New Binary Locally Repairable Codes with Locality 2 and Uneven Availabilities for Hot Data

Area of Science:

• Coding Theory
• Distributed Storage Systems
• Information Theory

Background:

• Distributed storage systems require efficient data repair mechanisms.
• Existing codes often face limitations in balancing availability and repair efficiency.
• Hot data requires specialized handling for high availability.

Purpose of the Study:

• To propose a new family of binary linear-secret-sharing-codes (BLRCs) with specific locality and availability properties.
• To address the challenge of efficiently repairing data in distributed storage systems, particularly for frequently accessed data.
• To achieve high information symbol availability and low parity symbol availability for local repair.

Main Methods:

• Development of a new family of binary linear-secret-sharing-codes (BLRCs).
• Analysis of code properties including locality (set to 2) and uneven availabilities.
• Focus on local repair mechanisms where information symbols are accessed only via parity symbols.
• Mathematical derivation and verification of code optimality.

Main Results:

• The proposed BLRCs provide high information symbol availability.
• The codes exhibit low parity symbol availabilities, crucial for efficient local repair.
• Local repair of information symbols is achieved solely through parity symbol access.
• For k=4, the BLRCs demonstrate optimality in information length relative to code length, minimum Hamming distance, locality, and availability against theoretical bounds.

Conclusions:

• The proposed BLRCs offer a significant advancement in distributed storage system design.
• These codes enhance data availability and repair efficiency, especially for hot data.
• The achieved optimality validates the effectiveness of the proposed coding scheme.