Efficient Constructions of Non-Binary Codes Over Absorption Channels

Motivated by the information transmission in neurons with various applications in in-vivo nano-machines or emerging medical applications, Ye and Elishco [2023] introduced a communication channel, called the absorption channel, and proposed codes correcting absorption errors. For a non-binary alphabet
$\Sigma_{q}$
, the authors presented constructions of codes of length
$n$
correcting a single absorption and the best construction yielded a redundancy of
$\log_{q}n+12\log_{q}\log_{q}n+O(1)$
symbols. In this work, we make progress on the code design problem above and show that the redundancy can be further reduced significantly as follows: When
$q=3$
, we construct “nearly optimal” ternary codes of length
$n$
with at most
$\log_{3}n+5.43$
redundant symbols. Note that such a redundancy is optimal up to a constant. • For a general alphabet
$\Sigma_{q}$
, we construct q-ary codes of length
$n$
correcting a single absorption error with
$\log_{q}n+3\log_{q}\log_{q}n+O(1)$
redundant symbols, providing an alternative. simpler construction that improves the results given by Ye and Elishco.