Codes Over Absorption Channels

In this paper, we present a novel communication channel, called the absorption channel, inspired by information transmission in neurons. Our motivation comes from invivo nano-machines, emerging medical applications, and brain-machine interfaces that communicate over the nervous system.For any given finite alphabet, we give codes that can correct absorption errors. For the binary alphabet, the known binary (multiple-)deletion correcting codes already provide a good solution. 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 [1], 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(log_q log_q(n)).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.