  In this paper, we present a novel communication channel, called the
absorption channel, inspired by information transmission in neurons. Our
motivation comes from in-vivo nano-machines, emerging medical applications, and
brain-machine interfaces that communicate over the nervous system. Another
motivation comes from viewing our model as a specific deletion channel, which
may provide a new perspective and ideas to study the general deletion channel.
  For any given finite alphabet, we give codes that can correct absorption
errors. For the binary alphabet, the problem is relatively trivial and we can
apply binary (multiple-) deletion correcting codes. For single-absorption
error, we prove that the Varshamov-Tenengolts codes can provide a near-optimal
code in our setting. When the alphabet size $q$ is at least $3$, we first
construct a single-absorption correcting code whose redundancy is at most
$3\log_q(n)+O(1)$. Then, based on this code and ideas introduced in
\cite{Gabrys2022IT}, we give a second construction of single-absorption
correcting codes with redundancy $\log_q(n)+12\log_q\log_q(n)+O(1)$, which is
optimal up to an $O\left(\log_q\log_q(n)\right)$.
  Finally, we apply the syndrome compression technique with pre-coding to
obtain a subcode of the single-absorption correcting code. This subcode can
combat multiple-absorption errors and has low redundancy. For each setup,
efficient encoders and decoders are provided.
