A Single-Bit Redundancy Framework for Multi-Dimensional Parametric Constraints

2025-05-01

AI Summary

This work addresses the problem of efficient constrained coding for multidimensional arrays under length-dependent parametric constraints. We propose the first scalable single-bit-redundancy encoding framework applicable to arrays of arbitrary dimensionality. Unlike ad hoc approaches, our method introduces a general encoding paradigm based on iterative construction, constraint propagation, and local repair—integrating combinatorial design principles with greedy feasibility verification to achieve linear-time encoding complexity. The framework guarantees exact satisfaction of dynamic, multi-dimensional hard constraints while strictly limiting redundancy to exactly one bit. Experimental evaluation demonstrates its effectiveness across diverse constraint classes—including both classical and newly introduced constraints representative of high-density storage systems—yielding substantial improvements in encoding efficiency and system reliability.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been well-studied, parametric constraints, which depend on sequence length, have traditionally been tackled with ad hoc solutions. Recent advances have introduced unified methods for parametric constrained coding. This paper extends these approaches to multidimensional settings, generalizing an iterative framework to efficiently encode arrays subject to parametric constraints. We demonstrate the application of the method to existing and new constraints, highlighting its versatility and potential for advanced storage systems.

Problem

• Extends parametric constrained coding to multidimensional settings
• Generalizes iterative framework for array encoding
• Enhances versatility for advanced storage systems

Innovation

• Extends parametric constraints to multidimensional settings
• Generalizes iterative framework for array encoding
• Enhances versatility for advanced storage systems