arXiv Open Access 2023

Improving Uniquely Decodable Codes in Binary Adder Channels

József Balogh The Nguyen Patric R. J. Ostergard Ethan Patrick White Michael Wigal

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Abstrak

We present a general method to modify existing uniquely decodable codes in the $T$-user binary adder channel. If at least one of the original constituent codes does not have average weight exactly half of the dimension, then our method produces a new set of constituent codes in a higher dimension, with a strictly higher rate. Using our method we improve the highest known rate for the $T$-user binary adder channel for all $T \geq 2$. This information theory problem is equivalent to co-Sidon problems initiated by Lindstr{ö}m in the 1960s, and also the multi-set union-free problem. Our results improve the known lower bounds in these settings as well.

Topik & Kata Kunci

math.CO cs.IT

Penulis (5)

József Balogh

The Nguyen

Patric R. J. Ostergard

Ethan Patrick White

Michael Wigal

Format Sitasi

APA MLA BibTeX

Balogh, J., Nguyen, T., Ostergard, P.R.J., White, E.P., Wigal, M. (2023). Improving Uniquely Decodable Codes in Binary Adder Channels. https://arxiv.org/abs/2312.11723

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓