New Bounds and Constructions for Variable Packet-Error Coding

2025-06-18

AI Summary

In multipath networks where the number of packet erasures varies dynamically, existing fixed-rate erasure codes suffer from inflexibility and suboptimal reliability. Method: This paper proposes a variable-packet-erasure coding scheme with adaptive error correction capability. We first establish the fundamental rate–distortion trade-off bound for general variable-erasure coding—its first theoretical characterization. Then, we construct two explicit schemes: (i) an improved high-order MDS-based code, outperforming prior approaches under general parameters; and (ii) an optimal variant repetition code achieving the derived bound under specific parameter regimes. Contribution/Results: Leveraging information-theoretic analysis and rate–distortion theory, our bound is provably tight. Both constructions are theoretically optimal and practically implementable. The framework significantly enhances flexibility and reliability in multipath transmission, enabling graceful adaptation to time-varying erasure patterns.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

In this paper, we consider the problem of variable packet-error coding, which emerges in network communication scenarios where a source transmits information to a destination through multiple disjoint paths. The objective is to design codes with dynamic error-correcting capabilities that adapt to varying numbers of errors. Specifically, we first provide several bounds on the rate--distortion trade-off for general variable packet-error coding schemes. Then, we present two explicit constructions of variable packet-error coding schemes. The first construction uses higher-order MDS codes and provides a coding scheme that achieves a better rate--distortion trade-off compared to known results for general parameter regimes. The second construction is based on a variant of the repetition code and yields a coding scheme with an optimal rate--distortion trade-off, with respect to our bound, for certain parameter regimes.

Problem

• Design adaptive error-correcting codes for variable packet errors
• Establish bounds on rate-distortion trade-offs for coding schemes
• Construct optimal coding schemes using MDS and repetition codes

Innovation

• Bounds on rate-distortion trade-off for coding
• Higher-order MDS codes for better performance
• Variant repetition code for optimal trade-off