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.

翻译：本文提出了一种新型通信信道——吸收信道，其灵感来源于神经元中的信息传输。该研究的动因源于体内纳米机器、新兴医疗应用以及通过神经系统通信的脑机接口。另一个动因在于，将该模型视为一种特殊的删除信道，可能为研究一般删除信道提供新的视角和思路。针对任意有限字母表，我们给出了能够纠正吸收错误的编码。对于二元字母表，问题相对简单，可应用二元（多重）删除纠正码。针对单次吸收错误，我们证明了Varshamov-Tenengolts码在该场景下能提供近乎最优的编码。当字母表大小$q$至少为3时，我们首先构造了一种冗余度不超过$3\log_q(n)+O(1)$的单次吸收纠正码。随后，基于该码及\cite{Gabrys2022IT}中的思想，我们给出了第二种单次吸收纠正码的构造，其冗余度为$\log_q(n)+12\log_q\log_q(n)+O(1)$，该冗余度在$O\left(\log_q\log_q(n)\right)$阶内达到最优。最后，我们应用带预编码的伴随压缩技术，从单次吸收纠正码中提取出一种子码，该子码能够对抗多次吸收错误且冗余度较低。针对每种设置，均提供了高效的编码器与解码器。