Totally orthogonal complementary binary codes sequences and applications to communications systems.

Abstract

Complementary binary code sequences were invented by M. J. E. Golay in the investigation of infrared multislit spectrometry. Complementary coding sequences have the property of an infinite correlation peak to peak ambiguity ratio when detected with a matched filter. Cooperative or totally orthogonal complementary code pairs are two sets of complementary pairs such that the cross correlation is zero in every position. A proof is given that every complementary pair has two totally orthogonal pairs, i.e., one the complement of the other. A proof that these pairs are the only pairs is also given. A communication system involving complementary code binary sequences is simulated on the hybrid computer and compared with an ideal receiver for an uncoded signal. By using both the totally orthogonal code and time shifting, a method of horizontal multiplexing of binary coded information is proposed and evaluated. Various other complementary coding systems and possible uses are discussed.