Work

A Continuous Projection Converse and a Weighted Construction for Uniquely Decodable Code Pairs

Year: 2026

Type: preprint

Abstract: We study the maximum sum rate of uniquely decodable code pairs. A weighted refinement of a complement-gluing construction yields an explicit code of length 672 and sum rate exceeding $1.318639029203$. An iterated projection argument, combined with a conditional entropy estimate and a justified continuous limit, gives an upper bound of $1.480063425539$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.33625

Author: Yu, Lei

Institution: Nankai University

Language: English

Topic: Coding theory and cryptography

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China

Awards: G3490976664, G5776708844

OpenAlex ID: W7214723476

Cites: 1

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Related to: 10