Pseudo-MDP Convolutional Codes for Burst Erasure Correction

2026-03-25

AI Summary

This work proposes a novel class of Pseudo-MDP convolutional codes to address the practical limitations of traditional MDP convolutional codes, which require large finite fields to correct long burst erasures—hindering real-world deployment—while codes with small parameters often fail to meet error-correction demands. By relaxing the requirement for optimal column distance across all time instants and preserving it only partially, the proposed construction significantly reduces the necessary field size. Grounded in convolutional coding theory and column distance analysis, this approach effectively balances error-correction capability against implementation complexity while maintaining low decoding delay. The resulting Pseudo-MDP codes achieve comparable burst erasure recovery performance to conventional MDP codes under identical parameters but operate over substantially smaller finite fields, thereby enhancing engineering feasibility without sacrificing robustness.

Technology Category

• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Convolutional codes are a class of error-correcting codes that performs very well over erasure channels with low delay requirements. In particular, Maximum Distance Profile (MDP) convolutional codes, which are defined to have optimal column distances, are able to correct a maximal number of erasures in decoding windows of fixed sizes. However, the required field size in the known constructions for MDP convolutional codes increases rapidly with the code parameters. On the other hand, if the code parameters are small, larger bursts of erasures cannot be corrected. In this paper, we present a new class of convolutional codes, which we call Pseudo-MDP convolutional codes. By definition these codes can correct large bursts of erasures within a prescribed time-delay and still keep part of the advantageous properties of MDP convolutional codes, in the sense that we require some but not all column distances to be optimal. This release in the condition on the column distances allows us to construct Pseudo-MDP convolutional codes over fields of smaller size than those required for MDP convolutional codes with the same code parameters.

Problem

• convolutional codes
• burst erasure correction
• Maximum Distance Profile
• finite field size
• column distances

Innovation

• Pseudo-MDP convolutional codes
• burst erasure correction
• column distances
• finite field size
• low-delay decoding