Error-Correcting Codes Based on Quasigroups

Error-correcting codes based on quasigroup transformations are proposed. For the proposed codes, similar to recursive convolutional codes, the correlation exists between any two bits of a codeword, which can have infinite length, theoretically. However, in contrast to convolutional codes, the proposed codes are nonlinear and almost random: for codewords with large enough length, the distribution of the letters, pair of letters, triple of letters, and so on, is uniform. Simulation results of bit-error probability for several codes in binary symmetric channels are presented.