manage node failures by replicating data across various nodes while maintaining minimal bandwidth requirements during data repair processes.

Key Contributions

The primary innovation is the construction of FR codes, combining an outer MDS (Maximum Distance Separable) code with an inner repetition framework. Unlike previously established models reliant on a random access approach, this provides a structured, table-driven repair methodology. Several constructions are presented for different system conditions, emphasizing regular graphs for single-node failures and Steiner systems for multiple-node failures, ensuring robustness across numerous failure instances.

Highlights of the Research:

• Construction of FR codes using regular graphs achieves an efficient single-node repair process. These constructions are proven to maintain the original system's data retrieval capabilities even under minimized node access conditions, efficiently meeting exact MBR requirements.
• For scenarios involving higher degrees of failure, the research utilizes Steiner systems, offering solutions for cases demanding more than two redundancy levels to ensure system reliability. This demonstrates the versatility and adaptability of FR codes in accommodating variable system parameters.
• The research introduces the concept of Fractional Repetition capacity, wherein the storage system's maximum data resilience is evaluated under strict uncoded repair conditions.

One of the paper's significant results is the formulation of universally good FR codes, applicable to a comprehensive range of scenarios, irrespective of the specific values of node parameters or failure conditions. This generalization permits broad applicability in real-world distributed storage environments, particularly where computational simplicity in repair processes is a priority.

Numerical Results and Analysis

Constructed FR codes demonstrate substantial capability in achieving or surpassing conventional MBR capacities. Specifically:

• In systems with a repetition degree (ρ) equaling two, explicit code constructions ensure system capacity achievement while permitting an uncoded repair protocol.
• Further investigation into systems where ρ exceeds two reveals that derived Transpose codes maintain capacity while permitting repair from a subset of nodes only, thus optimizing repair processes in practical deployment scenarios.

Implications and Future Directions

This research establishes a foundational method for constructing low-complexity exact MBR codes suited to varied and practical distributed settings. The concept of FR capacity challenges existing limitations by suggesting that table-based repair strategies can yield greater performance gains in storage efficiency than previously expected. The results imply that systems can be scalable, reliable, and economical in handling errors, particularly in cloud environments where data integrity and availability are critical.

Future research could explore optimizing FR codes for a wider variety of system parameters and exploring the theoretical boundaries of Fractional Repetition capacity. There is also potential for exploring integration with other coding frameworks to further enhance efficiency and resilience.

In summary, the paper contributes significantly to advancing distributed storage systems by presenting a robust alternative to traditional coded repair strategies, emphasizing practicality and reduced overhead in the event of unexpected node failures.