Function-Correcting Codes With Data Protection

2025-11-23

AI Summary

Existing function-correcting codes (FCCs) safeguard only function outputs, neglecting the confidentiality and integrity of underlying input data. Method: We propose the first generalized FCC framework jointly protecting both input data and function values. Our approach introduces a unified coding model ensuring simultaneous data confidentiality and function-value robustness; develops minimum-distance graph analysis to expose inherent limitations of classical perfect and MDS codes for function protection; extends the Plotkin and Hamming bounds to the data-protected FCC setting; and devises a two-step explicit construction method for linear FCCs. Contribution/Results: The framework strengthens data security without increasing redundancy, and yields concrete, implementable constructions for canonical function classes—including locally bounded functions and Hamming-weight functions—thereby bridging a critical gap between data privacy and functional reliability in coded computation.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Security and Privacy: Data transparency and provenance
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Function-correcting codes (FCCs) are designed to provide error protection for the value of a function computed on the data. Existing work typically focuses solely on protecting the function value and not the underlying data. In this work, we propose a general framework that offers protection for both the data and the function values. Since protecting the data inherently contributes to protecting the function value, we focus on scenarios where the function value requires stronger protection than the data itself. We first introduce a more general approach and a framework for function-correcting codes that incorporates data protection along with protection of function values. A two-step construction procedure for such codes is proposed, and bounds on the optimal redundancy of general FCCs with data protection are reported. Using these results, we exhibit examples that show that data protection can be added to existing FCCs without increasing redundancy. Using our two-step construction procedure, we present explicit constructions of FCCs with data protection for specific families of functions, such as locally bounded functions and the Hamming weight function. We associate a graph called minimum-distance graph to a code and use it to show that perfect codes and maximum distance separable (MDS) codes cannot provide additional protection to function values over and above the amount of protection for data for any function. Then we focus on linear FCCs and provide some results for linear functions, leveraging their inherent structural properties. To the best of our knowledge, this is the first instance of FCCs with a linear structure. Finally, we generalize the Plotkin and Hamming bounds well known in classical error-correcting coding theory to FCCs with data protection.

Problem

• Protecting both data and function values simultaneously in error correction
• Providing stronger protection for function values than underlying data
• Developing function-correcting codes with data protection without redundancy increase

Innovation

• General framework protecting both data and function values
• Two-step construction procedure for function-correcting codes
• First linear structure implementation for function-correcting codes