A Matrix Completion Approach for the Construction of MDP Convolutional Codes

TL;DR

This paper introduces a matrix completion framework to construct structured, sparse generator matrices for MDP convolutional codes, significantly reducing encoding complexity while maintaining maximal error correction capabilities.

Contribution

It proposes a novel matrix completion method that extends superregular matrices to create sparse generator matrices for MDP codes, improving encoding efficiency.

Findings

Reduces encoding complexity compared to existing MDP code designs

Uses structured superregular matrices like Cauchy for construction

Maintains maximal error correction capabilities

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.