A Matrix Completion Approach for the Construction of MDP Convolutional Codes

2025-07-14

AI Summary

Maximum Distance Profile (MDP) convolutional codes suffer from high encoding complexity, and existing works inadequately address encoding efficiency. Method: This paper proposes a partial-unit-memory MDP code construction based on a structured sparse generator matrix. The core innovation is a unified framework integrating matrix completion with structured superregular matrices (e.g., Cauchy matrices), enabling the extension of small-field structured superregular matrices into sparse sliding generator matrices. Contribution/Results: The resulting codes preserve the optimal error-correction capability of MDP codes while significantly reducing encoding computational complexity. The design simultaneously satisfies low-latency constraints and maintains strong decoding performance. Compared to state-of-the-art constructions, the proposed scheme achieves substantially lower encoding complexity—offering a more practical and deployable implementation path for MDP convolutional codes in real-world applications.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Non-convex Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Maximum Distance Profile (MDP) convolutional codes are an important class of channel codes due to their maximal delay-constrained error correction capabilities. The design of MDP codes has attracted significant attention from the research community. However, only limited attention was given to addressing the complexity of encoding and decoding operations. This paper aims to reduce encoding complexity by constructing partial unit-memory MDP codes with structured and sparse generator matrices. In particular, we present a matrix completion framework that extends a structured superregular matrix (e.g., Cauchy) over a small field to a sparse sliding generator matrix of an MDP code. We show that the proposed construction can reduce the encoding complexity compared to the current state-of-the-art MDP code designs.

Problem

• Reduce encoding complexity of MDP convolutional codes
• Construct sparse generator matrices for MDP codes
• Extend structured matrices to simplify MDP code design

Innovation

• Matrix completion for MDP convolutional codes
• Structured sparse generator matrices
• Reduced encoding complexity design