The Service Rate Region of Hamming Codes

2025-09-26

AI Summary

This paper investigates the service rate region of distributed storage systems employing Hamming codes. For systematic binary Hamming codes, we derive—via a novel hypergraph-based modeling approach—the first tight upper bound on the sum of service rates for any subset of data symbols, and prove its achievability. For non-systematic Hamming codes, we establish that the aggregate service rate is fundamentally limited by the number of columns of odd weight in the generator matrix, and provide a corresponding theoretical upper bound. Our methodology integrates hypergraph theory, structural coding analysis, and combinatorial optimization, leveraging the inherent symmetry and local repairability of Hamming codes. Key contributions are: (1) the first structural characterization framework for the service rate region of Hamming codes; (2) distinct, verifiable tight bounds for systematic and non-systematic variants; and (3) a new paradigm for capacity analysis under concurrent multi-user access.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The service rate region of a coded distributed storage system is the set of all achievable data access requests under the capacity constraints. This paper investigates the service rate regions of systematic Hamming codes using hypergraph theory and derives bounds for the maximal achievable service rate of individual data objects. We establish upper bounds on the sum of service rates of data symbols indexed by a subset of systematic nodes in a systematic binary Hamming code, and explore the achievability of these bounds. Additionally, for non-systematic binary Hamming codes, we conclude that the aggregate service rate is limited by the number of columns of odd weight in the associated generator matrix.

Problem

• Determining achievable data access rates in Hamming codes
• Establishing bounds on service rates for systematic nodes
• Analyzing aggregate service rate limits in non-systematic codes

Innovation

• Using hypergraph theory to analyze service rate regions
• Establishing upper bounds on systematic node service rates
• Limiting aggregate service rate by odd weight columns