The Cyclic Shift Channel

In several practical settings we wish to communicate an identifier based on flashing lights. Examples hereof are the brain computer interface using steady state evoked potentials (SSVEP) and device identification using LED’s. The communication channels here use small alphabets, are error prone, unsynchronized, and require short code words. Nevertheless the number of identifiers is relatively large. We model this situation as a cyclic shift channel where the shift length equals the code wordlength. We study the behaviour of the capacity of this channel and define a class of self synchronized error correcting codes. For this class we define a (Hamming) distance measure and prove a triangle inequality and thus show the feasibility of minimum distance decoding. We end with some code examples.