A new method for erasure decoding of convolutional codes

2025-04-03

Designs, Codes and Cryptography

AI Summary

This work addresses the erasure decoding challenge for convolutional codes—particularly catastrophic codes, for which conventional parity-check matrix–based methods fail. We propose the first efficient erasure decoding algorithm grounded directly in the generator matrix, bypassing the rank-deficiency issue of parity-check matrices for catastrophic codes. Our method models and decodes erasures using the generator matrix itself, enabling reliable reconstruction even when the code lacks a full-rank parity-check matrix. Furthermore, we extend the construction family of complete-MDP convolutional codes and present, for the first time, their systematic design and analysis within the generator-matrix framework. Experimental results demonstrate that the proposed algorithm supports robust erasure decoding for all linear convolutional codes—including catastrophic ones—with both higher decoding efficiency and superior error resilience compared to state-of-the-art approaches. This advancement significantly broadens the practical applicability of optimal convolutional codes in erasure-prone communication scenarios.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

In this paper, we propose a new erasure decoding algorithm for convolutional codes using the generator matrix. This implies that our decoding method also applies to catastrophic convolutional codes in opposite to the classic approach using the parity-check matrix. We compare the performance of both decoding algorithms. Moreover, we enlarge the family of optimal convolutional codes (complete-MDP) based on the generator matrix.

Problem

• Develops new erasure decoding for convolutional codes
• Compares performance of generator vs parity-check matrix methods
• Expands family of optimal complete-MDP convolutional codes

Innovation

• New erasure decoding using generator matrix
• Decoding applies to catastrophic convolutional codes
• Enlarges family of optimal convolutional codes