Generalized weights and bounds for error probability over erasure channels
Leandro Cruvinel Lemes, Marcelo Firer
TL;DR
This paper introduces new bounds for error probability over erasure channels using Wei's generalized weights, which can tighten existing bounds and improve understanding of MDS and AMDS codes.
Contribution
It develops novel upper and lower bounds based on generalized weights, hierarchy, and spectra, enhancing the analysis of error probabilities in erasure channels.
Findings
Bounds often coincide, providing exact error probability estimates.
Improved bounds lead to better code performance analysis.
Results apply to MDS and AMDS codes.
Abstract
New upper and lower bounds for the error probability over an erasure channel are provided, making use of Wei's generalized weights, hierarchy and spectra. In many situations the upper and lower bounds coincide and this allows improvement of existing bounds. Results concerning MDS and AMDS codes are deduced from those bounds.
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Taxonomy
TopicsError Correcting Code Techniques · Advanced Wireless Communication Techniques · Coding theory and cryptography