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arXiv · 2312.11723

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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Abstract

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{\"o}m in the 1960s, and also the multi-set union-free problem. Our results improve the known lower bounds in these settings as well.

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József Balogh, The Nguyen, Patric R. J. Ostergard, Ethan Patrick White, Michael Wigal. 2023-12-18. Improving Uniquely Decodable Codes in Binary Adder Channels. https://arxiv.org/abs/2312.11723

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